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Module Guide

FINANCIAL MANAGEMENT

Copyright © 2012

All rights reserved; no part of this book may be reproduced in any form or by any means, including photocopyingmachines, without the written permission of the publisher

Last Revision: November 2013

Financial Management Bachelor of Commerce (Honours)

Regent Business School Page 1

CONTENTS

CHAPTER TOPIC PAGE

1 Financial Statements and Ratio Analysis 05 – 30

2 Time Value of Money: Present Values and Future Values 31 – 55

3 Investment Appraisal Methods 57 – 70

4 Share Valuation 71 – 84

5 Bonds and Bond Valuation 85 – 100

6 Cost of Capital 101 – 115

7 Dividends and Dividend Policy 117 – 138

8 The Management of Working Capital 139 – 165

9 References 166



INTRODUCTION

This study guide on Financial Management has been devised in line with your syllabus and the

latest developments in the field of Financial Management. The structure of the guide is simple

and user- friendly and designed to maximise your learning experience.

This module assumes that you are familiar with basic financial concepts, which you have

encountered in your undergraduate studies. Notwithstanding this, this guide is written with a

view to refreshing the students’ knowledge as much as possible in order to ensure a seamless

transition to post graduate level.

Teaching and Learning Strategies: The delivery will include guided reading by students and

discussions at workshops. Students will engage in self-study in theoretical and practical topics,

and problem solving exercises.

Contents and Structure: There are many frameworks, which can be used in the study of

managerial finance. We have selected a framework, which gives an overview of the managerial

finance function as a whole. Accordingly, this module guide comprises of ten chapters.



MODULE OUTCOMESThis module looks closely at the financial well-being of the firm and its shareholders by

investigating the role of financial management and of long-term and working capital, and the

financial measurement and choice of projects to invest in.

After working through this guide, you should be able to:

Analyse the past performance of a business through ratio analysis.

Make long-term decisions on the acceptability of projects using investment appraisal

techniques.

Estimate a project’s cash flow and business risk, and its suitability for inclusion in a

firm’s portfolio of investments

Recognise the variety of sources of finance that exist, and appreciate the implications of

the usage of each of type. .

Use the Capital Assets Pricing Model (CAPM) to assess the cost of capital

Understand in detail the management of working capital.



READINGS

PRESCRIBED:

Els, G; Du Toit, E; Erasmus, P; Kotze, L; Ngwenya, S; Thomas, K; Viviers, S. (2010) CorporateFinance, A South African Perspective, Oxford University Press.

RECOMMENDED READINGS

Ross, S; Westerfield, RW; Jordan, BD; and Firer C. (2009). Fundamentals of CorporateFinance , 4th South African Edition, McGraw-Hill.

Correia, C; Flynn, D; Uliana, E and Wormald, M. (2008) Financial Management, 6th Edition,

Juta Publishing.

Marx, J; de Swardt, C; Beaumont Smith, M; Naicker, B; Erasmus, P. (2007) Financial

Management in Southern Africa, 2nd Edition, Pearson Education.



CHAPTER 1

1

FINANCIAL STATEMENTS AND RATIOANALYSIS



CCOONNTTEENNTTSS

1. Introduction

2. Users of Annual Financial Statements

3. The Need for Comparisons

4. Types of Ratios

5. Limitations of Financial Statement Analysis

6. Calculation and Interpretation of Ratios

7. Approaches to Financial Statement Analysis

8. Typical Exam Type Questions



2 Learning Outcomes

After working through this section you should be able to

Outline the various reports used to communicate financial information to

shareholders and other stakeholders.

Define what is meant by the interpretation of accounts.

Identify the parties who use financial analysis.

Calculate and interpret commonly used financial ratios.

Evaluate the results of the ratio analysis and make recommendations for future

action.

Identify the limitations of using accounting data to perform financial analysis.

Outline the various approaches to financial statement analysis and to identify

when each approach is appropriate.

Use Du Pont analysis for interpreting the financial results of a company.

And outline the limitations of ratio analysis.



READINGS

PRESCRIBED:

Chapters 2 and 3: Els, G; Du Toit, E; Erasmus, P; Kotze, L; Ngwenya, S; Thomas, K;

Viviers, S. (2010) Corporate Finance, A South African Perspective, Oxford

University Press.

Recommended:

Chapter 3: 4th South African Edition, Ross S, Westerfield RW, Jordan BD andFirer C, Fundamentals of Corporate Finance, (2009). McGraw Hill.

Chapter 5: Correia, C; Flynn, D; Uliana, E and Wormald, M. (2008) FinancialManagement, 6th Edition, Juta Publishing.



1. Introduction

Financial statement analysis concerns itself with the study of relationships within a set of

financial statements at a point in time and with the trends in these relationships over time.

It is a process which aims to evaluate the current and past financial results of an

organisation, with a view to testing its liquidity, solvency, profitability, asset management

and market value measures/ratios. The interpretation and evaluation of financial data

requires familiarity with the basic tools of financial statement analysis (ratio analysis).

Naturally, the type of financial analysis that takes place depends on the particular interest

that the analysts has in the enterprise.

2. Users of Financial statements

The following examples illustrate the different perspectives which various parties may

have when approaching the analysis of a company:

2.1. Shareholders and potential shareholders

They are interested in the profitability of the business as measured by the return on their

investment in equity. They will also wish to establish the financial stability of the company

in order to assess the risk attached to their investment.

2.2. Suppliers of short term credit

These may include banks that provide overdraft facilities or trade creditors supplying

goods on credit, will be interested in the ability of the company to pay its debts promptly.

Their time horizon is much shorter than shareholders, for example, in the normal course of

business, 90 days is the usual maximum credit term allowed by suppliers.



2.3. Suppliers of long term credit

For example long term loans, mortgage bonds and debentures. These parties will be

interested in the company’s ability to meet its interest commitments and its ability to repay

the long term debts on maturity. Their analysis may thus be similar to that of the

shareholders, as they look to a further horizon and often have large amounts of money

due to them.

2.4. Management

Management is concerned with every aspect of the company as their mandate is to

maximize the wealth of the shareholders and ensure continued operation. They must

ensure that the company is operating efficiently and effectively. Their particular focus will

be on profitability, risk and day to day running of the business.

2.5. Auditors

Are required to establish whether the company is a going concern and whether the

financial statements fairly present the published results of the company. To be in a

position to pass their opinion, an analytical review of the company is required.

2.6. Employees/Unions

Their primary concern is job security and n assurance that they are not being exploited.

3. The need for comparisons

Comparison is a vital analytical process, since in financial analysis no number in isolation

can be meaningful. However, when compared with some or other predetermined

standard, that number gains some meaning, relevance and usefulness. The most

important factor revealed by comparative financial statements is the trend. The trend



indicates the direction of change, the rate of change and the amount of change.

Comparison may be facilitated by using:

- Historical standards

- Industry standards.

Historical standards are based on the past performance of the company, and are used to

establish trends of the company’s performance over several industry years.

Industry standards are determined/influenced by the following:-

- Type of operation: The major operation of the entity, distinguishing between

manufacturing, wholesale, retail or service type.

- Type of product: The nature of the product or service will make a considerable

difference to the perception of the riskiness of the business.

- Location: The physical location of the outlets for the goods or services of a

company will to a large extent determine growth potential of a company.

- Clientele: Will be dependent upon the nature of goods or services provided,

spending capacity, and whether they have bargaining power and are there alternative

sources.

- Suppliers: Whether the company relies heavily on suppliers for raw materials and

other essential components.

- Competition: Free competition should result in the survival of efficient companies

and the demise of those which are not efficient. Of course, the key to success is to

remain ahead of your competition through productivity and innovation.



4. Types of Ratios

4.1. Liquidity ratios: indicate the ability of the company to meet its short term financial

obligations/debt

4.2. Profitability ratios: express the effectiveness of the company in earning profits and

show its return on capital invested.

4.3. Financial leverage ratios: show the relative extent to which the capital employed

has been provided by shareholders and loan capital.

4.4. Market ratios: reflect the performance of the share price on the stock exchange and

the implications for shareholders.

4.5. Efficiency ratios: reflect the management ability of the company with regard to its

turnover and working capital.


It is difficult to find comparable firms

Differences in accounting practices (depreciation, stock valuations)

Differences in financial year ends (28 February vs 31 December)

Differences in capital structure (zero gearing, low gearing and high gearing)

Seasonal variations (winter high sales vs summer high sales)

One-time events (extraordinary write-offs, acquisition of a company carrying

high assessed losses)

.

6. The calculation and interpretation of ratios

6.1. Liquidity Ratios

The ability of the firm to meet current debts is important in evaluating a firm’s

financial position as well as its ability to survive and grow. Certain basic ratios can

be computed that provide some guides for determining the enterprise’s short term

debt paying ability.



A. The Current ratioThe current ratio is the ratio of total current assets to current liabilities.

The components of current assets are: inventories, trade and other receivables

and cash.

It is expressed as:

Current ratio = Current Assets

Current Liabilities

This ratio indicates the extent to which the claims of short term creditors are covered by

current assets that can be translated into cash readily (or is already in the form of cash)

in the short term. The popular rule of thumb for this ratio is 2:1. Ratios marginally lower

than 2:1 are acceptable. Strangely enough ratios higher that say, 3:1 could be masking

liquidity issues, like, the business is holding too much of stock (but more of that later),

its investment in receivables is too high (thus resulting in exposure to bad debts and

holding too much cash in short term accounts. This is not the ideal situation, as the

task of the FM is to ensure that the business’ resources are well invested.

It must be noted that the current ratio is only one measure of determining liquidity, and

does not answer all the liquidity questions.

B. Acid-test (quick) ratio: As it normally takes longer to translate inventory into

cash, it is useful to measure the firm’s ability to pay off short term debt without

relying on the sale of inventory. The ratio is:

Acid Test Ratio = Current assets – Inventory

Current liabilities



Stated differently, current assets – Inventory = Receivables + Cash.

The popular rule of thumb is 1:1, but blind application should be avoided. If the ratio is

low, the firm may have difficulty in meeting its short term needs unless it is able to

obtain additional current assets through conversion of some of its long term assets,

through additional financing, or through profitable operating results. Another way of

evaluating liquidity is to determine how quickly certain assets can be turned into cash.

How liquid, for example, are the receivables and inventory?

C. The Cash Ratio: this measures the amount of cash available as compared to

current liabilities. There is no rule of thumb ratio for this suffice to say, that a firm

should have an open line of credit available if they do not have sufficient cash

reserves. The ratio is:

Cash ratio = Cash

Current liabilities

D. Interval MeasureThis ratio measures how many days of operating expenses are covered by current

assets. This ratio is useful as it gauges how long it will take for cash to dry up in

the event of a strike and a business is unable to receive any cash inflows. The

formula is:

Interval Measure = Current assets

Average daily operating Costs

Average daily operating costs = [Operating expenses – depreciation – interest

expenses]/365



6.2. Profitability

Profitability ratios indicate how well the enterprise has operated during the year.

These ratios answer such questions as: was the profit adequate? What rate of

return does it represent? What amount was paid in dividends? Generally, the ratios

are either computed based on sales or on an investment base such as total assets.

Profitability is frequently used as the ultimate test of management effectiveness.

A. Gross margin on salesThis is essentially the mark up ratio. This ratio is calculated as follows:

Gross Margin on Sales = Gross Profit x 100

Sales 1

This should be compared with the margins obtained over a number of years. A fall in

this ratio would indicate one or all of the following:-

a. A reduction in sales price to attract new customers or because of price

competition.

b. An increase in cost of purchases without a corresponding increase in sales

price.

c. An undervaluation of closing stock.

d. Possible stock theft.

e. Changes in sales mix.



B. Profit margin on salesThis is also known as the net profit margin. The formula is as follows:

Profit margin on sales = Net Income x 100

Net Sales 1

A decrease in the ratio in comparison to previous years would be the result of low

mark-ups, higher costs or a combination of these factors. One would have to analyse

individual components included in overheads to ascertain whether any specific item

has contributed to this decrease, e.g. disproportionate increases in advertising

expenditure.

C. Return on total assetsThe return on total assets measures the profitability of the firm as a whole in

relation to the total assets employed. It is frequently referred to as the return on

investments. This ratio is calculated by dividing earnings by total assets.

Return on Total Assets = Net income after tax X 100

Total Assets 1

D. Return on equityIn order to measure the earnings power on the shareholders equity, we calculate

the return on equity ratio. This ratio relates to net income after tax, after

deducting preference dividends to shareholders’ equity, and is computed as

follows:

Return on Equity = Net Income after tax – Preference Dividends

Equity (net worth)

Ordinary Shareholders Equity is made up of the following components:

. Ordinary share capital



. Share premium

. Distributable reserves

. Non-distributable reserves

6.3. Asset Management and Solvency Ratios

A. Inventory Turnover Ratio

This ratio measures how quickly inventory is sold. Generally, the higher the

inventory turnover, the better the enterprise is performing. It is possible; however,

that the enterprise is incurring high “stock out costs” because not enough inventory

is available. This ratio is useful because it may indicate that some items may be

turning over quite rapidly whereas others might have failed to sell at all. The

inventory turnover ratio is:

Inventory turnover = Cost of Goods Sold

*Average Inventory

*Average inventory = (inventory at beginning of year + inventory at end of year) dividedby 2

B. Stock Holding Ratio or Days Sales in Inventory

The ratio indicates the quantity of inventory on hand in relation to the quantity purchased

(the number of days the stock is held before it is sold). This ratio is calculated as follows:

Days sales in Inventory = Inventory x 365

Cost of Sales



C. Debtors (Accounts Receivable) Collection Period

This ratio measures the average number of days that it would take for the outstanding

accounts receivable to be collected and it is computed as follows:

Debtors Collection period = *Average Accounts Receivable (Debtors) x 365

Credit Sales

*Average Accounts Receivable = Accounts Receivable at beginning of year + Accounts

Receivable at end of year) divided by 2.

If this ratio is unduly high it may point towards an inefficient accounts receivable collection

department. To expedite collections, discounts may be offered to customers paying within

a certain time period say 15, 30 or 45 days.

The following methods may be used to ensure proper control of accounts

receivable:

Offer discounts for prompt settlement

Send statements timeously

Use reminder options, like SMS, emails, telephone calls, etc.

Charge interest on overdue accounts.

Reduce credit limits

Freeze available credit altogether on certain accounts

Hand over errant accounts for collection.

Blacklist clients who default.

Sue habitual offenders.



D. Creditors (Accounts Payable) Payment Period

This ratio is computed as follows:

Creditors payment period = Accounts Payable (Creditors) x 365

Credit Purchases

This ratio calculates the number of days it takes before creditors are settled. An increasing

trend in this ratio could indicate inability of the company to meet credit obligations within a

certain time period. And this will arise directly out of a poor debtors’ collection ratio. It is

important to ensure the business has a good reputation in the eyes of creditors. Poor

reputations tend to spread and may have a damaging effect on the credit worthiness of

the business.

E. Fixed Assets (Tangible Assets) Turnover RatioThis ratio indicates the utilisation of plant, machinery and equipment relative to operating

levels as reflected by turnover and is calculated as follows:

Fixed Asset Turnover = Sales (Turnover)

Fixed Assets

It indicates the efficiency with which operating assets are utilized to generate sales.

6.4. Market Value Measures

A. Earnings per Share (EPS):

The earnings per share figure ratio is probably the ratio most used by investment

analysts. EPS is computed by dividing earnings, by the ordinary shares in issue.

Earnings per share= Net Income after tax and Preference Dividends

Number of Ordinary Share Issued



Essentially, this ratio answers the question, how much has each share earned. The

trend in the earnings per share ratio is a useful indicator of performance of the

company. Generally, the higher this ratio, the better the performance of the company.

B. Dividends per Share (DPS)

This indicates the amount of dividend attributable to each share. From the investors’

point of view, the higher this ratio the better, as the dividend per share will be greater.

The formula is:

Dividends per share = Dividends

Issued Shares

C. Price Earnings Ratio

The price earnings ratio (P/E) is a statistic used by analysts in discussing the

investment possibility of a given enterprise. It is computed by dividing the market price

of the share by its earnings per share.

Price earnings ratio = Market Price of Share

Earnings per Share

If a company’s P/E ratio drops steadily this indicates that investors are not confident of

the firm’s growth potential. Generally the greater the P/E ratio, the better the

perception of investors regarding the future growth of the company. The P/E ratio is

also an indicator of the value of a business as it essentially asks the question: over how

many years will earnings take to pay off the purchase price?



D. Dividend Cover

This ratio, although not based on market values, affect the market value of shares. It

measures the extent of earnings that is being paid out in the form of dividends. A high

dividend cover would indicate that a large percentage of earnings is being retained and

reinvested within a firm while a low dividend cover would indicate the opposite. The

formula is:

Dividend cover = Earnings per Share

Dividend per Share

Generally, growth companies are characterised by high dividend cover since they re-

invest most of their earnings.

E. Dividend Yield

The dividend yield ratio indicates the return that investors are obtaining on their

investment in the form of dividends and is calculated as follows:

Dividend yield = Dividend per share

Market Price per share

F. Earnings yieldThe earnings yield is calculated by taking the earnings per share and dividing it by the

market value of the share. This ratio indicates the yield that investors are demanding.

Earnings Yield = Earnings per share

Market price per share



G. Market to Book RatioThe market to book ratio compares the market value of the firm’s investment to their

cost. A value of less than 1 means that the firm has not been very successful in

creating value for its shareholders. The formula is:

Market to Book Ratio = Market value per share

Book value per share

Think PointConsider how the market-to-book ratio could be interpreted

if you were considering the purchase of the company's

shares. Some might feel a ratio less than one would be

preferred since the shares are selling below the equity value

on the books. One could use this point to comment that the market is evaluating

the company's future earning power while the book value figures reflect the cost

at which shares had previously been issued and the amount of the past retained

earnings on the company's balance sheet.

6.5 Gearing and Insolvency

Debt management plays an important role in financial management and the extent of

financial leverage of the firm has a number of implications. The more the financial

leverage a firm has, the higher the risk attached to it. However, the greater the risk,

the greater the return and if a firm earns more on the borrowed funds than it pays in

interest, the return on owners equity is increased. Furthermore, by raising funds

through debt, the shareholders can obtain finance without losing control of the firm.



Equity is the basic risk capital of an enterprise. Every enterprise has some equity

capital which bears the risk to which it is unavoidably exposed. Equity capital is

permanent capital and not guaranteed to be repaid (excluding liquidation). Because

of their permanence, an enterprise can invest such funds in long term assets and

expose these to greater risks. However, debt (both short and long term) has to be

repaid. Funds are often raised from other sources than equity – the intention being

to increase the rate of return on equity – this is known as gearing or leverage. The

borrowed funds are used to generate a return and if this return exceeds the

borrowing cost then the company is trading profitability on the borrowed funds.

A. Debt RatioThe debt ratio is the ratio of total debt to total assets and measures the percentage of

total funds provided by creditors. Total debt includes long term liabilities and current

liabilities. Total assets include fixed assets, investments and current assets. The

higher the debt ratio, the higher the financial risk. The ratio is calculated as follows:

Debt Ratio = Total Debt

Total Assets

B. Interest CoverThis ratio is determined by dividing earnings before interest and tax (EBIT) by interest

charges. This ratio measures the extent to which earnings can decline without causing

financial losses to the firm and creating an inability to meet interest costs.

Interest cover = EBIT

Interest



A high interest cover ratio i.e. a situation where the interest expense is covered several

times by the EBIT earned reflects a very low interest charge in relation to profitability

and could be due to a large percentage of the debt finance being accounts payable

(creditors) which is effectively a free form of finance. One can conclude that the

interest cover ratio must be taken into account in determining the overall risk attached

to the company.

C. Debt Equity RatioThis ratio indicates the extent to which debt is covered by shareholders funds/equity.

The debt equity ratio is calculated as follows:

Debt Equity= Total Debt

Total Equity

This ratio indicates the relationship between borrowed capital and invested capital and

provides creditors with some idea of the company’s ability to withstand losses without

impairing the interests of creditors. The higher this ratio is, the less “buffer” there is

available to creditors if the company becomes insolvent. From the creditor’s point of

view, a low ratio of debt to equity is desirable. A high debt equity ratio would reduce

the company’s chances of borrowing additional funds without an increase in

shareholders’ equity because of the high risk factor attached to the company.

6.6. Du Pont Analysis

No individual ratio provides an adequate assessment of all aspects of a firm’s financial

health. However, the Du Pont system introduces a systematic approach to ratio

analysis. It is a financial analysis and planning tool that uses basic accounting



relationships, and is designed to provide an understanding of the factors that drive the

return on equity of the firm.

Equity

sTotalAssetX

sTotalAsset

SalesX

Sales

NPATROE

Profit margin Total Asset turnover Equity multiplier

Operational Efficiency is measured by the profit margin

Asset Use Efficiency is measured by the Total Asset Turnover

Financial leverage is measured by the equity multiplier

7. Typical Examination Type QuestionsBujumbura Plastics are a manufacturing business who make containers for

domestic use and sell directly to end users (households).

Balance Sheets for 2011 and 2010 financial years are below:

Assets 2011 2010

Non Current Assets 6 000 000 5 800 000

Inventory 300 000 200 000

Receivables 400 000 320 000

Cash 500 000 300 000

7 200 000 6 620 000



Equity and Liabilities

Share Capital (R2 shares) 4 000 000 3 500 000

Retained Income 500 000 400 000

Long term Debt 2 000 000 1 800 000

Payables 700 000 920 000

7 200 000 6 620 000

Their abbreviated Income Statement for the year ended 2011:

Sales (Credit sales is 60%) 2 300 000

Cost of sales 1 100 000

Depreciation 100 000

Interest expense 240 000

Tax (30%) 130 000

Net Income after Tax 300 000

Dividends 200 000

Retained Income 100 000

Required

1.1. Calculate the acid test ratio for 2011 (the ratio for last year was 0,65:1) and

comment.

1.2. Calculate their debt equity ratio for 2011. And comment on where the funds

generated have been utilised in 2011.

1.3. Calculate the earnings per share and dividends per share and comment on their

retention of funds.

1.4. Calculate the Debtors collection period (use average figures) and comment on your

findings, noting that debtors are given 60 days to pay their accounts. (Note:



Debtor’s collection in the previous year was 66 days). Can you offer suggestions to

the collection team in this regard?

1.5. Calculate the inventory turnover (use average inventory) and explain how this ratio

can be used to explain/improve operating efficiencies. Is this ratio healthy, noting

the type of industry that Bujumbura operate in?

1.6. Calculate the Return on Equity (using the DuPont Identity). If return on equity was

14% last year. Will shareholders be happy with the current return? Why or why

not?



Illustrative Example

Simply Red Ltd

Balance Sheet as at 31 December 2011

Equity and Liabilities 2011 2011

Share capital (Par value R2) 200 000 200 000

Retained profit 490 000 510 000

Shareholders’ funds 690 000 710 000

Long term debt 250 000 424 000

Trade and other Payables 60 000 66 000

Total Equity and Liabilities 1 000 000 1 200 000

Tangible Assets

Plant and equipment at cost 1 200 000 1 480 000

Accumulated depreciation -500 000 -560 000

Net fixed assets 700 000 920 000

Current Assets

Inventory 150 000 150 000

Trade and other Receivables 100 000 120 000

Cash 50 000 10 000

Total current assets 300 000 280 000

Net assets 1 000 000 1 200 000

Market price per share 8,20 9,10



Income Statement for the year ended 31 December 2007

Income Statement for the year ended 31 December

2010 2011

Sales (40% cash sales) 1 080 000 1 200 000

Cost of sales (50% purchased on cr) 842 000 900 000

Gross profit 238 000 300 000

Operating expenses 104 000 114 000

Depreciation 32 000 60 000

Net profit before interest and taxes 102 000 126 000

Interest 23 000 39 600

Net profit before taxes 79 000 86 400

Taxes (30%) 23 700 25 920

Net profit after tax 55 300 60 480

Required

Calculate and comment on the following ratios for both years.

1. The current ratio

2. Acid test ratio

3. Cash ratio

4. Interval Measure

5. Total debt ratio

6. Debt equity ratio

7. Earnings per share

8. Dividends per share

9. Price earnings ratio

10. Market to book ratio

11. Dividend yield

12. Earnings yield



13. Inventory turnover ratio

14. Days sales in inventory

15. Days sales in receivables

16. Days sales in payables

17. Total asset turnover

18. Gross margin on sales

19. Net profit/margin on sales

20. Return on total assets.

21. Return on equity (using the du Pont Identity)



CHAPTER 2

TIME VALUE OF MONEY AND THEEFFECT OF COMPOUND

INTEREST__________________________________________



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3 Learning Outcomes

After working through this section you should be able to:

Carry out calculations involving compound interest.

Calculate nominal and effective rates.

Use compound interest to calculate the present value and future value of an

investment.

Calculate the future value of an ordinary annuity.

Calculate the present value of an ordinary annuity.

Calculate an amount of sinking fund payment.

Calculate the amount of amortization payment



Prescribed Reading

Chapter 4: Els, G; Du Toit, E; Erasmus, P; Kotze, L; Ngwenya, S; Thomas, K; Viviers,

S. (2010). Corporate Finance, A South African Perspective, Oxford University Press

Recommended Reading

1. Chapter 2: Brecher, R. (2009) Contemporary Mathematics for Business and

Consumers. 5th Ed. USA: South-Western Cengage Learning.

2. Chapter 5: Firer, C.; Ross, S. A.; Westerfield, R. W. and Jordan, D. (2004)

Fundamentals of Corporate Finance. 3rd Ed. UK: McGraw Hill.



1. Compound interest

Compounded interest is interest charged on the original sum and un-paid interest.

Compound interest is applied a number of times during the term of a loan or investment.

Compound interest yields considerably higher interest than simple interest because it

pays interest on a previously earned interest. For compound interest, the interest earned

for each period is reinvested or added to the previous principal before the next calculation

(Brechner, 2009).

Example 1

An investment of R500 in a bank for 3 years at interest of 6% compounded per year.

At the end of year 1 you have (1.06) 500 = R530.

At the end of year 2 you have (1.06) 530 = R561.80.

At the end of year 3 you have (1.06) R56.80 = R595.51.

Note:

R595.51 = (1.06) 561.80

= (1.06) (1.06) 530

= (1.06) (1.06) (1.06) 500

= 500 (1.06)3

2. Concepts used in Compound Interest

This section uses a compound interest to explore various concepts including, the time

value of money, compound amount or future value (FV) and present amount or present

value (PV).

2.1. Time value of moneyTime value of the money refers to the idea that the money in the present, is more

desirable than the same amount of money in the future, because it can be invested and

earn interest as time goes by (Brechner, 2009). If the bank owed R12 000, you would

prefer to have it now instead of one year from now.



2.2. Compound amount (future value)A future value is the total amount of principal and accumulated interest at the end of loan

or investment.

2.3. Present amount (present value)A present value or a principal amount is an amount of money that must be deposited

today, at compound interest, to provide a specified lump sum of money in the future.

2.4. Compounding periodsThe interest can be computed annually, semi-annually, quarterly, monthly, daily and

continuously. Various compounding options and the corresponding number of periods per

year are shown in Table 1.1.

Table1: The number of compounding periods

Interest compounded Compounding period per year

Annually Every year 1

Semi-annually Every 6 months 2

Quarterly Every 3 months 4

Monthly Every month 12

Daily Every day 365 or 360

Continuously Infinite

To find the number of compounding periods of an investment, multiply the number of

years by the number of periods per year.

Computing periods = Years x Periods per year

For example, a principal amount invested for 3years with interest rate compounded semi-

annually is calculated as follows:

Computing periods = 3 x 2 = 6 periods



2.5. Conversion of interest per periodThe interest rate used per period is known as a periodic rate. This is the interest rate

charged (and subsequently compounded) for each period, divided by the amount of the

principal. The periodic rate is used primarily for calculations and is rarely used for

comparison. The periodic is different from the quoted annual rate known as nominalinterest.

To find the periodic rate we divide the nominal interest by the number of periods per year.

PERIODIC RATE =

An example of converting an annual nominal interest of 12% into periodic rates is shown

in Table 1.2.

Table 2: Periodic rates

Nominal interest rate Periods per year Periodic rate Decimal

12% compounded annually 1 12% 0.12

12% compounded Semi-annually 2 6% 0.06

12% compounded quarterly 4 0.3 0.03

12% compounded monthly 12 1.5% 0.015

2.6. Effective interest ratesTo put different rates and frequencies of conversion on a comparable basis, we determine

the effective rate. The effective rate is the rate converted annually that will produce the

same amount of interest rate per year as the nominal rate converted for periods per year

Effective annual rate is the total accumulated interest that would be payable up to the end

of one year, divided by the principal. (Els 2010: 93)

Example 2

A nominal rate of 6% compounded annually, will also have the effective rate of 6%.

However, if the nominal rate 6% is compounded semi-annually, the amount of R1 at the



end of one year will be the accumulation factor for a rate per period of 3% and two

periods. This is (1.03)2 = R1.0609.

The interest on R1 for one year is then R1.069 - R1 = 0.0609. This is equivalent to an

annual rate of 6.09%. Thus, 6.09% compounded annually will result in the same amount

of interest as 6% compounded semi-annually.

The formula for the effective interest rate is as follows:

= ( + ) −Where: r = the effective rate, i = the nominal rate per period and m = the number of

periods.

Applying this formula to our previous example, the effective rate is calculated as follows:= ( + . ) − = .It is important to note that economists generally prefer to use effective annual rates to

allow for comparability. In finance and commerce, the nominal annual rate may however

be the one quoted instead. When quoted together with the compounding frequency, a

loan/investment with a given nominal annual rate is fully specified (the effect of interest for

a given loan/investment scenario can be precisely determined), but the nominal rate

cannot be directly compared with loans/investment that have a different compounding

frequency.

3. Compound interest with present and future values

The compounding interest is use to calculate the future value of an investment when the

principal or present value is known. It is also used to calculate the present value to be

deposited now to earn a known future amount.

3.1 Future value and compound interest

Using the compounding interest rate the future value of the loan is calculated as follows:



= ( + )Where: F = future value, P = principal or present value, i = periodic interest rate (in

decimal form) and n = number of compounding periods.

Example 3

Jock Stein invested R1200 at 8% interest compounded yearly for 5 years. Calculate:

3.1. His total investment at maturity and

3.2. The total amount of interest earned for the five year period?

Solution

3.1. Total investment at end of period:= ( + ) = ( . ) = .3.2. The total interest earned:− = ( . ) = = .Example 4

Use the compound interest rate formula to calculate the compound amount of R5000

invested, at 10% interest compounded semi-annually, for 3 years.

Solution

Compounding periods (n) = 2periods per year x 3 years = 6 periods

Periodic interest rate (i) = 10/2 = 5% = 0.05= ( + ) = ( + . )= ( . ) = .



3.2. Present value and compound interest

Using the compounding interest rate, the present value of an investment is calculated as

follows:

= ( ) = ( + )Where: P = principal or present value, F = future value, i = periodic interest rate (in

decimal form) and n = number of compounding periods.

Example 5

Ken Rosewall invested a certain amount of money at 8% interest compounded yearly for 5

years and earned a total interest of R1 763.19. Calculate the total amount of investment.

Solution

Since the interest rate is compounded annually, there is no adjustment for the

compounding period and periodic interest rate. = ( ) = ( + )= .( + . ) = = . ( + . ) =

Example 6

Calculate the present value of R3 000 at interest rate of 16% compounded quarterly, for 6

years.

Solution

Compounding periods (n) = 4 periods per year x 6years = 24 periods

Periodic interest rate = 16/4 = 4% = 0.04= ( . ) = . = ( . ) = .



3.3 Summary of formulae for compound interest rate

These are the most basic formulae with compound interest rate:

1. The future value (FV) of an investment's present value (PV) accruing at a fixed interest

rate (i) for n periods. = ( + )2. The present value of an investment: = ( ) = ( + )3. The compound interest rate achieved: = −4. The number of periods required: = ( ) ( )( )3.4. Using compound interest tables

First estimate the number of compounding periods and interest rate period. Determine

whether you are using a table for a future value or present value and follow the necessary

steps. Tables for future value and present vale are in Table 1.1 and 1.2 respectively.

Steps for using compound interest tables

Step 1: Scan across the top row of the table to find the interest rate per period

Step 2: Look down that column to the row corresponding to the number of periods

Step 3: The table factor at the intersection of the rate per period column and the number

of periods row is the future value or the present value of R1 at compound interest rate.

Multiply the table factor by the principal to determine the compound amount.

4. Types of Annuities

Business situations frequently involve a series of equal payments or receipts, rather than

lump sums. These equal payments or receipts are called annuities. An annuity is the

payment or receipt of equal amount of money per period for a specified amount of time

(Brechner, 2009). Common application of annuities include insurance and retirement plan

premiums and payout, loan payments and saving plan for the future events such as

buying an expensive item or going to university.

4.1. Annuities Certain and Contingent Annuities



Annuities may be divided into two major categories namely, annuities certain and

contingent annuities.

An Annuity Certain is one for which the payments begin and end at fixed times. This

means that such annuity has a specified number of time periods such as R4000 per

month for 4years.

A Contingent Annuity is one the date of the first or last payment, or both, depends on

some event. This annuity is based on an uncertain time period. Retirement plans, social

security and various life insurance policies are examples of contingent annuities.

4.2. Ordinary Annuities and Annuities Due

Based on the date of the annuity payment, annuities can be classified into ordinary

annuities and annuities due.

Ordinary Annuity: this is when the annuity is made at the end of each period. E.g. A

salary paid at the end of each month is an example of an ordinary annuity.

Annuity Due: this is when the payment is made at the beginning of each period. E.g. A

rent payment paid at the beginning of each month is an example of an annuity due.

5. Future Value of an AnnuityThe future value of an annuity is the total amount of the annuity payments and the

accumulated (or compounded) interests on those payments. It is also called the amount of

an annuity. In this section, we will differentiate the calculation of the future value of an

ordinary annuity from that of an annuity due.

5.1. The future value of an ordinary annuityManual calculation of ordinary annuity



Calculate the future value of an ordinary annuity of R10 000 per year, for 3 years, at 6%interest compounded annually.

Time BalanceBeginning of period 1 0End of period 1 10 000 first annuity (P1)

Beginning period 2 10 000 from first period+ 600 interest earned in period (P2)+10 000 second annuity payment (P2)

End of period 2 20 600Beginning period 3 20 600 (P1, P2, interest P2)

+ 1 236 interest (P3)+ 10 000 third annuity

End period of three 31 836Future value of the ordinary annuity is R 31 836

This is cumbersome to calculate. An annuity of 10 years, with payments made monthly,

would require 120 calculations. It is therefore easy to use formulae to solve for a future

value of an annuity.

Formula for future value of an ordinary annuity= ( )Where: FVA= future value of annuity, P= annuity payment, i= interest payment and n=

number of periods (years x periods per year).

Example 7

Suppose that you have won the lottery and will receive R5 000 at the end of every year for

the next 20 years. As soon as you receive the payments, you will invest them at your bank

at an interest rate of 12 percent per annum compounded annually. How much will be in

your account at the end of 20 years, assuming you do not make any withdrawals?



Solution

Formula: = ( )Deposit made at the end of each period (R) = R5 000

Compounding: Annual and number of periods (n) = 20

Interest rate (i) = 12%

= 5000 (1.12) − 10.12 = 360 262.21Example 8

Calculate the future value of an ordinary annuity of R1 000 per month, for 3 years, at 12%

interest compounded monthly.

Solution

Formula: = ( )R = 1000 i = 12/12 = 1% n = 3 x 12 = 36periods

= 1000 × (1.01) − 10.01 = 1000 × 43.07688 = 43 076.885.2. The Future Value of an Annuity dueAn annuity due is one in which payments are made at the beginning of the payment

interval. The formula for a future value of the annuity due is a modification of a formula for

the future value of an ordinary annuity. A future value of an ordinary annuity of n+1

payments is similar to the amount of a corresponding annuity due.



Formula for future value of an annuity due

= ( + ) − × ( + )Where: FVA= future value of annuity, P= annuity payment, i= interest payment and n=

number of periods (years x periods per year).

Thus, the annuity due = ordinary annuity x (1+ i)

Example 9

Calculate the future value of an annuity due of R1 000 per month, for 3 years, at 12%


Solution

Formula: = ( ) × (1 + ) or FVA ordinary annuity x (1+i)

From Example 2.2, we know that FVA ordinary annuity = 43 076.88

FVA annuity due = 43 076.88 x (1.01) = R43 507.65

5.3 Present value of an annuity

Present value of an annuity is the sum of the present values of all payments or receipts of

the annuity. This is a lump sum amount of money that must be deposited now to provide a

specified series of equal payment (annuities) in the future. Similar to the future value, the

calculation of the present value of an ordinary annuity due is also different to that of an

annuity due.

5.3.1 Present value of an ordinary annuity

The present value of an ordinary annuity is calculated as follows:

= × − ( + )Where: PV = present value (lump sum), P= annuity payment, i= periodic interest rate and

n= number of periods (years x periods per year)



Example 10

Calculate the present value of an ordinary of R1 000 per month, for 4years, at 12%


Solution

Formula: = × ( )P = 1 000

i = 12/12 = 1%

n = 12 x 4 =48 periodsPVA = 1000 × ( . ). = 1000 x 37.97396 = R37 973.96

5.3.2 The present value of an annuity due

The present value of an annuity due is calculated as follows:

= × − ( + ) ( + )Thus, PVA annuity due x PVA ordinary annuity x (1 + i)

Example 10

Calculate the present value of an annuity due of R1 000 per month, for 4years, at 12%


Solution

We can use the PVA of an ordinary annuity from the previous example (2.3) multiplied by

(1+i).

PVA annuity due = 37 973.96 x 1.01 = R38 353.70 OR

PVA annuity due = 1000 × ( . ). (1.01) = R38. 353.70



6. Using annuity tablesAnnuity tables may be used to calculate the future and present values of ordinary annuity

and annuity due. Future and present values are shown in Tables 2.1 and 2.2 respectively.

Steps for calculating future value of an ordinary annuity

Step 1: Calculate periodic interest for the annuity (nominal rate / periods per year)

Step 2: Determine the number of periods of the annuity (years x periods per year)

Step 3: From Table 2.1, locate the present value table factor at the intersection of the

periodic rate column and the number of periods row.

Step 4: Calculate the present value of the ordinary annuity

Future value of an ordinary annuity = annuity table factor x annuity payment

Steps for calculating future value of an annuity due


Step 2: Calculate the number of periods of the annuity (years x periods per year) and add

one period from the total.

Step 3: From Table 2.1, locate the table factor at the intersection of the periodic rate

column and the number of periods row.

Step 4: Subtract 1 from the ordinary annuity factor to get to the annuity due table factor.

Step 5: Calculate the present value of the annuity due.

Steps for calculating present value of an ordinary annuity


Step 2: Determine the number of periods of the annuity (years x periods per year)

Step 3: From Table 2.2, locate the present value table factor at the intersection of the

periodic rate column and the number of period’s row.

Step 4: Calculate the present value of the ordinary annuity

Present value of an ordinary annuity = annuity table factor x annuity payment



For example, if the interest rate is 10 percent per year, the investment of R100 received in

each of the next 5 years is 3.791 x R100 = R379.1.

Steps for calculating present value of an annuity due


Step 2: Calculate the number of periods of the annuity (years x periods per year) and

subtract one period from the total.

Step 3: From Table 2.2, locate the table factor at the intersection of the periodic rate

column and the number of periods row.

Step 4: Add 1 to the ordinary annuity factor to get to the annuity due table factor.

Step 5: Calculate the present value of the annuity due.

For example, if the interest rate is 10 percent per year, the investment of R100 received at

the beginning of each of the next 5 years is (3.791 + 1) x R100 = R479.1.

7. Sinking funds and AmortizationIn the previous Sections, 2.2 and 2.3, the amount of the annuity payment was known and

we were calculating the future or present value (lump sum) of the annuity. In this section,

we will be calculating annuity payments when the future or present value is known. In this

case we will refer to sinking fund and amortization.

7.1. Sinking funds

A sinking fund situation occurs when the future value of an annuity is known, and the

periodic payments required amounting to that future value is known. A sinking fund is an

account used to set aside equal amounts of money at the end of each period, at

compound interest, for the purpose of saving for future obligation.



The sinking fund payments may be calculated using the following formula:

Sinking fund payment = × ( )Where: FV = amount needed in the future,

i = interest rate per period and

n = number of periods.

Example 11

El Loco needs R100 000 in 5years to pay off a bond issue. What sinking fund payment is

required at the end of each month, at 12% interest compounded monthly, to meet this

financial obligation?

Solution

Formula: sinking fund payment = × ( )i = 12/12 = 1% n = 5 x 12 = 60periods

Sinking fund payment = 100 000 × .( . )100 000 × .. = 100 000 × 0.0122444 = R1 224.44

7.1.1. Calculating the amount of an amortization payment by tableWe can use the future value of annuity table (Table 2.1) to calculate an amount of the

payment as follows:

Sinking fund payment =



Example 12

What sinking fund payment is required at the end of each 6-month period, at 6% interest

compounded semiannually, to amount to R12 000 in 4years?

Solution

Sinking fund payment = . = .7.2. Amortization

Amortization is the opposite of a sinking fund. Amortization is a financial arrangement

whereby a lump-sum obligation is incurred at compound interest now, such as a loan, and

is paid off or liquidated by a series of equal periodic payments for a specified amount of

time (Brechner, 2009).

Amortization payments may be calculated, by using a formula, as follows:

Amortization payment = × ( )Where: PV = amount of the loan or obligation,

i = periodic interest rate (nominal / periods per year) and

n=number of periods (years x periods per year)

Example 13

What amortization payment is required each month, at 18% interest, to pay off R5 000 in 3

years?

Solution

i = 18/12 = 1.5%

n = 3 x 12 = 36 periods

Amortization payment = × ( ) = × .( . ) = R180.76



7.2.1. Calculating the amount of an amortization payment by tableWe can use the present value of annuity table (Table 2.2) to calculate an amount of an

amortization as follows:

Amortization =

Example 14

What amortization payments are required each month, at 12% interest, to pay off a

R10 000 in loan 2 years?

Solution

Amortization = . = R470.73

8. End of Chapter Questions1. A finance company makes consumer loans at a nominal annual rate of 36%

compounded monthly. What are the nominal interest rate, the periodic interest rate

and the number of periods?

2. Find the effective interest rate equivalent to 8% compounded semi-annually.

3. An amount of R1 500 is deposited in a bank paying an annual interest rate of 4.3%,

compounded quarterly. Find the balance after 6 years.

4. Your goal is to accumulate R30 000 after 17 years from now. How much must you

invest now to have, at an interest rate of 8% compounded semi-annually?

5. If R500 accumulated to R700 in 5years with a certain interest compounded quarterly,

what is the rate of interest?



6. How many years will it take R175 to amount to R230 at interest rate of 4.4%

compounded annually.

7. An ordinary annuity starts on June 1, 1988, and ends on December 1, 1993.

Payments are made every 6 months. Find the number of periods (n).

8. Find the present value of an annuity of an annuity of R100 at the end of each month

for 30 years at 6% compounded monthly.

9. An investment of R200 is made at the beginning of each year for 10 years. If interest is

6% effective, how much will the investment be worth at the end of 10 years?

10. The premium on a life insurance policy is R60 a quarter, payable in advance. Find the

cash equivalent of a year’s premiums if the insurance company charges 6%

compounded quarterly for the privilege of paying a smaller amount every three months

instead of all at once for the year.

11. A family buys a R600 000 home and pays R100 000 down. They get a 25-year

mortgage for the balance. If the lender charges 12% converted monthly, what is the

size of the monthly payment?

12. A debt of R5000 is to be amortized by 5quarterly payments made at 3 month intervals.

If interest is charged at the rate of 12% convertible quarterly, find the period payment

and construct an amortization schedule. Round the payment up to the nearest cent.



Suggested Solutions1. Nominal rate = 36%

Periodic interest rate 36/12 = 3%

The number of periods = 12

2. Periodic rate 8/2 = 4% = 0.04 Number of periods = 2

r = (1.04)2 – 1 = 0.0816 = 8.16%

3. F = P(1 + i)P = 1500 r = 4.3/100 = 0.043 n = 4 x 6 = 24

= 1500 1 + 0.0434 = 1938.84The balance after 6 years is approximately R1 938.84

4. F = 30 000I =8/2 = 4% n = 17 x 2 = 34

Present value = ( . ) = R7 906.56

5. The formula for interest rate is: = − 1= 700500 − 1 = (1.4) . − 1 = 1.01697 − 1 = 0.01697

The quarterly interest rate is 0.01697 = 1.697%

The annual rate of interest is 1.697% x 4 = 6.788%

6. Formula used: n = ( ) ( )( )F=230 P = 175 i= 0.044n = log(230) − log(175)Log1.044 = 2.36173 − 2.243040.0187

= 6.347 years



7. Ordinary annuity is made at the end of each period

Year Month Day

1993 12 1

-1988 -6 -1

5years 6 months 0 days

Number of time periods = (5 x 2) 6/6 = 10 + 1 = 11

8. i =6/12 = 0.5% n = 12 x 30 = 360 periods= × ( )= 100 ( . ). = R16 679.16

9. P = 200 n = 10 i = 6%

Future value of annuity due = 200 × ( . ). (1.06) = R279.33

10. Present value of annuity due = = × ( ) ( + )P = 60 n = 4 i = 6/4 = 1.5%

Present value of annuity due = 60 × ( . ) (1.015)= R234.73

11. Amortization payment = × ( )PV = 600 000 -100 000 = R500 000 n = 25 x 12 = 300 i = 12/12 = 1%

Amortization payment = 500 000 × .( . ) = R5 266.12

12. Amortization payment = × ( )= 5000 × .( . ) = R1 091.78



Amortization schedule

(1)Paymentnumber

(2)Total

payment

(3)Payment on

interest (0.3 x 5)

(4)Payment on

principal (2) – (3)

(5)Balance of theloan (5) – (4)

1 R 1 091.78 R150.00 R941.78 R5000.00

2 R 1 091.78 R12.75 R970.03 R4058.22

3 R 1 091.78 R92.65 R999.13 R3088.19

4 R 1 091.78 R62.67 R1029.11 R2089.06

5 R 1 091.78 R31.80 R1059.95 R1059.95

Total R5 458.87 R458.87 R5000.00 0



CHAPTER 3

4

INVESTMENT APPRAISAL METHODS



CCoonntteennttss

What is our aim in appraising projects?Use of investment appraisal techniques in practiceFactors affecting cash flowsRelevant cash flowsSensitivity analysisProbabilityOther considerationsAnswer to Self-check Question



Objectives


Understand the importance of the investment appraisalprocess.

Distinguish between the various types of investmentprojects.

Calculate interpret and evaluate the payback method.

Calculate interpret and evaluate the Accounting Rate ofReturn method (ARR).

Calculate interpret and evaluate the Net Present ValueMethod. (NPV)

READINGS

Chapter 5: Els, G; Du Toit, E; Erasmus, P; Kotze, L; Ngwenya,

S; Thomas, K; Viviers, S. (2010) Corporate Finance, A SouthAfrican Perspective, Oxford University Press.

Chapter 9: Fundamentals of Corporate Finance , 4th SouthAfrican Edition, Ross S, Westerfield RW, Jordan BD and Firer C,2008



1. IntroductionFinancial managers are responsible for:

Investment decision (Capital budgeting)

Financing decision (Capital structure)

Day to day cash flow decisions (Financial planning)

Goal of financial management is to maximise the (present) value of the firm’s shares.

Therefore the objective is to maximise expected value from all projects and operations of

the company. So the focus should be on making value creating investment decisions. So

you need to identify and know when these opportunities exist and you need to measure

the expected value.

In investment opportunity requires funding. If efficient long term planning is not conducted,

a company may not be able to find the capital required to finance its investments.

2. Steps in the Capital Budgeting ProcessThe capital budgeting process consists of at least six steps:

2.1. Identify all possible investment alternatives. In this way due scrutiny and

attention is given to all possible options.

2.2. Determine the relevant cash flows associated with each of the possible

investment alternatives.

2.3. Determine the company’s cost of capital (this is discussed in greater detail in

the chapter headed Cost of Capital (Chapter 7)

2.4. Evaluate the various projects. Various investment appraisal methods are used

in order to test financial feasibility.

2.5. Make the investment decision. This is done when all projest cash flows (inflows

and outflows) have been ascertained.

2.6. This is the final step and known as the follow up step. This means that every

project is evaluated in order to ensure value creation.

3. Aims of Appraising Projects?

A firm will appraise investment projects because such projects could help it achieve its

overall objective. What is this likely to be? We’ll look at some possibilities:



• To maximise profit, either in terms of Rs or as a percentage of the capital invested –

this sounds like a good idea, but it should be realised that this would not necessarily

be in the company’s, and therefore the shareholders’, interest. Profit could increase

temporarily if quality were to be sacrificed or unsuitable forms of financing used, but

this would not result in long-term benefit for the firm

• To ensure the continuation of the business – in circumstances where the business

already has problems, this could be considered essential, but would be a rather

limited aim under more normal conditions

• To promote the growth of the business. This may take many forms and involve

many different tasks like: increasing market share, increasing sales volume or even

improving efficiencies.

• To maximise the wealth of shareholders – this covers business survival, return on

investment and future growth. Shareholders will perceive wealth maximisation

through dividends paid out and rising share values.

This concept may seem to ignore the needs of others involved with the firm –

employees, customers, suppliers, and long-term creditors – who surely should also be

entitled to a fair return for their input to the business. However, this is not necessarily

contradictory, because if no attention is paid to these providers the adverse effects of,

for example, poor industrial relations or inferior quality products are likely to reflect on

profit, dividends and share price, so shareholders’ wealth would not be maximised.

4. Types of Investment Projects4.1. Replacement Projects: these occur when certain assets are reaching the end

of their useful life and need to be replaced. For example the purchase of a new

printing machine to replace the more costly to maintain older machine. This

may entail calculating revenues from the sale of the older asset or costs

incurred in scrapping the asset and comparing these to the cost incurred and

revenue generated from the purchase of the newer asset.

4.2. Expansion Projects: these projects are undertaken to grow the size of the

business. This may entail the acquisition of a book binding machine that will

complement the printing process, thus reducing costs and increasing the

profitability of the firm. Of course other projects may also be assessed before

choosing the most viable one.



4.3. Independent Projects: These projects do not affect the current running and

profitability of the business but they are assessed and evaluated on the basis

that they may increase shareholder wealth. For example, the acquisition of an

electricity generator that may assist in the production process, should there be

electricity blackouts.

4.4. Mutually Exclusive Projects: generate their own savings or possibly their

own revenue streams, thus resulting in an improvement in the bottom line.

Essentially such choices do not hinge on the current status quo or projects

being undertaken.

4.5. Complementary Projects: this occurs if the acceptance of one project will

have a positive effect on the other projects being undertaken. For example, a

vacuuming machine being added to a car wash business may give that

business a competitive edge over other businesses in the same field.

4.6. Substitute Projects: are those projects that may have the effect of negatively

affecting the cash flows generated by the company’s other projects. This is

often referred to as cannibalization.

4.7. Conventional Projects: these are projects that require an initial large cash

outlay but result in positive cash inflows over the lifetime of the project.

4.8. Unconventional Projects: this requires a substantial cash outlay initially and it

yields cash inflows in some years and cash outflows in some other periods.

(Els 2010: 142-4)

5. Payback PeriodPayback Period calculates the number of years after the initial investment amount of an

investment project is recovered from a projects net cash inflows. The rule is, if payback is:

Less than the maximum time allowed then invest in the project.

Greater than the maximum time allowed then don’t invest in project.

Illustrative ExampleAn initial outlay of R2200 is required and cash flows of R400, R800 and R1 200 accrue in

years 1, 2 and 3 respectively. Should the project be accepted and what is the payback

period?



Year Cash flow (p.a) Accumulated Cash Flow1 600 600

2 900 1 500

3 1 400 2 900

Solution:By inspection we note that payback must occur between year 2 (with cumulative revenue

of R1 500 and year 3 (cumulative revenue of R2 900). To calculate the exact period (or

time in year 3), we need to make an important assumption: that revenue is earned equally

throughout the period. A workable formula is:

= years before full recovery + unrecovered cash flow at beginning of year X 365

Cash flow during the year 1

Our answer is, therefore = 2 years + [700/2900 X 365]

= 2 Years and 88 days

NB

The amount of R700 is arrived at by taking the investment of R2 200 and

deducting the R1 500 from it. Essentially we are asking ourselves, how long it will

take us to earn the R700 in year 3.

We use 365 because it is more useful to have our answer in days.

Example 1

Messi Motors have just made an investment of R420 000 in a state of the art wheel alignment

machine, details of which are below:

Expected useful life 6 years (straight line depreciation)

Salvage value 120 000

Cost of Capital 10 %

Tax rate 30%

Expected cash flows after tax are as follows:



Year Cash Flows

1. 66 000

2. 96 000

3. 126 000

4. 181 000

5. 68 000

6. 50 000

Solution

Year Cash Flow Cumulative Cash Flow

1 66 000 66 000

2 96 000 162 000

3 126 000 288 000

4 181 000 469 000

5 68 000 537 000

6 50 000 587 000

Payback is: 3 years and [132 000/181 000 X 365]

3 years and 266,18 days. (You may round off to 267 days)

5.1. Advantages of the Payback Period1. It is easy to understand and calculate.

2. It adjusts for uncertainty of later cash flows. (Ross: 277)

3. It serves as a criterion to measure liquidity, because the quicker the initialinvestment is paid off, the earlier the generated cash is available for alternate use.(Els: 148)

5.2. Disadvantages of the Payback Period1. It ignores the time value of money.

2. It is very subjective.



3. It insists on a cut off period

4. It ignores cash flows beyond the cut off period

5. There is a definite bias against long term projects that require a large research and

development outlay.(Ross 277).

6. It ignores the order in which cash flows occur within the payback period.

7. It does not consider the cost of capital in any way.

8. It makes no distinction between projects of different sizes with different capital

requirements and with different lifetimes.

6. Accounting Rate of Return (ARR)/Average Accounting Return (AAR)

The accounting rate of return method takes the average accounting profit that the

investment will generate and expresses it as a percentage of the average investment in

the project as measured in accounting terms. A flawed approach to making a capital

budgeting decision is the ARR. It requires the following data to be available:

a. Average profit = Total profits/no of years

b. Average Investment = [Initial investment + salvage value]/2

The Formula

ARR = Average annual profits x 100Average investment* 1

* Average investment = Initial capital employed + residual value

2

The Decision Criteria

To decide whether the return is acceptable, we must compare the percentage with the

minimum required by the business. If the firm has a target ARR less than the percentage

achieved, then this investment is acceptable, otherwise not.



An exampleWe can use the same data from the previous example:






Tax rate 30%

Expected cash flows after tax are as follows:

Year Cash Flows

1. 66 000

2. 96 000

3. 126 000

4. 181 000

5. 68 000

6. 50 000

Required:

Calculate the ARR.

Solution

Cash flows need to be converted to net profit. This will entail adding back the depreciation

tax shield.

Depreciation per annum, calculated as follows:

Cost of investment R420 000

Salvage value R120 000

Depreciable value R300 000

Depreciation per annum = 300 000/6

= 50 000 per annum.



Depreciation tax shield = R50 000 X 30%

= R15 000

Year Cash Flows Net Profit

1 66 000 81 000

2 96 000 111 000

3 126 000 141 000

4 181 000 196 000

5 68 000 83 000

6 50 000 65 000

Total Net Profit 677 000Average Net Profit 677 000/6 = R112 833Average investment [420 000 + 120 000]/2 = 270 000

ARR = Average Profits/Average Investment X 100= 112 833/270 000 X 100

= 41, 79%

Advantages of the ARR1. It is relatively easy to calculate

2. Data that’s needed is easily available in the annual financial statements. (Ross;279)

Disadvantages of the ARR1. It ignores the time value of money

2. The salvage value may not be realistic

3. It is based on accounting profits (these are merely book entries), not on cash flows(which are the lifeblood of any business).

4. It is not a rate of return in any meaningful sense (Ross; 279)

7. Net Present Value (NPV)Relevant cash flows

We already know that investment appraisal involves actual cash flows, so that we must

adjust if necessary for such things as accruals and prepayments and depreciation if we

are working from a profit and loss account.



We also know that we are dealing with uncertainty – we are attempting to forecast future

flows, which will be more doubtful the further into the future we try to go. We may have to:

• consult all those who will be concerned with a project to obtain their estimates for the

level of revenue and expenditure that should arise

• undertake market research, to ensure project success.

• utilise statistical techniques to derive future data from past performance.

When using NPV, we must apply the following.

• Compare the Present Value (PV) of the project in respect of:

• Net operating benefits (cash inflows)

• Net costs of investment (cash outflows)

• This is then discounted at an appropriate risk adjusted discount rate (reflecting the

correct risk adjusted opportunity cost of the project). In layman’s terms, the

business seeks to adjust costs and revenues with an estimated inflation rate in

order to ensure that what may have started as a lucrative project does not become

less so or even a loss as a result of the ravages of inflation.

The formula of Net Present Value is:

The decision rule is:

a. If NPV > 0, invest.

b. If NPV < 0, do not invest.

c. If NPV = 0, indifferent between investing or not

NPV: An example






t

n

t

n 0 r)(1

FlowsCashInvestmentNet

0 r)(1

FlowsCashOperatingNetNPV

nn



Tax rate 30%

Expected cash flows after tax are as follows:Year Cash Flows

0 (420 000)

1 66 000

2 96 000

3. 126 000

4. 181 000

5 68 000

6 50 000

Required:

Calculate the NPV of this project and state whether the project should be accepted or

rejected.

Year Cash Flows DF (10%) Discounted Cash Flow

0 (420 000) 1 (420 000)

1 66 000 0.9091 60 001

2 96 000 0.8264 79 334

3. 126 000 0.7513 94 664

4. 181 000 0.6830 123 623

5 68 000 0.6209 42 221

6 50 000 0.5645 28 225

120 000 0.5645 67 740NPV 75 808

The project should be accepted as its NPV is positive.

Notesa. The PVIF tables are used at a factor of 10%.

b. The factors can be worked out using the formula PV = 1/(1+r)t

c. Cash flows must be after tax. If it is before tax, it must be converted to after tax.



Advantages of NPV1. It accounts for the time value of money.

2. It is logically consistent with the company’s goal of maximising shareholder wealth.

3. It is relatively easy to calculate.

4. It uses all the cash flows of a project and discounts them consistently.

5. It is realistic in outlook.

Disadvantages of NPV

1. Fixed assumptions are made around the variables affecting project cash flows suchas: exchange rates, selling prices, inflation.

2. NPV’s major problem is that it relies crucially on predicting the future.End Of Chapter QuestionsShukriya Salvagers have just made an investment of R350 000 in a new VW Amarok delivery

vehicle.

Further details:




Year Cash flows

1. 120 000

2. 70 000

3. 70 000

4. 100 000

5 (12 000)

Required:

1. Calculate the Payback Period and the Accounting Rate of Return

2. Shukriya requires a payback period of no more than 3 years and a return of at least

30%. Purely on the basis of these criteria, should this project be accepted

3. Use the NPV method to determine project viability. On the basis of this calculation,

should the project be accepted? Why/why not?



Chapter 4

Share Valuation



CCoonntteennttss

1. Introduction

2. Ordinary shares and Preference shares

3. Defining Value

4. Share Valuation

5. End of chapter questions



ObjectivesAfter working through this section you should be able to:

Distinguish between ordinary shares and preference shares.

Distinguish between par value, market value, book value and intrinsic value.

Explain the importance of share valuation.

Calculate and interpret the various methods used to value company shares.

Apply the appropriate method to calculate the intrinsic value of a share.

Assess the growth prospects of a firm from its P/E ratio.



READINGSReadings

This unit has been designed to be read in conjunction with the following textbooks:

PRESCRIBED:


S. (2010) Corporate Finance, A South African Perspective, Oxford University Press.


Chapter 8: Ross, S; Westerfield, RW; Jordan, BD; and Firer C. (2009). Fundamentalsof Corporate Finance, 4th South African Edition, McGraw-Hill.




1. IntroductionIn this chapter we discuss what is considered to be an acceptable return and also how a

company values its shares. The concepts of preference shares and ordinary shares are

also dealt with. Then a few models are presented to assist financial managers in their

financial decision making procedures. The focus then shifts to expected and required

returns and then to market efficiency. The overriding concern with this chapter is the

consistent wish to maximise shareholder wealth. Whilst this term is used to merely pay lip

service to this very important concern, we nevertheless explore this ideal at length.

2. Ordinary Shares and Preference Shares

2.1. Ordinary Shares

The owners of these shares are essentially the owners of the company. They become the

owners of the productive assets of the company and have a vote at the AGM. They have

the right to elect the board of directors who in turn appoint the managers to oversee the

day to day running of the business. Ordinary shareholders also have the preemptive right

to purchase any fresh issue of shares before they are offered on the open market to the

general public. (Els 2010: 255)

2.2. Preference Shares

Preference shares are also known as preferred stock. Preference shares are shares in the

equity of a company, and which entitle the holder to a fixed dividend amount by the

issuing company. This dividend must be paid before the company can issue any dividends

to its ordinary shareholders. Also, if the company is dissolved, the owners of preference

shares are paid back before the holders of ordinary shares. However, the holders of

preference shares do not usually have any voting control over the affairs of the company,

unlike the ordinary shareholders.

2.2.1. Types of Preference Shares

Redeemable Preference Shares: The issuing company has the right to buy back

these shares at a certain price on a certain date. Since the call option tends to cap

the maximum price to which a preference share can appreciate (before the

company buys it back), it tends to restrict stock price appreciation.

Convertible Preference Shares. The owner of these preference shares has the

option, but not the obligation, to convert his/her preference shares to ordinary



shares at some conversion ratio. This is a valuable feature when the market price

of the common stock increases substantially, since the owners of preference

shares can realize substantial gains by converting their shares.

Cumulative Preference Shares: If a company does not have the financial

resources to pay a dividend to the owners of its preference shares, then it still has

the payment liability, and cannot pay dividends to its common shareholders for as

long as that liability remains unpaid.

Non-cumulative Preference Shares: If a company pays a scheduled dividend,

then it does not have the obligation to pay the dividend at a later date. This clause

is rarely used.

Participating Preference Shares: The issuing company must pay an increased

dividend to the owners of preference shares if there is a participation clause in the

share agreement. This clause states that a certain portion of earnings (or of the

dividends issued to the owners of ordinary shares) will be distributed to the owners

of preferences shares in the form of dividends.

3. Defining Value3.1. Market ValueBuyers and sellers determine the market value of each share of stock through the prices

they're willing to sell for or to pay for each share. When the demand for a particular stock

is greater than the supply of shares available, the price increases. Buyers choose to pay

more to receive a share of stock. If the demand for that share is less than the supply of

shares, the price decreases --- buyers aren't willing to pay as much for each share.

3.2. Par ValuePublic arbitrarily attach a rand value, or par value, to each class of share it issues. The

business uses par value to record the shares issued in the financial records. The actual

price received for the stock usually includes an amount greater than par value. The

company records the amount received above par value as additional paid in capital and

this is known as share premium. Par value never changes.



3.3. Intrinsic Value

The actual value of a company based on an underlying perception of its true value

including all aspects of the business, in terms of both tangible and intangible assets. This

value may or may not be the same as the current market value. Value investors use a

variety of analytical techniques in order to estimate the intrinsic value of shares/securities

in the hope of finding investments where the true value of the investment exceeds its

current market value.

3.4. Book Value

The book value of a share is the total value of the company’s assets less the total value of

its liabilities and then divided by the total number of shares issued to ordinary

shareholders.

4. Share Valuation: Discounted Cash Flow Models and Techniques

These models are based upon the premise that the price of a share must be equal to the

discounted present value of the cash flows that an investor expects to receive. This model

reflects reality for the investor. The cash flow the investor expects to receive in the long

term will take the form of dividends. These models rely upon the accurate prediction of

future dividend flows. Variations in the model are due to the timing and variations in

amount of the expected dividends. The discount rate used is the cost of equity funds

invested. There are two basic steps: first to estimate the cash flows and secondly to

determine the present value of the cash flows.

For a short-term investor (assume a 1 year investment):

Value = PV of dividends at year-end + PV of share price at year end.

In the longer run an investor or succession of investors expect to receive a stream of

future dividends.

Value = PV of all future dividends.

A general formula for this would be:

Po = D1(1 + r) t



4.1. Zero Growth Dividends

This is used for stocks that have earnings and dividends that are expected to remain constant

over time (zero growth). Thus Dividend income can be viewed as perpetuity.

Example

A preference share pays a R2,00 dividend and the share has a required return of 10%. What

is the most that a person will pay for this share?

P0 = D/r

= R2/0.10

= R20

4.2. Constant growth dividends

This is used for stocks that have earnings and dividends that are expected to grow at a

constant rate forever. This implies that:

D1 = D0(1 +g)

The intrinsic value is = ×( )Where g = perpetual growth rate in dividends and D0 (1+g) = D1

If the price of a share is known, we can use the above formula to estimate the required rate of

return (k):

k = +Example

An ordinary share has just paid a dividend of R2 and the share has a required return of 10%.

Dividends are expected to grow at 6% per annum. What price would you be willing to pay for

this share?

r

DP 0



Solution = × (1 + )−= R2 X 1,06

0,10 -0,06

= R53

4.3. Supernormal growth or Multistage Growth Models

This model assumes that two stages of dividend growth exist:

A first stage with a high growth rate for n years (say years 1 to 5, the ‘supernormal’

period) and

A second stage with a constant growth rate forever (say years 6 to 20, the ‘normal’

period).

The equation for the supernormal or two-stage DDM is:

Pn represents the terminal value of the stock at the end of period n.

Example

An ordinary share has just paid a R2.00 per share dividend and the share has a required

return of 15%. Dividends are expected to grow at 20% in the first 2 years and from the year 3

the growth will be 5% per year forever. What is the price you should be willing to pay for the

share?

Solution

D0 = 2.00 g1 = 20% g2 = 5% k = 15%

D1 = 2(1.2) = 2.40 D2 = 2.4 (1.20) = 2.88 D3 = 2.88(1.05) = 3.46 D4 = 3.63

nn

nn

n

tn

nt

t

gr

DPSP

r

P

r

DPS

1

1

where,)1()1(

shareperVal



Stage 1: Terminal value = Share price at the end of year 3

P3 = .. . = 36.3

Stage 2: Find the intrinsic value (P0)

Po = .. + .. + .. + ..= 2.09 + 2.18 + 2.27 + 23.86

= R30.40

4.4. Price Earnings Ratio

This is the most common method used in share market valuations and it concentrates on the

firm’s price/earnings multiple. This is the ratio of the price per share to its earnings per share.

As an ongoing entity, minority shareholders’ expectations of dividends depend upon the firm’s

ability to earn a positive return on equity capital. This return is described in the financial

statements as earnings attributable to ordinary shareholders (after allowing for payment of

interest on loans and debentures, taxes, and preference dividends). These attributable

earnings divided by the number of ordinary shares outstanding is the earnings per share

(EPS). The relationship between a share price and its EPS is the P/E ratio. Generally a high

P/E ratio signals a favourable perception by the market of a share’s earning power, or its

ongoing ability to earn a positive EPS.

P/E ratio = P0 / EPS

Where EPS is expected earnings per share (E1).

Thus, P0 = P/E x E1

P/E Ratios are a function of two factors

• Required Rates of Return (k) (inverse relationship)

• Expected Growth in Dividends (direct relationship)

If g = 0 then the P/E ratio simplifies to:

gk

b

E

P

)1(

1

0



Example

Given the following information estimate P/E ratio and V0:

E1 = R2.50 g = 0 k = 12.5%

Suggested Solution

Since g = 0, P/E = 1/k

P/E = 1/0.125 = 8

V0 = P/E x E1 = 8 x R2.50 = R20.00

An Example with Growth

Given the following information estimate P/E ratio and V0:

b = 60%; ROE = 15%; k = 12.5%; (1-b) = 40%, E0 = R2.50

Suggested Solution

g = ROE x b = 15% x 60% = 9%

E1 = R2.50 (1.09)

= R2.725

P/E = (1-b) /(k-g)

= (1 - 0.60) / (0.125 - 0.09)

= 11.4

P0 = P/E x E1 = 11.4 x R2.73

= R31.14

kE

P 1

1

0



Pitfalls in Using P/E Ratios

Earnings management is a serious problem,

P/E should be calculated using pro forma earnings,

A high P/E implies high expected growth, but not necessarily high stock returns,

Simplistic, assumes the future P/E will not be lower than the current P/E. If

expected growth in earnings fails to materialize the P/E will fall and investors may

incur large losses.

Intrinsic value and Market Price

Market value (P0): the market value is a consensus value of all traders. In equilibrium the

current market price will equal intrinsic value (V0). The comparison of market value to the

intrinsic value is used by investors as a trending signal.

Trading Signals

If V0 > P0 Buy: it is underpriced

If V0 < P0 Sell or short sell: it is overpriced

If V0 = P0 Hold as it is fairly priced

4.6. Market to Book Ratio:

High ratio indicates a large premium over book value, and a ‘floor’ value that is often

far below market price.

Formula = Market price per share

Book value per share

5. End of Chapter Questions1. Differentiate between the following terms: Earnings Yield, Dividend Yield, and the PE

Ratio.



2. Do shares with low dividend yields tend to have a high or a low PE ratio?

3. List the most important factors that would influence an investment analyst in the rating

of PE ratios.

4. A firm projects an ROE of 20%; it will maintain a plowback ratio of 0.3. The firm is

expecting earning of R2 per share and investors expect a return of 12% on the stock.

What is expected price and P/E ratio of the firm?

Suggested Answers

1. Earnings Yield is the earnings before payment of dividends, divided by the current

share price.

Dividend yield is the actual dividend itself divided by the current share price.

The PE ratio is the current share price divided by the earnings – it is in fact the inverse

of the earnings yield. Therefore a low earnings yield is indicative of a high PE ratio and

both usually indicate a highly sought after share.

2. A share with a low dividend yield usually has a low earnings yield and therefore a high

PE ratio.

3. An analyst would consider the following as important factors:

The growth of future earnings per share is the most important factor.

Investors prefer a minimum fluctuation from expected earnings. Volatile shares

consistently get a lower share market rating.

Investors prefer companies having favourable prospects for long term growth.

Companies heavily involved in research and development project an image of

growth. As a result these companies enjoy a much higher market rating than

companies not committed to research and development projects.

The frequent introduction of new products is a factor that helps a firm to acquire a

high PE ratio.

Companies that are operating in markets or sectors enjoying a rapid growth in

demand for their products have a much superior market rating than companies

that have reached a maturity stage in the product life cycle.



4. g = ROE b = 0.20 0.30 = 0.06 = 6.0%

D1 = R2 (1 – b)

= R2 (1 – 0.30)

= R1.40

33.2306.012.0

40.110 R

R

gk

DP

P/E = R23.33/R2

= 11.67



CHAPTER 5

BONDS AND BOND VALUATION



CCoonntteennttss

1. Introduction

2. Bonds

3. Why invest in Bonds?

4. Pricing of Bonds

5. Calculation of YTM on Bonds

6. Bond Prices and YTM

7. Duration

8. End of chapter questions



ObjectivesAfter working through this section you should be able to:

Explain fixed income markets and securities.

Understand the relationship between bond prices and interest rates.

Estimate the present value of a bond.

Understand the yield curve and its usefulness as an analytical tool.

Calculate the duration of a bond.



READINGSPRESCRIBED:




Chapter 7: Ross, S; Westerfield, RW; Jordan, BD; and Firer C. (2009). Fundamentalsof Corporate Finance, 4th South African Edition, McGraw-Hill

Chapter 10 and 11. Bodie, Z.; Kane, A. and Marcus, J. A. (2010) Essentials ofInvestment.8th Edition. New York: McGraw Hill



1. Introduction

Businesses and governments do not have sufficient capital to fund all their projects and

therefore borrow in order to fund their activities. Historically, companies have borrowed

money from banks who in turn have secured the money from bank depositors. Smaller

companies can only borrow from banks. However, larger companies have access to and

can borrow directly from all lenders in the market. This can be advantageous to both the

lender and the large company because the lender can earn a higher rate and the borrower

can borrow at a lower rate.

An example to illustrate this

The prevailing rate with banks on wholesale deposits at present is 5%, the bank then in

turn lends at say prime 9% (July 2012).The bank is making a spread of 4%. However if

the borrower goes directly to the lender, the lender may elect to only charge the borrower

7%. It is easy to see how both parties score, provided the borrower honours his obligation.

This process whereby the borrower borrows directly from the lender without using banks

is known as disintermediation.

Modern day governments have always been able to borrow directly from investors in this

way. The instrument that enables this lending and borrowing process to be undertaken is

generally a fixed-income security, commonly called a bond. The bond is in essence the

“IOU” of the borrower.

2. Bonds

A bond can be described as a tradeable debt instrument that is issued by a borrower. It

pays interest (known as ‘a coupon’) for a fixed period of time, at a predetermined rate, at

regular intervals until maturity, when principal amount is then repaid in full. A bond is

tradeable, unlike a deposit with a bank where the depositor is only entitled to repayment.

Tradeable means that the bondholder (lender) can either retain the bond until repayment

date, or he can sell the bond on to another investor.



Bond characteristics and terminology

The par value or face value is the original value of the bond which must be repaid

upon expiry. In South Africa, the usual par value of a bond is R1 000.

The coupon is the interest paid on the bond. These coupon payments are paid at

regular intervals usually annually, semi-annually or quarterly.

The maturity date, describes the term of the loan, when the bond is to be redeemed.

Yield to Maturity (YTM): it is a required return on a bond. This is a discount rate used

in the valuation of bonds.

A zero coupon bond: A special type of bond that does not pay interest. It is traded at

a deep discount, rendering profit at maturity when the bond is redeemed for its full

face value.

At par: When a bond is selling at price = Par Value (This would happen when the

coupon rate = YTM).

Discount bond: When a bond is selling at price < Face Value (The coupon rate <

YTM).

Premium bond: When a bond is selling at price > Face Value (coupon rate > YTM).

3. Why Invest in Bonds?

Bonds offer investors (lenders) a fixed income, with the possibility of limited capital

growth. They are less risky than shares because interest payments are made from

company profits, before dividends and if the company goes into liquidation, bondholders

are repaid before shareholders. Bonds issued by companies are often secured by the

fixed assets of the issuing company. Government bonds are more secure than corporate

bonds; a government is less likely to default on payment.



4. Pricing of bondsThe value of a bond depends upon the expected yield from fixed interest investments

given current interest rates and the investors’ expectation of the issuer defaulting on the

bond terms. When valuing a bond we are effectively valuing the cash flows from the bond

coupon and the redemption value of the bond.

Thus, the value of a bond is the present value (PV) of the expected future cash flows:

Bond Value = P V of Coupons + PV of Face Value

PV of a bond = C(PVFAr,t) + FV(PVIFr,t)

PV of a bond = + ( )Where: C = coupon payment,

FV= Face Value,

r= yield to maturity, and

t = time to maturity

An Illustrative Example of calculating a price of a bond

A firm borrows R1 000 by issuing a bond with coupon rate of 10% per annum paid

annually and promises to pay back the principal in 20 years. If the current market interest

rates on a similar bond are 10%, what is the value of this bond?

Solution

PV of a bond = ( ) + ( )PV of a bond = ( . ). + ( . )

= (100 x 8.51356) + (1000 x 0.14864)

= 851.36 + 148.64 = R 1000



Note: This bond is trading at par (R1000) because the coupon rate = YTM.

If market interest rates (r) increase, the bond would sell at a discount (below R1 000).

If market interest rates (r) decrease, the bond would sell at a premium (above R1000).

Calculation of the price of a bond with semiannual compounding

We will use our previous example but we will assume that the coupon is paid

semiannually and has 10 years to maturity:

A firm borrows R1 000 by issuing a bond with coupon rate of 10% per annum paid semi-

annually and promises to pay back the principal in 10 years. If the current market interest

rates on a similar bond are 10%, what is the value of this bond?

Solution

r = 10%; matures in 10 years; 10% coupon paid semiannually.

Step 1: Determine Cash flows

Face value = R1 000

Annual coupon payments = coupon rate × face value

= 0.10 x 1000

= 100

Semiannual coupon payment = 100/2 = 50

Step 2: Determine number of periods

(10 years to maturity) x (number of periods in a year) = 10 x 2 = 20

Step 3: Determine the discount rate per a period

(Annual rate / 2) = 10/2 = 5%

Step 4: Use PV formula to find price of bond

PV of a bond = C ( ) + ( )PV of a bond = 50 ( . ). + ( . )



= (50 x 12.4622) + (1000 x 0.37689)

= 623.11 + 376.89

= R 1000

5. Calculating YTM on a bond

We want to establish how you might calculate the interest rate (YTM) on any bond

that is trading in the secondary market. Given the market price of a bond and its

coupon, we want to estimate its implied YTM.

An Illustrative Example

A company borrows R1 000 by issuing a bond with coupon rate of 6% per annum paid

annually and promises to pay back the principal in 30 years. If the current market price of

the bond is R1 153.72, what is the YTM (r) of this bond?

Solution

Step 1: calculate coupon

Coupon = coupon rate × par value = 6% × R 1 000 = R 60

Step 2: Calculate YTM or r

PV of a bond = C ( ) + ( )PV of a bond = 60 ( ) + ( )

Unfortunately, other than using a financial calculator or excel, there isn't an easy formula

to calculate YTM. One solution is to use the Trial and Error Method, which states:

choose YTM such that

Left Hand Side = Right Hand Side of equation

Step 2A: Identify the starting discount rate (r) by comparing the market value of bond to

the par value.

If the market value > the par value, then the YTM < the coupon rate



If the market value < the par value, then the YTM > the coupon rate

In this example the market value > par value, thus the YTM should be less than the

coupon rate.

The coupon rate is 6% so we need to try a number lesser than 6%.

Step 2B: Try YTMs below the coupon rate

PV of a bond @ 4% = 60 ( . ). + ( . ) = R1 346.35

R1 346.35 > R1 153.72 we need to increase the YTM to 5%

PV of a bond @ 5% = 60 ( . ). + ( . ) = R1 153.72

This is exactly the price of a bond, thus the YTM is 5%.

Step 2C: If we don’t get the PV of the bond through “trial and error” we proceed

with a linear interpolation.

YTM = + × (ℎ − )Where l= lower

h = higher rate

H = bond value at the higher rate

L = bond value at lower rate

VB = Market value of the bond value

NB: this step, 2C is not part of our syllabus.



6. BOND PRICES AND YIELD TO MATURITY

The YTM is the yield on the stock, which combines the income together with any loss

arising on maturity (or if the bond is trading at less than par value it combines the income

together with the profit arising on maturity).

Bond prices and YTM have an inverse relationship

• When YTM is very high the value of the bond will be very low.

• When YTM approach zero, the value of the bond approaches the sum of the cash

flows.

The graphical relationship between the yield to maturity and the term to maturity is called

the Yield Curve. See yield curve in Figure 6.2.

Figure 5.1: Yield curve

It would be an over simplification to assume that a single interest rate existed and all bond

prices varied uniformly in response to a change in it. Governments usually have absolute

control over short term interest rates through monetary policy and their ability to set

reserve requirements in the banking system. Rates for longer dated commitments are

established by market forms, i.e. an interest rate to persuade people to lend balanced



against a rate to encourage people to borrow. This will give rise to different rates of

interest for borrowing over different time periods. The relationship between the yield to

maturity and the term to maturity is called the term structure of interest rates because it

relates yield to maturity to the term of each bond. A typical yield curve and its variations

are shown by Figure 6.3.

Figure 5.2 variations of the yield curve

Yield

B

A Normal Yield Curve

C

D

Years to Maturity

The distinct features of a normal yield curve (curve A above) are as follows:

Longer dated bonds have higher yields than shorter dated ones, because money is

tied up for longer.

Potential investors will usually need to be persuaded to lend for longer periods and

must therefore be offered a higher return.

The curve is virtually flat when one considers longer dated bonds. In fact there is

virtually no difference in lending for 15 – 20 years.

If there is an anticipated increase in interest rates then curve B will become the

new yield curve. It will have the following distinct features:

The curve will rise more sharply and flattens out at a higher level.



This indicates that bond investors do not believe that current low values of interest

are sustainable but that economic pressures will cause a rate rise.

If there is an anticipated decrease in interest rates then curve C will become the

yield curve with the following features:

The flatter curve indicates that expectations are for rates to fall in the longer term.

Borrowers will not enter into long-term commitments because they believe that by

maturity, they can achieve low interest rates.

Curve D illustrates a yield curve when it is strongly felt that interest rates will fall.

This is a negative yield curve and is a more extreme version of our previous

scenario. If the government raises short-term rates to very high levels then all

bond investors will expect a fall in long term rates. This will be reflected by yields in

longer dated bonds.

7. DurationThe concept of duration was introduced by Frederick Macaulay in 1938. It is “a measure

of the effective maturity of a bond, defined as the weighted average of the times until each

payment, with weights proportional to the present value of the payment (Bodie, et al.,

2010:337).

7.1. The Duration formula

Where: Wt = Weight of time t, present value of the cash flow earned in time t as

a percent of the amount invested,

CFt = Cash Flow in Time t, coupon in all periods except terminal period

N

tt tWD

1

0

1 )1(

P

TYM

CF

W

N

tt

t

t



when it is the sum of the coupon and the principal,

YTM = yield to maturity,

P0 = bond’s price, and D = Duration

Example

Calculate the duration of a bond priced R1 033.12. The bond has a 9% coupon rate, 4

year annual payments and its yield to maturity is 8%.

Solution

Year (t) Cash Flow PV @ 8% PV/P0 Weight (PV/P0) x t

1 R90R 83.33 0.0806 0.0806

2 R90R77.16 0.0747 0.1494

3 R90R71.45 0.0692 0.2076

4 R1 090R801.18 0.775 3.1020

Totals 1 033.12 1 3.5396

Duration = 3.5396 years

7.2. Characteristics of duration

Characteristics of duration can be summarised as follows:

Duration increases with maturity

A higher coupon results in a lower duration

Duration is shorter than maturity for all bonds except zero coupon bonds

Duration is equal to maturity for zero coupon bonds

All else equal, duration is shorter at higher interest rates

The duration of a level payment perpetuity is

YTMyy

yDperpetuity

;

1



8. End of Chapter Questions

1. Explain in simple terms, the concept of rising interest rates producing a capital loss in

bonds.

2. In a commentary on the market, a South African Fund Manager says the following:

“The gilt market is firmer today and is 3 points lower at 11.365%.” Explain what he is

saying.

3. Find the duration of a bond with a 6% coupon rate paid annually. If it has three years

to maturity and a yield to maturity of 6%. What is the duration if yield to maturity is

increased to 10%.

Answers

1. A general increase in interest rates will mean that the required return on interest

bearing securities (bonds) will also have to increase in order to remain competitive.

The interest on bonds is known as the coupon and is a predetermined or fixed

percentage of its face value. In order for that coupon to represent a higher percentage,

the actual amount paid for the bond will have to decrease. This results in the inverse

relationship between the price of a bond and its yield. PBα (1/i).

2. The answer to this is described by the inverse relationship between the price of bonds

and their yield. This fall in rates will result in a stronger or firmer gilt price. Three points

lower means that the rate has fallen from 11.395% to 11.365% (100 basis points is 1%

and therefore 3 points is 0.03%).



3. a. Duration: YTM = 6%

(1) (2) (3) (4) (5)

Time until

Payment

(Years)

Payment

Payment

Discounted at

6%

Weight

Column (1)

×

Column (4)

1 60 56.60 0.0566 0.0566

2 60 53.40 0.0534 0.1068

3 1060 890.00 0.8900 2.6700

Column Sum: 1000.00 1.0000 2.8334

Duration = 2.833 years

b. Duration if YTM = 10%

(1) (2) (3) (4) (5)

Time until

Payment

(Years)

Payment

Payment

Discounted at

10%

Weight

Column (1)

×

Column (4)

1 60 54.55 0.0606 0.0606

2 60 49.59 0.0551 0.1101

3 1060 796.39 0.8844 2.6531

Column Sum: 900.53 1.0000 2.8238

Duration = 2.824 years, which is less than the duration at the YTM of 6%



CHAPTER 6

The Cost of Capital



CCoonntteennttss

11.. Introduction

22.. The Importance of calculating Cost of Capital

33.. Elements of the Cost of Capital

44.. The Weighted Average Cost of Capital (WACC)

55.. Calculating the Cost of Equity

66.. Calculating the Cost of Preference Share Capital

77.. Calculating the Cost of Debt

88.. End of Chapter Questions



Objectives


Calculate the cost of equity using the dividend valuation method

Compute the cost of redeemable debt, and convertible securities

Use CAPM to calculate the beta of a company and to estimate the cost of capital toappraise projects.

READINGSReadings

This unit has been designed to be read in conjunction with the following textbooks:

PRESCRIBED:




Chapter 14: Ross, S; Westerfield, RW; Jordan, BD; and Firer C. (2009).

Fundamentals of Corporate Finance, 4th South African Edition, McGraw-Hill.


Chapter 15: Marx, J; de Swardt, C; Beaumont Smith, M; Naicker, B; Erasmus, P.

(2007) Financial Management in Southern Africa, 2nd Edition, Pearson Education.



1. Introduction

What do we mean by the cost of capital?

It represents the total cost of funds raised by a company.

It’s the return that different types of investors are paid to ensure that they place theirfunds within the company and keep their funds in that company.

It’s the minimum return that a company must get on its projects to earn sufficient to paythis expected return to investors.

This means that it is also the opportunity cost because, if investors don’t get therequired return, they will move their funds elsewhere.

2. The Importance of Calculating the Cost of Capital

Benchmarking the firm’s return against similar firms in the industry.

Assessing the value creation potential of new projects as compared to the cost of capital.

It is an important calculation to make as it forms the basis of calculating the value of the

firms

3. The Elements of the Cost of Capital

3.1. The Risk-free Rate of Return

Here we are referring to investments with a risk-free yield, such as government bonds.

3.2. The Premium for Business Risk

This is an addition to the risk-free rate of return to allow for uncertainties connected with

the cash flows of a particular project, or the health of the company as a whole. The

higher the anticipated risk, the higher this additional percentage will be.

3.3. The Premium for Financial Risk

This is an addition that takes into account the gearing of the company: for example, if

this increases, then equity-holders will need a higher return to compensate them for the

increased amounts of interest which must be deducted from operating profit.



Many firms use both equity and borrowed capital. As equity capital carries the greater

risk, investors will require a greater return than lenders of borrowed capital. In addition,

long-term and short-term lenders may expect different rates of return.

4. Weighted Average Cost of Capital (WACC)

Basic Assumptions

1. Dividends on ordinary shares are expected to remain at their current rate during the lives of

the project/s to be appraised.

2. Preference shares and debentures are irredeemable.

The cost of equity capital will, therefore, be based on the current rate of dividend but, as it is

extremely unlikely that equity and debt are in equal proportions, we shall need to calculate a

weighted average

The basic formula for the WACC is:

WACC = [Proportion of Debt X Cost of Debt] + [Proportion of Equity X Cost of Equity]

= [(D/V) X Rd (I – Tc)] + [(E/V) X Re]

5. Weighted average cost of Debt - Rd

When estimating the cost of debt, we have to include the Long Term debt and Short Term debt,

we need to consider the historic (coupon rate) vs future (Yield to Maturity) costs. When looking

at debt (traded as well as untraded) we need to observe the cost of debt, risk ratings (from

credit rating agencies) and use the risk free yield curve (maturity) and add a premium for credit,

and liquidity risk. Lastly we need to consider whether the interest rate is floating or fixed.

Interest expenses are deductible for tax purposes and thus this also needs to be considered

when calculating WACC.

6. Weighted average cost of capital – Return on Equity

When estimating the cost of equity, two options are available:

6.1. The Dividend Growth (DG) Model Approach

• assume a constant growth in dividends

i.

ii.

gP

D

gR

DP

e

0

1e

10

RgivesgRearrangin



6.1.1. Advantages of the Dividend Growth Model

The dividend valuation model is simple to use.

It allows for the fact that future dividends should grow if profits are re invested

and that shareholders are likely to value their shares according to their future

dividends expectations.6.1.2. Disadvantages of the Dividend Growth Model

The DG method also assumes that that the market value of the share is in equilibrium

so that the share price is correct.

although it allows for the fact that future dividends should grow if profits are

reinvested, and that shareholders are likely to value their shares according to their

future dividend expectations, it assumes that all shareholders behave in the same

way – which is improbable

Where no growth in dividends is expected in the future, we used the formula:

Cost of equity Ke = (D1/P0) + g

Our calculation is based on the assumption that the market price of a share will be the

discounted future cash flows of revenues from that share, and on a constant growth rate in

dividends. It is sometimes called the ‘Gordon Growth model’. (DG Model)

So, for example, if we have a company with shares currently valued by the market at R800 000,

but with a nominal value of R500 000, last declared dividend 15% and an expected growth rate

of 5%, we would have for cost of equity:

Current dividend R500 000 x 15% = 75 000

So d1 will be 75,000 x 1.05 = 78,750

Ke = (78,750/800,000) + 0.05 = 0.1484375 or 14.84%

We do not simply relate the 78,750 back to the nominal value of the shares, as we are

trying to find the expected return based on what owners would have to invest now, i.e. the

market value.



Cost of Equity – the dividend valuation model

Self-check Question 1

Makhanya Ltd wishes to calculate its cost of equity, andprovides the following information.

Number of shares: 1,000,000

Nominal value of each share: R2

Market price of each share: R2.80

Last declared dividend: 12%

Expected growth rate: 6%

Calculate the cost of equity using the DG Model

SolutionLet’s calculate the current dividend:Dividend = R2 X 0,12

= R0,24

However we need to calculate the value of D1. Hence, we project this dividend at a growth rateof 6%.D1 = Do x gD1 = 12% x 1.06

= 12.72%

Now let’s calculate the cost of Cost of equityKe = (D1/P0) + gKe = 0.24 + 0,06

2,8

= 15.09

6.2. The Capital Assets Pricing Model (CAPM) Approach

The formula

Re given by: RE = Rf + βE [RM - Rf ]



Represented by:

P0 = the current price of the share

D1 = Dividend in Year 1

g = growth rate

Rf = the risk free rate

β = the risk co-efficient (also known as beta)

RM = the market risk premium

6.2.1. The CAPM shows that the expected return is dependent on three variables:

1. The pure time value of money: this is measured by the risk free rate [Rf]. This is the

reward for merely waiting for your money without taking any risks. The best indicator of

the risk free rate is the yield on government bonds (also referred to as treasury bills).

2. The reward for bearing systematic risk: this is measured by the market risk premium,

which is denoted as follows: E(Rm) – Rf. This component is the reward the market offers

for bearing an average amount of systematic risk in addition to waiting.

3. The amount of systematic risk: as measured by β. This is the amount of systematic risk

that is present in a particular asset, relative to an average asset.

Beta factor: The beta factor is ‘the measure of a share’s volatility in terms of market

risk’. The beta factor of the market as a whole is taken to be 1. This means that:

results for individual shares which are greater than 1 imply a greater degree ofvolatility

Results which are less than 1 imply a lower degree of volatility.

It should then be possible to predict what will happen to the return on a share if thereis a change in the market return.

Using CAPM

In Section 2, we looked at the use of the Capital Asset Pricing Model in assessing a project’s

systematic risk. We did not, however, attempt to calculate . Now we are going to see how ,

once derived, can be used to obtain the cost of a firm’s equity.

Example

Suppose that we have this information about the current market return and the risk-free return:



The market return is 12%, the risk free return is 8%, and the β is 1,4. Then:

Re = Rf + βE [RM - Rf ]

Re = 8% + 1,4[12% - 8%]

Re = 8% + 1,4. 4%

Re = 13,6%

Test your Knowledge

The risk-free rate of return is 10%.

The expected market rate of return is 15%.

The beta factor for Manje Ltd share is 0.9.

Calculate the expected return on Manje Ltd’s shares, i.e. Its costof equity, and the expected rate of return on its shares if themarket return falls to 13%.

How will this differ from using the dividend valuation model? If we assume that prices in the

stock market are in equilibrium, and that a firm’s dividends reflect systematic risk only, then the

two methods produce approximately the same result. However, in practice:

The dividends used in the dividend valuation model may include an allowance for

specific as well as systematic risk.

The current share values used in the model may not in fact be in equilibrium.

The CAPM assumes that there is equilibrium in the stock market, and considers

systematic risk only.

So far, we’ve presumed that we know what the beta factor for a share is. We can in

fact calculate it, although in practice it’s easier to look it up.



6.2.2. Advantages of the CAPM The CAPM allows for variations in share prices and returns as the result of market

risk. Therefore it can indicate whether the share at the moment is higher or lower

than it should be and what it should change to.

6.2.3. Disadvantages of the CAPM

It assumes the stock market is a perfect market with no dealing charges and with all

investors having the same perception of security.

It also assumes that there is a risk- free rate at which all investors may borrow

without limit.

It ignores taxes.

An Example

Suppose La Roja Beperk has the following capital structure (ignore reserves):

Equity: 5 000 000 R1 ordinary shares, market price currently R1,70

Preference Shares: 2 000 000 @ R0.50 yielding 10%, market price currently R0.55

Debentures: R2 000 000, 15% debentures, issued at R1,00, market price currently

R108,00

Bank loan: R1 000 000 12% bank loan

They have paid a dividend of 20c per share last year and they expect dividends to grow by 5%.

The corporate tax is 30%.

Calculate their cost of capital, using the Dividend Growth Model as your basis for valuingequity.

Solution

First, we need to calculate the overall market value of these investments, by multiplying theoriginal values by the market price divided by the nominal value in each case, and totaling.

R

Ordinary Shares: 5 000 000 x 1.7 8 500 000Preference Shares: 1 000 000 x 0.55/0.50 1 100 000Debentures: 2 000 000 x108/100 2,160,000



Bank Loan: 1 000 000 1,000,000Overall market value 12 760 000

Now let’s find the proportion of this total represented by each type of capital:

Equity: 8 500 000/12 760 000 = 0.6661

Preference: 1 100 000/12 760 000 = 0.0862

Debentures: 2 160 000/12 760 000 = 0.1693

Bank loan: 1 000 000/12 760 000 = 0.07841.0000

Let’s calculate the rate of return for each type of capital

Equity = D1 + g

Po

= 0.20 (1 + 0,05) + 0,05 Workings [0,21/1,7 = 0,1235]

1,7

= 17,35%

Preference shares = D/P X 100 (note: dividends at present = 50c X 0,05 = 5C)

= 0,05/0,55 X 100

= 9,1%

Debentures = 15 x 100108 X [1- Tc]

= 13.89% X 0,7

= 9,72%

Loans = [0,12 X (1 – Tc]

= 0,12 X 0,7

= 8,4%



Rate of Return Proportion Unit Cost

Equity: 17,35 X 0,6661 = 11,5568

Preference shares: 9,09 X 0,0862 = 0,7836

Debentures: 9,72 X 0,1693 = 1,6456

Loans 8,40 X 0,0784 = 0,6586

WACC = 14,65%

This would be the minimum rate to apply for investment appraisal, assuming that all projects tobe evaluated bear the same risk, and that finance would be raised in the same proportions ascurrently exist.

Key 1 2 1 x 2 3 4 3 X 4

Equity TypeNominalValue

PresentUnitvalue

Presenttotalvalue Proportion ROI

IndividualCost ofCapital

Ordinary Shares 5 000 000 1.78 500

000 0.6661 17.35 11.5576PreferenceShares 2 000 000 0.55

1 100000 0.0862 9.1 0.7845

Debentures 2 000 000 1.082 160

000 0.1693 9.72 1.6454

Loans 1 000 000 11 000

000 0.0784 8.4 0.6583

Total 10 000 00012 760

000 1 14.6458

NB: The calculation for debentures and the loan interest is multiplied by 70 per cent, ie. [1 – Tc]Debentures and interest on loan are tax deductible and as a result, do not bear tax.

The same cannot be said of dividends, as it is an after tax cost.

In order to equalise the tax effect, the debenture and bank-loan interest weighting is reduced bymultiplying it by 1 minus the given corporate tax rate (30 per cent).



Exercise 1

Tigerbrands Ltd has the following capital structure:Equity 2 000 000 R2 ordinary shares, market price R2,50

Preference 1 000 000 12% R1 preference shares, market price R1,20

Reserves R1 500 000

Bank loan R500 000 15% bank loan

Debentures R1 750 000 16% debentures, market price R110 (issued at R100).

The current and expected future rate of ordinary share dividend is 20%.What is the firm’s weighted average cost of capital?

Solution

Calculate overall market value Market Value Proportion

Ordinary shares 4,000,000 x R2.50/2 = 5,000,000 57.97Preference shares 1,000,000 x 1.20/1 = 1,200,000 13.91Bank loan = 500,000 5.80Debentures 1,750,000 x 110/100 = 1,925,000 22.32Total 8,625,000 100.00

Relevant returns: %

Ordinary shares 20 x 2/2.50 = 16.00Preference shares 12 x 1/1.20 = 10.00Debentures 16 x 100/110 = 14.55

Weighted average cost of capital: %

Ordinary shares 57.97 x 16 = 9.28Preference shares 13.91 x 10 = 1.39Bank loan 5.80 x 15 x 67/100 = 0.58Debentures 22.32 x 14.55 x 67/100 = 2.18

WACC 13.43

6. Cost of Preference Share Capital

Because this is fixed dividend capital, i.e. amounts paid to shareholders will not fluctuate(unless, of course, there are no profits from which to pay the obligation), we can consider the



cost of preference share capital to be similar to the cost of debt capital, ignoring taxation, whichis dealt with below.

Kp = D/P0

D = Dividend. We do not consider a D1, as dividends on preference shares are constant.

P0 = the current value/price of the preference share.

Example

The Brandon group has a target capital strructur of 50% equity, 5% preference shares and 45%

debt. Their cost of equity is 16%, preference shares 7,5% and debt 9%. Their tax rate is 35%.

Calculate:

a. Their WACC

b. Their non executive director has approached you and asked your thoughts on using

preference equity to finance a new project, as she believes that this is cheaper than debt

financing.

Solution

a. Using the equation to calculate the WACC, we find:

WACC = 0,50(0,16) + 0,05(0,075) + 0,45(0,09)(1 – 0,35)

= 0,1101 (11,01%)

b. It must be remembered that interest is tax deductible and dividends are not, hence we mustlook at the:

After-tax cost of debt, which is = 0,09 (1 – 0,35)

= 0,0585 or 5,85%

Hence, on an after-tax basis, debt is clearly cheaper than preference shares whichcost 7,5%%

7. End of Chapter Questions (taken from previous exam papers)

1. Suppose AA Carriers has a beta of 1,3. The return on market is 12% and the risk free rate is

7%. AA's last dividend was R2 per share and they expect a growth rate of 8%. The share is

currently trading at R20.

1.1. Using the CAPM approach, calculate the Return on equity.



1.2. What is their return on equity using the Dividend Growth (DG) Model?

1.3. Discuss 2 advantages of the CAPM approach.

2. Bugsy’s Bag Manufactures (BBM) shares have a beta of 1,32. Market analysts suggest a risk

free rate of 4,5% and a market return of 11 %. BBM paid a dividend of R2,10 per share last year

and expect dividends to grow by 5%. Their shares sell for R28 per share at present (the par

value of their shares isR20). Calculate BBM cost of equity using:

2.1. The Dividend Growth Model

2.2. The Capital Assets Pricing Model.

2.3. Explain briefly the reason for the difference in your answers above.

3. Bassa Braziers Ltd, operate in the fabrication industry. They feel that some of their older gas

welding machines need to be replaced. They seek your help in order to calculate their cost

of capital. Their present capital structure is as follows:

600 000 R2 ordinary shares now trading at R2,40 per share.

200 000 preference shares trading at R2,50 per share (issued at R3 per share). 10 %

p.a. fixed rate of interest.

A bank loan of R1 000 000 at 12 % p.a. (payable in 5 years time)

Additional data

a. The company’s beta is 1,4. A return on market of 15% and a risk free rate of 6 %.

b. Its current tax rate is 28 %.

c. Its current dividend is 50c per share and they expect their dividends to grow by 7 % p.a.

Required

3.1. Assuming that the company uses the CAPM to calculate their cost of equity, calculate their

weighted average cost of capital.

3.2. A further R500 000 is needed to finance the expansion which option should they use (from

ordinary shares, preference shares or loan financing) and why?



CHAPTER 7

DIVIDENDS AND DIVIDEND POLICY



CCoonntteennttss

1. Introduction2. The Clientele Effect3. Dividend Policy: Is it Relevant?4. Types odf Dividends5. Real World Factors affecting a High Dividend Payout6. Practical Issues in respect of the Payment of Dividends7. Signaling8. The Dividend Decision9. The Residual Dividend Approach10. Share Repurchase: An alternative to Cash Dividends11. Share splits and scrip dividends



Objectives


The various types of dividends and how they are paid. Be aware of the practical issues behind dividend decisions How dividend policies work in practice. Why share repurchases is an alternative form of dividend. understand the theory of dividend irrelevancy Discuss the dividend payment process and the various dividend options

available to the company. The difference between cash and scrip dividends.

READINGSChapter 17: Fundamentals of Corporate Finance 4th South African Edition, Ross S,

Westerfield RW, Jordan BD and Firer C, 2008




Chapter 18: Marx, J; de Swardt, C; Beaumont Smith, M; Naicker, B; Erasmus, P. (2007)

Financial Management in Southern Africa, 2nd Edition, Pearson Education.



1. Introduction

A company’s dividend policy is the approach they adopt towards dividend payments. Key

questions start to emerge, like:

a. Will they pay their shareholders a dividend, or not?

b. How large will it be?

c. How often will they make payments? (Els 2010: 366))

Dividends are non-contractual payments to shareholders as compensation for their investment.

Profit after tax (and minority interests, if any) will either be distributed as cash dividends or

retained and reinvested in the firm. The traditional view of dividends is that the level will affect

share prices, although no clear relationship has been found in various research studies.

It’s not always the case that firms would want to declare as high a dividend as possible. The key

questions are:

Should the firm pay out money to its shareholders? or

Keep the money and invest it for the shareholders?An assumption underlying much of the academic finance literature is that managers make

decisions that lead to maximizing the wealth of their firm’s shareholders as reflected in ordinary

share prices.

Most economists would answer: managers have a criterion for evaluating performance and

deciding between alternative courses of action, and that the criterion should be maximization of

the long-term market value of the firm. . . . This Value Maximization proposition has its roots in

200 years of research in economics and finance.

The decisions of corporate financial managers fall into two broad categories:

1. Investment decisions: Investment decisions involve determining the type and amount

of assets that the firm wants to hold.

2. Financing decisions concern the acquisition of funds in the form of both debt and

equity to support a firm’s operating and investment activities.

Dividend decisions, as determined by a firm’s dividend policy, are a type of financing decision

that affects the amount of earnings that a firm distributes to shareholders versus the amount it

retains and reinvests. Dividend policy refers to the payout policy that a firm follows in

determining the size and pattern of cash distributions to shareholders over time. The board, with



the input of senior management, sets a corporation’s dividend policy. Under real-world

conditions, determining an appropriate payout policy often involves a difficult choice because of

the need to balance many potentially conflicting forces.

Conventional wisdom suggests that paying dividends affects both shareholder wealth and the

firm’s ability to retain earnings to exploit growth opportunities because investment, financing,

and dividend decisions are interrelated.

For example, if a firm decides to increase the amount of dividends paid, it retains fewer funds

for investment purposes, which may force the company into the capital markets to raise funds.

In practice, managers carefully consider the choice of dividend policy because they believe such

decisions affect firm value and hence shareholder wealth.

Investors view dividend policy as important because they supply cash to firms with the

expectation of eventually receiving cash in return. Thus, managers act as though their firm’s

dividend policy is relevant despite the controversial arguments set forth by Miller and Modigliani

(1961) that dividends are irrelevant in determining the value of the firm.

Others are less sanguine about how dividends affect the value of a firm’s shares. In their

pioneering study, Miller and Modigliani (1961) (hereafter MM) provide an elegant analysis of the

relationships among dividend policy, growth, and the valuation of shares. On the basis of a well-

defined but simplified set of perfect capital market assumptions (e.g., no taxes, transaction and

agency costs, and information freely available to everyone), MM set forth a dividend irrelevance

theorem. In their idealized world, investment policy is the sole determinant of firm value.

Therefore, if managers focus on making prudent investment choices, payout policy and capital

structure should take care of themselves. MM’s irrelevance message suggests that payout

policy is an economically trivial issue that managers can largely ignore if they make sensible

investment decisions. Early studies by Black and Scholes (1974), Miller (1986), and Miller and

Scholes (1978, 1982) support the dividend irrelevance argument.

As De Angelo and De Angelo (2007) point out, MM’s dividend irrelevance principle rests on an

unstated assumption that forces firms to choose among payout policies that distribute 100

percent of the free cash flow generated each period by investment policy. In addition,



shareholders are indifferent to receiving a given amount of cash as a dividend or through stock

repurchases.

Thus, MM’s theory leads to the contentious conclusion that all feasible payout policies are

equally valuable to investors. Yet De Angelo and De Angelo contend that the set of possible

payout policies is not as limited as MM assumes and that payout policy matters. Bernstein

(1992: 176) notes, however, that the “MM theory was admittedly an abstraction when it was

originally presented,” and “no one—least of all Modigliani and Miller—would claim that the real

world looks like this.” Although examining dividend policy in perfect capital markets can provide

useful insights about the conditions under which dividends may affect stock prices, the dividend

irrelevance theorem can also be misleading. Bernstein (1992: 180) notes, “The final test of any

theory is how accurately it portrays the real world, blemishes and all.”

Black (1976; 05) assesses the contributions of dividend researchers post-MM and concludes,

“The harder we look at the dividend picture, the more it seems like a puzzle, with pieces that just

don’t fit together.” Feldstein and Green (1983, p. 17) echo Black’s sentiments, stating, “The

nearly universal policy of paying substantial dividends is the primary puzzle in the economics of

corporate finance.”

2. The Clientele EffectIt is important to remember that not all investor have the same or similar needs. Some investors

may prefer a cash dividend, others would prefer to have their funds reinvested so that the

company can grow and thus the share price grows. (Els 2010; 369). Investors such as retirees

would prefer a cash dividend as their need for cash is far greater than an employed person.

Dividends and capital gains are taxed at different rates and at different times and these have a

further effect on investor preferences.

The clientele effect implies that an investor in need of current income will invest in a company

that has a high payout ratio. Whereas an investor not interested in current income will prefer

shares in a company with low dividend payouts, but with high capital growth potential (Els 2010:

369). When a company’s dividend policy changes, investors may adjust their shareholdings

accordingly and this may influence the share price.



3. Dividend Policy: Is it Relevant?Consider a firm that can pay out dividends of R10 000 per year for each of the next two years or

can pay R9 000 this year, reinvest the other R1 000 into the firm and then pay R11 120 next

year. Investors require a 12% return.

If the company will earn the required return, then it doesn’t matter when it pays the dividends.

Assuming that the second dividend is a liquidating dividend and the firm ceases to exist after

period 2, then:

Market Value with constant dividendPV = 10 000 / 1.12 + 10 000 / 1.122

= 16 900.51

Market Value with reinvestmentPV = 9 000 / 1.12 + 11,120 / 1.122

= 16 900.51

Explanation

Recall the dividend growth model: P0 = D1 / (RE – g). In the absence of market imperfections,

such as taxes, transaction costs and information asymmetry, it can be shown that an increase in

the future dividend, D1, will reduce earnings retention and reinvestment. This will reduce the

growth rate, g. Therefore, both the numerator and the denominator increase and the net effect

on P0 is zero.

3.1. There are 4 reasons as to why Dividend Policy should be regarded as relevant:

a. “A bird in the hand is worth two in the bush” If a dividend is declared, you are quite certain of

receiving it. This is not necessarily so for a capital gain.

b. The signaling process: this is when the dividend announcement is used to communicate

information to the shareholders about the company.

c. The tax preference explanation. In South Africa, dividends and capital gains are subject to

capital gains tax (CGT). Because capital gains tax is delayed until the shares are sold,

investors may prefer capital gains to dividends.

d. The agency explanation: This theory states that if funds are retained in the company, it may

not always be used optimally. Paying larger dividends thus reduces the the internal cash

flow subject to management discretion.



Terminology

Dividend: This is a payment made out of a firm’s profits to its owners (called shareholders).

This may take the form of a cash payment or further shares.

4. Different Types of Dividends:

4.1. A regular cash dividend: This takes place once or twice a year. Once in mid year if

earnings are already healthy. This is called an interim dividend. And one at year end. This

is called a final dividend.

4.2. Special Dividend: occurs as a result of an unusual event, perhaps the sale of a part of

the business.

4.3. Liquidating Dividend: usually declared when the business is sold off.

4.4. Homemade Dividends: is the selling of shares in the appropriate proportion to create an

equivalent cash flow to receiving the dividend stream you want. If you receive dividends

that you don’t want, you can purchase additional shares and likewise, if you don’t receive

dividends you need, then you sell off a portion of that investment to compensate for the

shortfall in dividends not received. So if an investor expected a dividend of R200 in period

1 and R190 in period 2, but only receive R170 in period 1, then the investor will sell shares

to the value of R30 to compensate for this loss in dividend. In the same way if an investor

received more that he expected in period 1, then he may use the additional sum of

dividends to buy more shares in the company in order to compensate for a possible loss

of dividend in the next period.

These examples indicate that even if shareholders are not happy with the dividend policy of a

company, they can create their own “homemade dividends”. It must be noted that homemade

dividends do not take costs and taxes into account. If they did, the scenario can be entirely

different.

Dividend reinvestment plans (DRIPS) allow investors to reinvest dividend income back into the

issuing company without paying commissions. Many plans also allow shareholders to buy

additional shares directly from the company, often on a set schedule. This again avoids

commissions, although in some cases you pay a small service fee. You are still liable for any

taxes owed on the dividend payments.

5. Real-World Factors Favouring a Low Dividend Payout



5.1. TaxesInvestors that are in high marginal tax brackets might prefer lower dividend payouts. If the firm

reinvests the capital back into positive NPV investments, then this should lead to an increase in

the stock price. The investor can then sell the stock when she chooses and pay capital gains

taxes at that time. Taxes must be paid on dividends immediately, and even though qualified

dividends are currently taxed at the same rate as capital gains, the effective tax rate is higher

because of the timing issue.

However with STC (Secondary Tax on Companies) now being phased out and converted into a

new dividends tax, whereby 10% (the current rate) is held from the amount declared to

shareholders. This amount is then paid by the company. Thus if dividends of R100 000 is

declared, then only R90 000 is paid out to the shareholders. CGT is also charged at 10% of the

capital appreciation amount. (Els 2010; 374)

5.2. Flotation CostsIf a firm has a high dividend payout, then it will be using its cash to pay dividends instead of

investing in positive NPV projects. If the firm has positive NPV projects available, it will need to

go to the capital market to raise money for the projects. There are fees and other costs (flotation

costs) associated with issuing new securities. If the company had paid a lower dividend and

used the cash on hand for projects, it could have avoided at least some of the flotation costs.

5.3. Desire for Current IncomeIndividuals that want current income, i.e., retirees, can either invest in companies that have high

dividend payouts or they can sell shares of stock. An advantage to dividends is that you don’t

have to pay commission. Trust funds and endowments may prefer current income because

they may be restricted from selling stock to meet expenses if it will reduce the fund below the

initial principal amount.

A fascinating real-world example of the desire for increased dividend payout can be found in

Kirk Kerkorian’s battle with the management at Chrysler. In late 1994, Mr. Kerkorian demanded

that Chrysler use its cash hoard (about $6.6 billion at the time) to increase the cash dividend on

common stock and to institute a stock repurchase program. The management of Chrysler

contended that, in the interest of prudent management, they were amassing cash with which to

ride out the next cyclical downturn. Unhappy with Chrysler’s response, Mr. Kerkorian offered

$55 per share (nearly $23 billion total) to take over Chrysler. This bid ultimately failed, but



Chrysler’s management did raise the dividend. Incidentally, Ford and GM subsequently found it

necessary to publicly defend their large cash positions in the period after the Chrysler takeover

bid.

5.4. Tax and Other Benefits from High DividendsCorporate investors –at least 70% of dividends received from other corporations does not have

to be included in taxable income

Tax-exempt investors – tax-exempt investors do not care about the differential tax treatment

between dividends and capital gains. And, in many cases, tax-exempt institutions have a

fiduciary responsibility to invest money prudently. The courts have found that it is not prudent to

invest in firms without an established dividend policy

6. Practical Issues in respect of the Payment of Dividends

Let’s start by looking at actual restrictions on payment of dividends.

• While dividends can be paid from past and present earnings, they cannot be paid from any

capital reserve.

So, if any funds have been transferred from income statements, or another revenue reserve,

into a capital reserve, such as a capital redemption reserve, then this reserve is not available for

payment of cash dividends.

This rule also covers funds which have been entered directly into a capital reserve, and have

never come from the income statement, such as share premium and revaluation reserves. As

we have already seen, such reserves may be used for the issue of bonus shares, which may be

considered to take the place of cash dividends in a particular year.

• Companies that are insolvent cannot legally pay dividends; that is, if their external liabilities

exceed their assets.

Now we’ll look at some practical restrictions.

• A company with high profits but poor liquidity may be unable to pay cash dividends – it’s no

use expecting the bank to increase overdraft facilities just so that a company can try to

impress its shareholders.

• A company with a loan requiring redemption may need to retain funds for this purpose.



• Companies with various kinds of debt capital may in fact have agreed to restrictions on

dividend payments to protect long-term creditors.

• If a company is expanding quickly, it will need to retain funds to finance new fixed assets

and working capital.

Companies that do not have wildly fluctuating profits are more likely to pay out a higher

percentage of earnings than companies with more volatile profits.

Listed companies with a good profit record are better able to raise additional capital when

they need to – other companies will need to retain more of their own earnings to finance

operations. Also, remember that issuing new shares or debentures involves issue costs,

which obviously do not apply to using retained earnings.

• If companies sell additional equity, control by existing shareholders is diluted (control may

even change hands), whereas if additional debt is sold, there is a greater risk of fluctuating

earnings for these shareholders (remember that, the higher the gearing, the better ordinary

shareholders do in good years, but in poor years they will probably receive a very low

return). To prevent this, a company may choose to retain more of its earnings rather than

distribute them in cash dividends.

• Shareholders do not all pay the same marginal tax rate – if a company believes that its

shareholders are higher-rate taxpayers, they may believe that capital gain from rising share

prices (which is only taxable when the shares are actually sold) is preferable to a high cash

dividend on which tax is assessable now. The reverse would obviously apply if a company

believes it has only standard-rate taxpaying shareholders.

Important Dividend Dates: An Example



1. Declaration date: the board of directors declares the payment of a dividend

2. Last day to trade: last day to qualify for the dividend

3. Ex-dividend date: next working day after the last day to trade – The shareholder registered

on this day is no longer entitled to receive the dividend

4. Record date: This is the date on which the shareholder register is accessed to determinewho will receive a dividend.

5. Payment date: the dividends are actually paid to shareholders

If we consider taxation, we should note that its impact is caused not only by the rates of tax on

income and capital gains, but the type of tax system in force in a particular country. Taxes on

income tend to be higher than those on capital gains, and, of course, in most countries capital

gains are only taxable when realised. Tax systems can involve the payment of tax by the

company and the shareholder on the same amount of money (the dividend) – this is double

taxation and happens in countries using the classical system.

7. Signaling

Is it possible that when a dividend is announced, particularly if there is a significant rise in its

level, that the firm is trying to signal its confidence in its future? If so, and if the stock market

reacts favourably to this ‘information’, there is an implication that some information available to

the management of the company is not already incorporated in the share price, i.e. the stock

market is not ‘strong form’ efficient.

It is noticeable that, in a hostile takeover bid, the target company often announces a higher

dividend level in its efforts to prevent its shareholders from accepting an offer from a predator.

What happens when firms change dividends?

Share prices decline on div cuts because future dividends are expected to be lower, not

because of a change in pay-out ratio. Share price increases on increased dividends because

market reacts to managements signal about the future

Researchers have found evidence that the stock market takes notice of dividend

announcements as information on which to base the level of share prices.



8. The Dividend Decision1. Firms have longer term target dividend payout ratios.

2. Managers focus more on dividend changes than on absolute levels.

3. Dividends changes follow shifts in long-run, sustainable levels of earnings rather than short-

run changes in earnings.

4. Managers are reluctant to make dividend changes that might have to be reversed. Thus they

prefer to select sustainable levels of dividends.

9. Residual Dividend Approach

The term residual dividend refers to a method of calculating dividends. A dividend is a

payment made by a company to its shareholders. It is essentially a portion of the company's

profits that is divided amongst the people who own shares in the company. A residual

dividend policy is one where a company uses residual or leftover equity to fund dividend

payments. This is done after funding is set aside for projects that they wish to engage in.

Typically, this method of dividend payment creates volatility in the dividend payments that

may be undesirable for some investors.

9.1. Procedure to calculate residual dividend

1. Determine the amount of funds available without having to sell new equity or raiseloans.

2. Decide whether or not a dividend will be paid.

3. If funds needed are less than the generated, then a dividend will be paid.



Illustrative Example

Du Pont Ltd follows a strict residual dividend policy. Their debt equity ratio is 3. (3:1)

a. If their profits are R180 000 for the current year, what is the maximum amount of capitalspending possible with no new equity?

b. If planned investment outlays for the current year are R760 000, will du Pont be able topay a dividend? If so, how much?

c. Does Du Pont maintain a constant dividend payout? Explain.

Solutiona. Since the company has a debt-equity ratio of 3, they can raise R3 in debt for every R1

of equity. The maximum capital outlay with no outside equity financing is:

Maximum capital outlay = R180 000 + 3(R180 000) = R720 000.

b. If planned capital spending is R760 000, then no dividend will be paid and new equitywill be issued since this exceeds the amount calculated in a.

c. No, they do not maintain a constant dividend payout because, with the strict residualpolicy, the dividend will depend on the investment opportunities and earnings. Asthese two things vary, the dividend payout will also vary.

10. Stock Repurchase: An Alternative to Cash DividendsA stock repurchase occurs when a company buys back its own shares. They may do this via:

1. A Tender offer – where the company states a purchase price and the desired number of

shares it wishes to acquire

2. An Open market transaction – where the company buys stock in the open market

A stock repurchase is also similar to a cash dividend in that it returns cash from the firm to the

stockholders. This is another argument for dividend policy irrelevance in the absence of taxes or

other imperfections



If we assume no market imperfections, then stockholder wealth is unaffected by the choice

between share repurchases and cash dividends.

10.1. Real-World Considerations in a RepurchaseStock repurchases send a positive signal that management believes the current price is low.

Tender offers send a more positive signal than open market repurchases because the company

is stating a specific price. The stock price often increases when repurchases are announced.

Stock repurchase allows investors to decide if they want the current cash flow and associated

tax consequences. Given our tax structure, repurchases may be more desirable due to the

options provided stockholders

One of the most important market imperfections related to cash dividends versus share

repurchases is the differential tax treatment of dividends versus capital gains. When a company

does a share repurchase, the investor can choose whether to sell their shares and take the

capital gain (loss) and the associated tax consequences. When a company pays dividends, the

investor does not have a choice and taxes must be paid immediately.

Although share repurchases have traditionally been viewed as positive signals from

management, not everyone agrees. An article in the November 17, 1997 issue of Forbes

magazine suggests that some buybacks are ill-advised.

“In the early 1980s, IBM began a big buyback program. Between 1985 and 1990 it bought back

nearly 50 million shares, shrinking its common capitalization by 8%. The buybacks ended with

the collapse of IBM‟s stock in 1991. Before the declinewas over, IBM was down 75% from its

high. Why, at a time of huge expansion in the computer industry, didn’t IBM have better uses for

its cash?”

A quick search of stock repurchase announcements following the terrorist attacks on September

11 found at least nine companies that specifically cited a desire to support American financial

markets and confidence in the long-term prospects of the economy and the company as

reasons for the repurchase. Some of these companies were Cisco, E-Trade, and Pfizer. At least

fourteen other major companies made repurchase announcements in the week that followed the

attacks. These announcements were for new or continuing repurchases without specifically

mentioning the attacks or support for the markets. These companies include Intel, Federal

Express, and PeopleSoft.



It should be pointed out that distributing cash via share repurchases is desirable from the

viewpoint of the investor even in the absence of a capital gains tax differential. Essentially, a

repurchase allows the investor to choose whether to take cash now (and incur taxes) or hold on

to the stock and benefit from the (unrealized) capital gain. Additionally, empirical evidence

indicates that repurchase announcements are often viewed by market participants as favourable

signals of future firm prospects and/or as evidence that management believes that shares are

undervalued.



Share Repurchase and EPSWhile EPS rises with a repurchase (there are fewer shares and presumably net income doesn’t

decrease), the market value of those earnings is the same as with a cash dividend.

An Example

Spoedig Handelaars is a logistics company based in Polokwane, South Africa. They are

currently deciding whether to pay out R120 000 in excess cash in the form of an extra dividend

or implement a share buyback/repurchase. Their profits for the current year are R1,95 per

share and the share sells for R18. Their summarised balance sheet prior to the dividend

payment is as follows (All figures ZAR)

Equity 800 000

Debt 200 000

Tangible assets 600 000

Inventories 5 000

Receivables 275 000

Bank/cash 120 000

Evaluate each alternative by:

1.1. Calculating the number of shares in issue.

1.2. The dividends per share (for the first alternative, i.e. pay the dividend)

1.3. Calculate: the new share price, the EPS and the price-earnings ratio

1.4. What alternative do you consider to be the best? Why?

11. Scrip Dividends:A scrip dividend is a dividend that is not paid out in cash. Shareholders are given additional

shares in lieu of their shareholding. Since there are more shares in issue, each is worth less.

There are no cash flow implications. What actually occurs is that funds are transferred from the

distributable reserves account to the share capital. It is in effect a mini rights issue with

substantially reduced costs.



Illustrative ExampleThe owner’s equity accounts for SKR International are shown below:

Ordinary shares (par value R1) R 10 000

Share premium R180 000

Retained income R586 500

Shareholder’s equity R776 500

a. If SKR shares sell currently for R25 per share and a 10% scrip dividend is declared, how

many new shares will be distributed?

b. Show the effect on the equity accounts.

c. If SKR declared a 25% scrip dividend, how would the accounts change?

Solution

a. Shares in hands of shareholders at present is 10 000.

New shares will amount to 1 000 (10 000 X10%)

Since the par value of the new shares is R1, the share premium per share is R24. The

total share premium is therefore:

Share premium on new shares = 1 000 X R24 = R24 000

b. Shareholders’ equityOrdinary share (R1 par value) 12 500

Share premium 240 000

Retained profits 524 000

R776 500

c. The shares outstanding increases by 25 per cent, so:

New shares outstanding = 10 000(1,25) = 12 500

New shares issued = 2 500

Since the par value of the new shares is R1, the share premium per share is R24. The

total share premium is therefore:

Share premium on new shares = 2 500(R24) = R60 000



Ordinary share (R1 par value) R 12 500

Share premium 240 000

Retained profits 524 000

R776 500

Question 1

Consider four different shares, all of which have a required return of 15 percent and a most recent

dividend of R4,50 per share. Shares W, X, and Y are expected to maintain constant growth rates in

dividends for the foreseeable future of 10 percent, 0 percent and -5 percent per year, respectively.

Share Z is a growth share that will increase its dividend by 20 percent for the next two years, and

then maintain a constant 12 percent growth rate thereafter.

1.1. What is the dividend yield for each of these four shares?

1.2. What is the expected capital gains yield?

1.3. Discuss the relationship among the various returns that you have calculated for each

of these shares

SolutionNOTEWe are asked to find the dividend yield and capital gains yield for each of the shares. All of the

shares have a 15 per cent required return, which is the sum of the dividend yield and the capital

gains yield. To find the components of the total return, we need to find the share price for each

share. Using this share price and the dividend, we can calculate the dividend yield. The capital

gains yield for the share will be the total return (required return) minus the dividend yield.

W: P0 = D0(1 + g) / (R – g) = R4,50(1,10)/(0,15 – 0,10) = R99,00

Dividend yield = D1/P0 = 4,50(1,10)/99,00 = 5%

Capital gains yield = 0,15 – 0,05 = 10%

X: P0 = D0(1 + g) / (R – g) = R4,50/(0,15 – 0) = R30,00

Dividend yield = D1/P0 = 4,50/30,00 = 15%



Capital gains yield = 0,15 – 0,15 = 0%

Y: P0 = D0(1 + g) / (R – g) = R4,50(1 – 0,05)/(0,15 + 0,05) = R21,38

Dividend yield = D1/P0 = 4,50(0,95)/21,38 = 20%

Capital gains yield = 0,15 – 0,20 = – 5%

Z: P2 = D2(1 + g) / (R – g) = D0(1 + g1)2(1 + g2)/(R – g) = R4,50(1,20)2(1,12)/(0,15 – 0,12)

= R241,92

P0 = R4,50 (1,20) / (1,15) + R4,50 (1,20)2 / (1,15)2 + R241,92 / (1,15)2 = R192,52

Dividend yield = D1/P0 = R4,50(1,20)/R192,52 = 2,8%

Capital gains yield = 0,15 – 0,028 = 12,2%

In all cases, the required return is 15%, but the return is distributed differently between

current income and capital gains. High growth shares have an appreciable capital gains

component but a relatively small current income yield; conversely, mature, negative-growth

shares provide a high current income but also price depreciation over time.

Question 2

Bujumbura Inc has declared a 12% scrip dividend.

The market value of its shares is R20 per share. Its Equity Accounts are as follows:

Ordinary share capital (R1 per share) 350 000

Share Premium 1 650 000

Retained Profits 3 000 000

Ordinary Shareholders’ equity 5 000 000

Show the effect on the equity section that the scrip dividend will have. (Show your

workings)



Solution

With a share dividend, the shares outstanding will increase by one plus the dividend amount,

so: New shares outstanding = 350 000(1,12) = 392 000

The share premium is the capital paid in excess of par value, which is R1, so:

Share premium for new shares = 42 000(R19) = R798 000

The new share premium will be the old share premium plus the additional share premium for

the new shares, so:

Share premium = R1 650 000 + 798 000 = R2 448 000

The new equity portion of the balance sheet:

Ordinary share(R1 par value) R 392 000

Share premium 2 448 000

Retained profits 2 160 000

R5 000 000

11. End of Chapter QuestionsCorleone Collieries is deciding whether to pay out R60 000 in excess cash in the form of an

extra dividend or a share repurchase. Current profits are R3,00 per share and the share sells for

R30. Their abbreviated balance sheet before paying out the dividend is:

Equity 240 000 Bank/cash 60 000

Debt 60 000 other assets 240 000

300 000 300 000Evaluate each alternative (i.e.: pay the dividend or repurchase the shares) by:

1.1. Calculating the number of shares in issue.

1.2. The dividends per share (for the first alternative, i.e. pay the dividend)

1.3. Calculate:

1.3.1. The new share price.

1.3.2. The EPS

1.3.3. The price-earnings ratio



Question 2

2.1 Distinguish between a residual dividend policy and a stable dividend policy.

2.2 Mphela Manufacturing is unsure as to whether to pay out R50 000 in excess cash in the

form of an extra dividend or a share repurchase. Current profits are R 2,25 per share and each

share sells for R 20.

Their abbreviated balance sheet before paying out the R50 000 dividends is:

Equity 250 000

Debt 50 000

Total Capital 300 000

Cash 50 000

Other Assets 250 000

Evaluate the two alternatives in terms of the effect on the price per share, earnings per share

and Price Earnings Ratio

Question 3

The Equity accounts of Blydskap Ltd are shown below:

Ordinary Share Capital (R2 par value) R200 000

Share Premium 80 000

Retained Profits 100 000

Total Shareholders’ Equity 380 000

3.1. If Blydskap’s shares sell for R10 per share, and a 10% scrip dividend is declared, how

many new shares will be distributed?

3.2. Redraft the Equity accounts section of the balance sheet.

3.3. Has this been a wise decision? Explain.

3.4. Tygerberg Ltd has declared an annual dividend of 90c per share. Their after tax profits for

the year was R60 000 and they have 12 000 share in issue.

3.4.1. Calculate profit per share.

3.4.2. What is their payout ratio?



CHAPTER 8

_______________________________

WORKING CAPITAL MANAGEMENT



CCOONNTTEENNTTSS

1. Introduction

2. Annual Reports

3. Objective of Financial Statement Analysis


5. Approaches to Financial Statement Analysis

6. Application of Ratio Analysis

7. Du Pont Analysis



Learning Outcomes

After working through this section you should be able to

Outline the various reports used to communicate financial information to

shareholders and other stakeholders.

Define what is meant by the interpretation of accounts.

Identify the parties who use financial analysis.

Calculate and interpret commonly used financial ratios.

Evaluate the results of the ratio analysis and make recommendations for future

action.

Identify the limitations of using accounting data to perform financial analysis.

Outline the various approaches to financial statement analysis and to identify when

each approach is appropriate.

Use Du Pont analysis for interpreting the financial results of a company.

And outline the limitations of ratio analysis.



READINGS

PRESCRIBED:

Chapter 19 Fundamentals of Corporate Finance , 4th South African Edition, Ross, S;

Westerfield, RW; Jordan, BD; and Firer C, 2009.

Chapter 11: Financial Management, 6th Edition, Juta Publishing, 2000 Correia, C; Flynn,

D; Uliana, E and Wormald, M

Chapter 14: Corporate Finance, A South African Perspective, Oxford University Press,

2010 Els, G; Du Toit, E; Erasmus, P; Kotze, L; Ngwenya, S; Thomas, K; Viviers, S.

Chapter 9: Financial Management in Southern Africa, 2nd Edition, Pearson Education,

2007,



1. Introduction

Working capital management incorporates a range of items that needs to be managed in

order to ensure the smooth everyday operations of the firm. In an entity like Vodafone,

these items may include:

Inventory: This may include handsets (phones) which will be handed to contracted

customers, modems, routers, laptops, etc. this used to be referred to as stock in

trade in years gone by and is integral to the growth and development of any

institution.

Receivables: These are the debtors of the business. They may be internet and

contract customers, tenants, etc. if they are not managed optimally, the business will

experience cash flow problems that may eventually lead to bankruptcy.

Cash: This will include cash in the current account, investment accounts, petty cash

and cash float. Cash is really the lifeblood of any institution. Weak cash inflows can

stymie the growth of any business.

Payables: this will include suppliers from whom Vodafone relies on for materials,

supplies, banks, etc. if creditors terms are not adhered to regularly, they may

eventually alter their credit terms, thus placing a strain on the firm’s finances. (Els;

393)

It goes without saying that working capital must be managed according to the

business’ individual needs. However, the basic principles of working capital

management apply to all businesses, irrespective of their size or stage of

development. If net working capital is positive in value, it means that the firm is able

to pay its current liabilities as they become due.

Low working capital means that the business is going to battle to pay back its

current liabilities. Further, too high levels of working capital may mean that the

business has too much cash tied up in debtors and inventory.



2. The Working Capital Cycle

A typical cycle in a manufacturing firm will be similar to the following:

The business orders and then receives the raw materials that are required for

their production processes.

It follows that this transaction will reduce their cash balances or incur debt in the

form of accounts payable.

Labour will then be used to turn the raw materials into finished goods. The cash

will then be reduced further.

The finished goods will then be sold. This may either be a cash sale or a credit

sale. A credit sale will increase the accounts receivable and a cash sale will

increase their cash balance.

The creditors account by this time will fall due and must then be settled. The

cash balance may then be depleted and if this is indeed the case, then an

overdraft may need to be negotiated.

Eventually, the cycle is completed when the monies are received from the

debtor/s and the cycle thus continues in much the same way. (Correia: 11-2)

Some ratios worth noting here are:

1. Raw material Inventory Days: Raw material Inventory X 365

Purchases

This answer tells us the number of days for which the business has materials on handfor the manufacturing process.

2. Work-in-process Inventory Days: Work in Process Inventory X 365

Purchases

3. Finished Goods Inventory Days: Finished goods Inventory X 365

Cost of Sales

This ratio highlights the period for which the business has sufficient stock for resalepurposes.



Management’s ultimate goal must be to shorten the working capital cycle by as much as

possible without affecting the efficient running of the business. The cycle can be

shortened by reducing material processing time. Offering lucrative discounts to debtors to

settle their accounts before due date. And paying creditors as per credit agreement to

secure cash discounts or avoid interest charges.

3. Sales Forecasting

The following factors must be considered when forecasting sales:

a. The availability of historical data. This is used to predict future sales. Notice that in

many restaurants, their service is much faster and efficient during peak periods. This

is so because they take cognizance of their sales and what are the fast moving items

during the peak periods (which may be Friday and Saturday lunch and dinner time).

They may start the cooking processes for spare ribs and steaks well before peak time

arrives and may just need a few minutes to finish off a meal that may take more than

45 minutes to prepare.

b. Economic indicators: they give some sort of idea of the state of the economy.

These indicators may be interest rates, GDP, inflation rates and exchange rates.

c. Competitors activities: Apple’s IPad revolutionized the tablet PC industry and forced

key competitors to review their product offering/s. the same may be said of the

television monitor industry that moved from analogue to digital over a 20 year operiod

but from plasma to LCD to LED to 3D in less than 5 years, such is the rapid pace of

change.

d. Supplier activities: businesses can only be as efficient as their suppliers. For this

reason businesses strive to have as many suppliers as they possibly can get on their

data base, this to improve supplier service delivery and have alternate sources

available in case of non performance by supplier.

e. Government Regulations: tariffs, duties and other protective elements must also be

considered.

f. Plant Capacity: is an overriding factor when forecasting. Is the plant capable of

running 2 shifts or even 3 shifts when necessary?



g. Market Surveys: give management an idea about customer tastes and preferences.

h. Promotional Campaigns: are designed purely to create awareness of the product

offerings in the consumer domain. (Correia: 11-11)

4. What is Inventory Management?

Inventory management is the process of efficiently overseeing the constant flow of units into and

out of an existing inventory. This process usually involves controlling the transfer in of units in

order to prevent the inventory from becoming too high, or dwindling to levels that could put the

operation of the company into jeopardy. Competent inventory management also seeks to

control the costs associated with the inventory, both from the perspective of the total value of

the goods included and the tax burden generated by the cumulative value of the inventory.

Balancing the tasks of inventory management means paying attention to three key aspects:

a. The first aspect has to do with time. In terms of materials acquired for inclusion in the

total inventory, this means understanding how long it takes for a supplier to process an

order and execute a delivery. Inventory management also demands that a solid

understanding of how long it will take for those materials to transfer out of the inventory

be established. Knowing these two important lead times makes it possible to know when

to place an order and how many units must be ordered to keep production running

smoothly.

Calculating what is known as buffer stock is also key to effective inventory management.

Essentially, buffer stock is additional units above and beyond the minimum number required to

maintain production levels. For example, the manager may determine that it would be a good

idea to keep one or two extra units of a given machine part on hand, just in case an emergency

situation arises or one of the units proves to be defective once installed. Creating this cushion or

buffer helps to minimize the chance for production to be interrupted due to a lack of essential

parts in the operation supply inventory.

b. Inventory management is not limited to documenting the delivery of raw materials and

the movement of those materials into operational process. The movement of those

materials as they go through the various stages of the operation is also important.



Typically known as a goods or work in progress inventory, tracking materials as they are

used to create finished goods also helps to identify the need to adjust ordering amounts

before the raw materials inventory gets dangerously low or is inflated to an unfavourable

level.

c. Finally, inventory management has to do with keeping accurate records of finishedgoods that are ready for shipment. Accurately maintaining figures on the finished goods

inventory makes it possible to quickly convey information to sales personnel as to what

is available and ready for shipment at any given time.

5. Successful Inventory ManagementSuccessful inventory management involves balancing the costs of inventory with the benefits of

inventory. Many small business owners fail to appreciate fully the true costs of carrying

inventory, which include not only direct costs of storage, insurance and taxes, but also the cost

of money tied up in inventory. This fine line between keeping too much inventory and not

enough is not the manager's only concern. Others include:

a. Maintaining a wide assortment of stock but not spreading the rapidly moving ones too

thin as this will result in costly stock outs.

b. Increasing inventory turnover, but not sacrificing the service level.

c. Keeping stock low, but not sacrificing service or performance.

d. Obtaining lower prices by making volume purchases, but also ensuring that the business

does not end up with slow-moving inventory.

e. Having adequate inventory on hand, and at the same time ensuring that the business

does not getting caught with obsolete items.

6. Inventory Control TechniquesTo maintain an in-stock position of wanted items and to dispose of unwanted items, it is

necessary to establish adequate controls over inventory on order and inventory in stock. There

are several proven methods for inventory control. They are listed below, from simplest to most

complex.



a. Visual control enables the manager to examine the inventory visually to determine if

additional inventory is required. In very small businesses where this method is used,

records may not be needed at all or only for slow moving or expensive items.

b. Tickler control enables the manager to physically count a small portion of the inventory

each day so that each segment of the inventory is counted every so many days on a

regular basis.

c. Click sheet control enables the manager to record the item as it is used on a sheet of

paper. Such information is then used for reorder purposes.

d. Stub control (used by retailers) enables the manager to retain a portion of the price

ticket when the item is sold. The manager can then use the stub to record the item that

was sold.

Today, the use of computer systems to control inventory is far more feasible for small business

than ever before, both through the widespread existence of computer service organizations and

the decreasing cost of small-sized computers. Often the justification for such a computer-based

system is enhanced by the fact that company accounting and billing procedures can also be

handled on the computer.

a. Point-of-sale terminals relay information on each item used or sold. The manager

receives information printouts at regular intervals for review and action.

b. Off-line point-of-sale terminals relay information directly to the supplier's computer who

uses the information to ship additional items automatically to the buyer/inventory

manager.

7. Developments in Inventory ManagementIn recent years, two approaches have had a major impact on inventory management: Material

Requirements Planning (MRP) and Just-In-Time (JIT and Kanban). Their application is primarily

within manufacturing but suppliers might find new requirements placed on them and sometimes

buyers of manufactured items will experience a difference in delivery.

Material requirements’ planning is basically an information system in which sales are

converted directly into loads on the facility by sub-unit and time period. Materials are scheduled

more closely, thereby reducing inventories, and delivery times become shorter and more



predictable. Its primary use is with products composed of many components. MRP systems are

practical for smaller firms. The computer system is only one part of the total project which is

usually long-term, taking one to three years to develop.

Just-in-time inventory management is an approach which works to eliminate inventories rather

than optimize them. The inventory of raw materials and work-in-process falls to that needed in a

single day. This is accomplished by reducing set-up times and lead times so that small lots may

be ordered. Suppliers may have to make several deliveries a day or move close to the user

plants to support this plan.

8. Inventory Costs are basically categorized into two majorheadings

8.1. Ordering Cost

Cost of procurement and inbound logistics costs form a part of Ordering Cost. Ordering

Cost is dependant and varies based on two factors - The cost of ordering excess and the

Cost of ordering too less.

Both these factors move in opposite directions to each other. Ordering excess quantity will

result in carrying cost of inventory whereas ordering less will result in increase of

replenishment cost and ordering costs.

8.2. Carrying Cost

Inventory storage and maintenance involves various types of costs namely:

8.2.1. Inventory Storage Cost

Inventory storage costs typically include Cost of Building Rental and facility maintenance

and related costs. Cost of Material Handling Equipments, IT Hardware and applications,

including cost of purchase, depreciation or rental or lease as the case may be. Further

costs include operational costs, consumables, communication costs and utilities, besides

the cost of human resources employed in operations as well as management.



8.2.2. Cost of Capital

This includes the costs of investments, interest on working capital, taxes on inventory

paid, insurance costs and other costs associate with legal liabilities.

The inventory storage costs as well as cost of capital is dependent upon and varies with

the decision of the management to manage inventory in house or through outsourced

vendors and third party service providers.

9. Economic order quantity (EOQ)

9.1. Definition

EOQ is that size of the order which gives maximum economy in purchasing any material and

ultimately contributes towards maintaining the materials at the optimum level and at the

minimum cost. In other words, EOQ is the amount of inventory to be ordered at one time for

purposes of minimizing annual inventory cost.

The quantity to order at a given time must be determined by balancing two factors:

1. The cost of possessing or carrying materials and

2. The cost of acquiring or ordering materials. Purchasing larger quantities may decrease

the unit cost of acquisition, but this saving may not be more than offset by the cost of

carrying materials in stock for a longer period of time.

5.6.1.1.1. EOQ Model










9.1. Definition




















9.1. Definition













Example

Bayer Ltd produces chemicals to sell to wholesalers. One of the raw materials it buys is sodium

nitrate which is purchased at the rate of R22,50 per ton. Bayer’s forecasts show a estimated

requirement of 5 750 000 tons of sodium nitrate for the coming year. The annual total carrying

cost for this material is 40% of acquisition cost and the ordering cost is R595. What is the Most

Economical Order Quantity?

The EOQ Formula is:

Where:

D = Annual Demand

C = Carrying Cost

S = Ordering Cost

Data

D = 5 750 000 tons

C = 0.40(22.50) = R9.00 per ton, pa.

S = R595 per order

Calculate the EOQ

= 27 573,135 tons per Order.

This model makes certain key assumptions:

No safety stock is carried. There is no shortage in the delivery of the order. Demand is at uniform rate and does not fluctuate. Lead Time for order delivery is constant.



Example






The EOQ Formula is:

Where:

D = Annual Demand

C = Carrying Cost

S = Ordering Cost

Data

D = 5 750 000 tons

C = 0.40(22.50) = R9.00 per ton, pa.

S = R595 per order

Calculate the EOQ






Example






The EOQ Formula is:

Where:

D = Annual Demand

C = Carrying Cost

S = Ordering Cost

Data

D = 5 750 000 tons

C = 0.40(22.50) = R9.00 per ton, pa.

S = R595 per order

Calculate the EOQ






Another Example:

Slindile runs a mail-order business for gym equipment. Annual demand for the exercise cycle is

16 000 units. The annual holding cost per unit is $2.50 and the cost to place an order is $50.

Calculate economic order quantity (EOQ)

EOQ =

9.2. Re-order Level or Ordering Point or Ordering Level

9.2.1. Definition of a Re-order Point

This is that level of materials at which a new order for supply of materials is to be placed. In

other words, at this level a purchase requisition is made out. This level is fixed somewhere

between maximum and minimum levels. Order points are based on usage during time

necessary to requisition order, and receive materials, plus an allowance for protection against

stock out.

The order point is reached when inventory on hand and quantities due in are equal to the lead

time usage quantity plus the safety stock quantity.



9.2.2. Formula of Re-order Level or Ordering Point:

The following two formulae are used for the calculation of reorder level or point.

Ordering point or re-order level = Maximum daily/weekly/monthly usage X Lead time

The above formula is used when usage and lead time are known with certainty. Therefore, no

safety stock is provided. When safety stock is provided then the following formula will be

applicable:

Ordering point/re-order level = Max daily/weekly/monthly usage x Lead time +Safety stock

9.3. Example

Maximum daily requirement 800 units

Time required to receive emergency supplies 4 days

Average daily requirement 700 units

Minimum daily requirement 600 units

Time required for refresh supplies One month (30 days)

Calculate the ordering point or re-order level

Solution

Ordering point = Maximum daily or weekly or monthly usage x Lead time

= 800 x 30

= 24 000 units

10. Minimum Limit or Minimum Level of Stock:10.1. Definition

The minimum level or minimum stock is that level of stock below which stock should not be

allowed to fall. In case of any item falling below this level, there is danger of stopping of

production and, therefore, the management should give top priority to the acquisition of new

supplies.



10.2. Formula:

Minimum level/limit can be calculated by the following formula or equation:

Minimum level = Re-order level – Average or normal usage X Normal re-order period

Or the formula can be written as:

Minimum level = Re-order level or ordering point – Average usage for Normal period

Self-check Question

Data per day

Normal usage 100

Maximum usage 130

Minimum usage 70

Re-order point 25 – 30 days.

Calculate the minimum limit or level

NB: To calculate minimum limit of materials we must calculate

re-order point or re-order level first.

Calculation:

Ordering point = Maximum daily or weekly or monthly usage X Maximum re-order

= 130 X 30

= 3 900 units

Minimum limit = Re-order level – Average or normal usage X Normal re-order period



= 3900 – (100 × 27.5*) [25 + 30] / 2

= 1150 units

11. Danger Level of Materials or Inventory Stock

11.1. Definition and Explanation:Some enterprises also calculate danger level. When this level of stock is reached, then

emergency steps are taken by the management to acquire material supplies.

When danger level is reached, the business attempts to purchase materials from the nearest

possible source so that the workers and plant and machinery may not remain idle due to

shortage of materials supplies.

11.2. Formula:

Danger level can be calculated by the help of the following formula or equation:

Danger level = Average daily requirement X Time required to get emergency supply

11.3. Example:

Self-check Question

Normal usage/average requirement 700 units per day

maximum usage 800 units per day

Minimum usage 600 units per day

Reorder period 25 to 30 days

Time required to receive emergency supplies 4 days.

Required

Calculate the danger level.



Solution:

Danger level = Average daily requirement × Time required to get emergency supply

= 700 × 4

= 2,800 units

12. The Cash Conversion Cycle

Calculating the cash conversion cycle (CCC) is an easy way to assess a business’

liquidity. The key elements of the CCC are inventory, receivables and payables. The cycle

is calculated as follows:

Average age of inventory (AAI)

Average collection period: debtors (ACP)

Average payment period: creditors (APP)

The formula is:

CCC = AAI + ACP - APP



Self-check QuestionBlack Box Limited has an inventory turnover of 6 an

average collection period of 37 days and an average

payment period of 62 days.

Additionally credit sales are R2 200 000 p.a. and cost of

sales is 60% of sales.

Calculate:

a. The CCC

b. The average investment in the CCC

Solution

a. AAI = 365/6 = 60, 83 days. (inventory turns over every 60,83 days)

Therefore:

CCC = AAI + ACP – APP

= 60,83 days + 37 days – 62 days

= 35,83 days.

This means that Black Box Ltd has to wait an average of 35,83 days from when the

inventory is purchased on credit until it receives its cash from its debtors.

b. Inventory = 60,83/365 X (R2 200 000 X 0,6) = R219 912

Debtors = 37/365 X R2 200 000 = R223 014

Creditors = 62/365 X (2200 000 X 0,6) = R224 219

Resources Invested = R667 145

This simply means that at any given time R667 145 is “tied up’ in the business and is

not available for day to day transactions.

13. Strategies for the Effective Management of the Cash Conversion Cycle



Businesses with positive cash conversion cycle have options of pursuing certain

strategies to minimise the cash conversion cycle. Caution must be exercised to ensure

that such strategies don’t do more harm than good. Three such strategies are available:

13.1. Stretching Accounts Payable

This entails paying accounts payable as late as possible without damaging their credit

rating and also not incurring additional charges.

Think PointWhilst the strategy may be financially attractive, it does raise ethical

issues. (Store credit cardholders’ accounts are due on the 1st of each

month but debtors are given until the 7th day to pay their instalments.

What if all customers chose to exercise this option?

What of the accounts payable situation for that store?

Would the store take kindly to this course of action?

A possible solution may be to offer the client a settlement discount for earlier settlement.

Sometimes a firm may prefer to settle after the discount period as it may have cash flow

issues. In order to calculate the cost of foregoing the discount, the following formula is

used:

Cost of foregoing = CD X 365

(1 - CD) N

Where:

CD = Cash discount

N = Number of days foregone

365 = The calendar year



Self-check QuestionAssume that a firm is offered 2/10 net 30, indicating that if the

account is settled in 10 days, the firm may keep a discount of

2%. If the discount is not taken, then the full amount is payable

in 30 days. The cost of foregoing the discount is calcutaed as

follows:

Cost of foregoing = CD X 365

(1 - CD) N

= 0,02 X 365

(1 – 0,02) 20

= 37,25%Conclusion: If the rate at which the firm can borrow (overdraftrate is, say 16%, they would be better off using their overdraft toclaim the discount on offer.

13.2. Efficient Purchasing and Inventory ManagementThis can be achieved by:

Increase inventory turnover by forecasting demand better and by planning to

ensure that purchases coincide with the forecasts made.

With better purchasing planning, scheduling and control techniques, the firm can

reduce the length of the purchasing cycle and this in turn will lead to an increase in

the inventory turnover.

13.3. Speeding up the Collection of Accounts Receivable

This has been discussed elsewhere, but a brief summary follows:

Offer discounts for prompt settlement

Send out statements timeously

Send out reminders for accounts that are not settled promptly

Charge interest on overdue accounts

Hand over errant clients for collection.



14. Working Capital Financing Policies

There are essentially three approaches a firm may use to determine their short term

and long term financing. These approaches are:

a. The Conservative Approach

b. The Moderate Approach

c. The Aggressive Financing Approach

14.1. The Conservative Approach

A firm using this approach will tend to finance all their permanent assets and most

projects with long term funds. It must be noted, however, that the cost of long term

financing is higher interest charges, their costs will obviously be higher. But there risk

level is lower as they make less use of short term debt. (Marx: 152). The conservative

approach is depicted in figure 1 below.

Figure 1: The Conservative Approach



14.2. The Moderate Approach

This is also known as the Maturity Matching Approach. Essentially this method

involves matching the asset and liability maturities to minimise the risk of the firm not

paying off its maturing liabilities. The ideal situation is to match revenue streams

perfectly with cash outflows. For example, inventory expected to be sold within 30

days could be financed with a 30 day short term loan (or suppliers credit if it is easily

available). (Marx: 152)

The matching of maturities does become a little complicated and can be fraught with

uncertainty if the life span of the asset is expected to change (become shorter). What

could happen if for example, the inventory is not sold within 30 days? Raise another

loan?

It is worth noting that firms with limited borrowing capacity could actually close their

doors if they cannot raise sufficient funds. The moderate approach is depicted in

figure 2 below.

Figure 2: The Moderate Approach



14.3 The Aggressive Financing Approach

This approach aims at financing seasonal needs and even long term needs with short

term funds. Firms using this approach operate with less working capital. It must be

conceded however that the degree of aggressiveness varies from firm to firm. This is

obviously a risky approach. If the total financing requirement turns out to be higher

than anticipated, then the firm may find that short term financiers refusing to extend

credit to the firm. (Marx 152)

And if this is the case then long term borrowers may also be reluctant to advance

funds as well. Using short term funds is far cheaper than using long term funds and if

well managed, then the increase in income margins may be very high. The

aggressive approach is depicted in figure 3 below.

15. John Maynard Keynes identified 3 reasons for holding cash

1. The Speculative Motive: the underlying principle here is that cash is held for unexpected

opportunities that may arise, e.g. Bargain purchases, “fire” sales, attractive interest rates,

etc.



2. The Precautionary Motive: emphasises the need for a financial reserve. The belief here is a

safety net is needed for that emergency moment where a business may be vulnerable.

3. The Transaction Motive: this need to hold cash is based on the need to conduct normal

business, ie. Purchase materials, pay bills, etc.

16. Unsecured Sources of Short term Financing

16.1. Accounts payable: Credit from suppliers’ (interest bearing or non interest bearing).

16.2. Accruals: bills that are paid in arrears.

16.3. Unsecured Bank loans.

16.4. Open lines of credit made available by banks.

16.5. Revolving credit.

16.6. Bankers acceptance (bill of exchange). (Marx: 155)

17. Secured Sources of Short term Financing17.1. Characteristics of Secured Sources of Short term Loans17.1.1. Lenders prefer collateral with a duration that is closely linked with the term of the loan.

17.1.2. Accounts receivable and inventory are preferred sources of collateral as they are highly

liquid

17.1.3. Interest rates on secured short term loans are higher than on unsecured short term

loans. This is due to the large amount of administration tasks that need to be

preformed. Besides in order to qualify for a secured loan, the business has exhausted

all its unsecured loan facilities. (Marx: 159)

18. Accounts Receivable as CollateralAccounts receivable are regarded as short term security as a result of the high liquidity

level of this asset.

18.1. The pledging process is as follows:b. The lender compiles a list of acceptable accounts with billing dates and sums

due.

c. Then the lender analyses the historical payment pattern on the account to

calculate the average payment period for each customer.



d. Once the lender selects the accounts they wish to accept, they then adjust the

values for returns, discounts etc in order to protect themselves should the

customer make use of such options.

e. The lender then determines the percentage to be advanced against this

collateral. (Marx: 159)

Terminologya. Notification Pledge: The customer is told to remit the amount due directly to

the lender.

b. Non-Notification Pledge: the customer pays the supplier who then remits the

amounts due to the lender.

c. Pledging Cost: this cost is usually 2% -5% above prime rate and is charged in

addition to the interest charge. An administration fee in addition to this may also

be charged.

18.2. FactoringThis entails the sale of accounts receivable to a factor or other financial institution to

obtain funds. A factoring cost is levied and includes costs such as commission (1% -

3%), interest charges (which are inevitably above prime rate).

18.2.1. Advantages of Factoring Cash is received immediately after the sale is made, thus reducing the working

capital that is needed.

The collection function is handled by the factor, thus reducing time spent on

collection and the myriad of administration costs attached to this task.



Self-check QuestionJoylands (Pty) Ltd factors all its accounts

receivables. The factoring agreement that they have

in place is:

A 10% reserve is held and a 2,5% commission is

charged on the book value of the account. Further

more interest is charged at 1,5% per month (18%

per annum) on advances. Joylands wants to factor

an account of R5 000 which is due in 30 days. What

advance will they receive?

SolutionBook value of the account 5 000

Reserve (10% of R5 000) (500)

Cost of factoring (2,5 of R5 000) (125)

Funds available for advance 4 375

Interest on advance (1,5% of R5 000) 75

Net value of advance 4 300

So, if the debtor pays in full, Joylands net cost is R200 (the cost of factoring and

interest, R125 + R75)



REFERENCES1. Els, G; Du Toit, E; Erasmus, P; Kotze, L; Ngwenya, S; Thomas, K; Viviers, S. (2010)

Corporate Finance, A South African Perspective, Oxford University Press.

2. Ross, S; Westerfield, RW; Jordan, BD; and Firer C. (2009). Fundamentals ofCorporate Finance , 4th South African Edition, McGraw-Hill.

3. Correia, C; Flynn, D; Uliana, E and Wormald, M. (2008) Financial Management, 6th

Edition, Juta Publishing.

4. Marx, J; de Swardt, C; Beaumont Smith, M; Naicker, B; Erasmus, P. (2007) FinancialManagement in Southern Africa, 2nd Edition, Pearson Education.

5. Brecher, R. (2009) Contemporary Mathematics for Business and Consumers. 5th Ed.

USA: South-Western Cengage Learning

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