notes to business & finance (knowledge levele)

CONCEPT & DESIGN BY

SAYEED

Professional Stage (Knowledge Level)

Business Finance Page 1

Sayeed@MTB Hello-01716-025103

1. What is economic value added? How can we calculate EVA? Economic value added (EVA) is a financial performance method to calculate the true economic profit of an organization. EVA can be calculated net operating after taxes profit minus cost of the capital invested. Economic value added (EVA) can be used for the following purposes: Setting organizational. Performance measurement. Communication with shareholder and investor. Motivation of manager. Capital budgeting. 2. What is Economic Order Quantity (EOQ)? Economic order quantity (EOQ) is the amount of inventory to be ordered at one time for purposes of minimizing annual inventory cost. 3. Define strategic management. Strategic management is the art and science of formulating, implementing and evaluating cross functional decision that will enable an organization to achieve its objective. 4. What is corporate strategy? What are levels of strategy? Corporate Strategy - is concerned with the overall purpose and scope of the business to meet stakeholder expectations. Corporate strategy is often stated clearly in a "mission statement”. This is heavily influenced by investors in the business to guide strategic decision-making throughout the business. Strategy can be formulated in three different levels: Corporate level Business unit level Functional or departmental level. 5. Explain about different stages of product life cycle. The stages through which individual products develop over time are called commonly known as the "Product Life Cycle".

Introduction Stage In the introduction stage, the firm seeks to build product awareness and develop a market for the product. Growth Stage In the growth stage, the firm seeks to build brand preference and increase market share. Maturity Stage At this point the market reaches saturation. Producers begin to leave the market due to poor margins. Promotion becomes more widespread and it puts price ahead of the competition. Decline Stage At this point there is a downturn in the market. For example more innovative products are introduced or consumer tastes have changed



6. What is the hierarchy of needs suggested by Abraham Maslow for an individual’s motivation? How management can use the model while designing an employee valuation system?

The physiological needs: includes basic life needs - air, food, drink, shelter, warmth, sex,

sleep, etc. The safety and security needs: includes Protection, security, order, law, limits, stability, etc. The love and belonging needs: includes family, affection, relationships, work group, etc. The esteem needs: includes achievement, status, responsibility, reputation. Self actualization: Personal growth and fulfillment.

7. How would you explain risk and uncertainty? What are the various types of risks? How the risks can be avoided or minimized?

Risk: The possibility that an event will occur and adversely affect the achievement of objectives. Uncertainty: The inability to predict the outcome from any activity due to lack of information.

Classifications of Risks:

Business risk: includes strategy, enterprise, product, economic, technology. Financial risk: includes liquidity, gearing, default, credit, foreign exchange, interest rate, market. Operational Risk: includes process, people, systems and legal. Event Risk: includes physical, social, political etc.

By compliance of standard all the above risk can be avoided or minimized.

8. What is span of control in Management? Narrate the factors influence the span of control in an organization.

The number of subordinates that a manager or supervisor can directly control is called span of control.

The following factors affecting span of control: Geographical Location: if the branches of a business are widely isolated, then the manager will find it difficult to supervise each of them; as such the span on control will be smaller. Capability of workers: if workers are highly capable, need little supervision, and can be left on their own, e.g.: Theory Y type of people, they need not be supervised much as they are motivated and take initiative to work; as such the span of control will be wider. Similarity of task: if the task that the subordinates are performing is similar, then the span of control can be wider, as the manager can supervise them all at the same time.



9. Explain why SWOT analysis is important for corporate appraisal process.

The SWOT analysis is a key component in strategic planning. The analysis subjectively evaluates the impact of internal and external factors for a business objective. Internal processes and resources are considered strengths and weaknesses (S and W, respectively). External factors affecting the business and industry are considered opportunities and threats (O and T, respectively). An evaluation of these factors develops a strategic perspective that includes the competitive landscape and current market conditions.

10. What is Gap analysis? How does this help management in setting future strategies?

Gap analysis is an examination of where your business currently is and where you want your business to be, resulting in an apparent gap between the two. It is an insight into the needs for the improvement of your business and helps you determine what steps to take to attain your business goals.

11.What do you understand by Cost Volume Profit (CVP) analysis?

Cost-volume-profit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income.

12. What is corporate governance? What are the objectives of corporate governance?

Corporate governance is a term that refers broadly to the rules, processes, or laws by which businesses are operated, regulated, and controlled.

The core Objectives of Corporate Governance can be defined as under: • Strategic Focus • Predictability • Transparency • Participation • Accountability • Efficiency & Effectiveness • Stakeholder Satisfaction.

13. Define crisis management and what are the different types of business crisis? How business crisis can be addressed.

The identification of threats to an organization and its stakeholders, and the methods used by the organization to deal with these threats.

Lerbinger categorized seven types of crises Natural disaster Technological crises Confrontation Malevolence Organizational Misdeeds Workplace Violence Rumors



14. What is an organization? An organization is a social arrangement for the controlled performance of collective goals, which has a boundary separating it from its environment. 15. List six ways in which organization may differ from each other? a) Ownership. b) Control. c) Activity. d) Profit or not profit organization. e) Size. f) Legal Status. 16. Describe the types of manager. A line manager. A staff manager A functional Manager. A project manager. 17. Define the elements of management process. The following elements are included in management process:

Planning: It denotes what is to be done.

Organizing: It denotes how it is to be done including staffing and coordinating.

Controlling: It denotes what has been done.

Leading: It denotes to arrange in a desired pattern or structure.

18. Define marketing and marketing mix. Describe the 4 p’s in marketing mix. Marketing mix: Combination of the four controllable variables of Product, Price, Place, and Promotion those are essential to define and fulfill a target market. 4 p’s in marketing mix: Product Quality; Appearance; Packaging; Brand; Service; Support; Warranty. Price Discounts; Financing; Leasing Options; Allowances. Place Locations; Logistics; Channel members; Market Coverage. Promotion Advertising; Public Relations; Direct Sales; Sales; Media. 19.Describe Likert's leadership styles. Rensis Likert identified four main styles of leadership, in particular around decision-making and the degree to which people are involved in the decision. These are as under: Exploitive authoritative Benevolent authoritative Consultative Participative



20. What is psychological contract? A psychological contract represents the mutual beliefs, perceptions, and informal obligations between an employer and an employee.

21. Describe the theory X and Y by Douglas McGregor? Douglas McGregor (1960) defined two sets of assumptions about human nature that are explained as under:

Theory X Assumptions: People inherently dislike work. People are controlled to do work to achieve objectives. People prefer to be directed.

Theory Y Assumptions: People view work as being as natural as play and rest. Peoples are self-directed and controlled towards achieving objectives. People learn to accept and seek responsibility.

22. List down Team Roles.

(a) Action Oriented Roles Shaper Implementer Completer Finisher

(b) People Oriented Roles Coordinator Team Worker Resource Investigator

(c) Thought Oriented Roles Plant Monitor-Evaluator Specialist

23. Describe the types of promotions. Four types of promotion that support marketing objectives, including Advertising Personal selling, Publicity and Sales promotions

Work (employees input)

Pay(employers reward)

Time

Security Effort Safety

Performance Training Results Recognition

Commitment Promotion Loyalty Life balance

Leadership Ownership/equity Sacrifice Benefit/pension



24. Human Resource management functions. Describe the 4c’s of HRM. There are many functions of HRM including: HRM Functions 4 C’s Model Resource Planning Job Analysis Candidate selection. Training & Development Evaluating Staffing Appraisal Performance Building Employee Commitment Equal opportunity for all Employees Health and Security

Competent Commitment Congruence Cost Effectiveness

25. Describe the Elements of product or Product mix strategy. Product Mix Strategy deals with: The product life cycle Brand name Packaging Design Quality Safety After sales service. 26. Describe the types of managerial power. In 1959 John French and Bertram Raven identified five bases of power which are as under: Legitimate: It comes from the manager’s position, experience or status. Reward: It includes pay raises, days off, award or recognition. Expert: This is based on a person's superior skill and knowledge. Referent: Referent power is based on the relationship of the manager and employee. Coercive: Coercive power is a source of power that relies on an employee’s high dependency

on job. 27.Describe Herzberg’s Motivation-Hygiene Theory In 1959 Herzberg split his factors of motivation into two categories called hygiene factors and motivation factors. The two types of factors may be listed as follows: Hygiene factors (leading to dissatisfaction): including company policy, supervision, work conditions, salary etc. Motivators (leading to satisfaction): including achievement, recognition, responsibility, growth etc.



28. Describe Mint berg: The Managerial Roles.

Mint berg (1973) groups managerial activities and roles as involving:

Managerial activities Associated roles

Interpersonal roles

figurehead liaison leader

Information processing roles monitor disseminator spokesman

Decision roles improver/changer disturbance handler resource allocator negotiator

29. What is organizational structure? What are the building blocks of organizational

structure? An organizational structure consists of activities such as task allocation, coordination and supervision, which are directed towards the achievement of organizational aims. Building blocks: Operating core. Support staff. Middle line. Techno structure. Strategic apex. Ideology.

30. Describe the classical principles of fayol. Fayol's fourteen principles of management are as follows: Division of Work Authority and Responsibility Discipline Unity of Command Unity of Direction Subordination of Individual Interest to General

Interest Remuneration of Personnel

Centralization Scalar Chain (line of authority with peer level

communication) Order Equity Stability of Tenure of Personnel Initiative Esprit de Corps

31. What are the features of partnership business? Two or more Members Agreement Lawful Business Competence of Partners Sharing of Profit Unlimited Liability

Voluntary Registration Principal Agent Relationship Restriction on Transfer of Interest Continuity of Business



32. How to analyze the general environment by using PESTEL. Political: Taxation policy, International trade, War, Inter country relationship. Economic: Interest rate, inflation, exchange rate, Unemployment. Social: Population ageing, Income distribution, Attitudes of work. Technological: Innovation, New product development, Rate of technological obsolescence. Ecological: resources, pollution, green issues. Legal: Competition law, environmental protection law, employment law, health & safety law. 33. Describe BCG Growth-Share Matrix The BCG growth-share matrix displays the various business units on a graph of the market growth rate vs. market share relative to competitors:

34. Describe SWOT analysis. SWOT analysis can be expressed by the following diagrams: Strengths: includes strong brand names, good reputation among customers, and favorable

access to distribution networks.

Weaknesses: includes location, damaged reputation, poor quality of product and services. Opportunities: Developing market, a new international market, merger-joint venture or strategic

alliances. Threats: New competitor, taxation policy, superior distribution channel of new competitor.

a. Stars High growth, High Market Share

b. Cash Cows Low growth, High market share

c. Dogs Low growth, Low market share

d. Question Marks High growth, Low market share



35. Describe Ansoff’s matrix.

Ansoff Matrix

Existing product New Product Existing Market Market Penetration Product development New Market Market Development Diversification

Ansoff's matrix provides four different growth strategies: Market Penetration: To increase market share, the firm seeks to achieve growth with existing

products & existing market segments. Market Development: By targeting its existing products, the firm seeks growth to the new market

segments. Product Development: The firm develops new products targeted to its existing market segments. Diversification: The firm grows by diversifying into new businesses by developing new products

for new markets.

36. What is involved in the risk management process? The four explicit stages of the Risk Management process are:

Identify: Find, list and characterize elements of risk. Assess: Prioritize identified risks against agreed criteria. Plan: Develop, analyze, and recommend risk responses. Implement: Implement, monitor, report and review risk management actions against objectives.

37. Describe the types of financial information. Financial information can be classified as under: Planning information Operational information. Tactical information Strategic information.

38. Who are the users of financial information? Present and potential investors(shareholder) Employees. Customers. Suppliers and other business partner. Lenders. Government and its agencies. Public.



39. What are the qualitative characteristics of financial statements? Why financial information is needed?

The followings are the qualitative characteristics of financial statements: Understandability. Relevance. Reliability. Comparability.

Necessity of financial information: To make economic decision. To hold management to account. To predict cash flow.

40. What are the factors that affect demand? The following factors which affect demand: Price Marketing research Advertising Sales promotion

Effectiveness of distribution After sales service Granting a credit to customer

41. How pricing policy influences the business? (1) Costs: In order to make a profit, a business should ensure that its products are priced above their

total average cost.

(2) Competitors: If the business is a monopolist, then it can set any price but if a firm operates under conditions of perfect competition, it has no choice and must accept the market price.

(3) Customers: Price must be addressed according to the customer expectation.

(4) Business Objectives:

To maximize profits To achieve a target return on investment To achieve a target sales figure To achieve a target market share

42. What is discounted cash flow? A method of investment analysis in which anticipated future cash income from the investment is estimated and converted into a rate of return on initial investment based on the time value of money.

43. Define control activity. What are generally included in the control activities? The policies and procedures that help ensure management directives are carried out.

The following things are generally contained in the control activities: Approval. Authorization. Verifications. Reconciliation. Security of assets and Segregation of duties.



44. Describe the Purpose of Budget. A Budget is basically a list of all the planned expenses as well as sources of revenues. It is a plan for saving as well as spending. It is an important concept from microeconomics. The Budget have the following key purpose: - It helps in planning the money as well as spending for the future. - It provides a forecast of revenues as well as expenditures. - It enables to measure the actual financial operations of a business against the forecasts.

45. Describe the function of treasury management. Treasury management is all about the efficient management of liquidity and financial risk. Some of the major roles/functions of Treasury management are as follows:

Cash management Currency management Funding management Banking Corporate finance Venture Capital Financing

46. What aspects of performance are measured? Performance may be measured in operational and financial aspect: Operational aspect:

Efficient use of labor and material. Control of labor rates of pay and material prices. Effectiveness of planning and control mechanism.

Financial aspect: Profitability. Liquidity and solvency. Efficiency and working capital management.

47. Why measurement of business performance is required? Managers need to measure performance in order to assess whether objectives of SBU’s are being met, and if so how:

Productivity: What is output relative to what is input? Effectively: How far are targets and objectives achieved? Efficiently: what is the gain that the business has achieved?

48. What are the components for balancing liquidity and profitability? Following are the components for balancing liquidity and profitability: Cash Receivable. Inventory. Payables.



49. What are the solutions to liquidity problem? Liquidity problem can be solved by --- Reducing the inventory-holding period. Reducing the production period. Reducing customer credit period and accelerating on cash collection. Extending the period of credit taken from suppliers. 50. How credit ratings are being accomplished? Credit rating should be based on: An assessment of the ability of the customer to meet the liabilities. An assessment of financial statements particularly for major customers. An analysis of ongoing trading experience with each customer. Trade and Bank references.

51. What are the motives that influence on cash balances? Transaction motive: to meet current day to day financial obligations. Finance motive: to cover major item such as the repayment of loans and the purchase of

non-current assets. Precautionary motive: to give the caution against unplanned expenditure rather the buffer

inventory. Investment motive: to take advantage of market opportunities.

52. How surplus fund can be invested? Surplus funds can be invested in various financial products: Treasury bill. Deposits. Gift (longer term govt. debt). Bonds. Equities.

53. What are the money market financial instruments? The following financial instruments that are traded in money market: Bills. Deposit. Commercial paper.

54. Define primary and secondary market? Primary market: where new financial instruments are issued for cash. Secondary Market: Where existing financial instruments are traded between participants in the

market.



55. What are the fundamental professional principles? The fundamental professional principles are as under: Integrity. Objectivity. Professional competence and due care. Confidentiality. Professional behavior.

56. What are the threats to professional principles? Self-interest threat. Self-review threat. Advocacy threats. Familiarity threats. Intimidation threats. 57. What do you mean by acting “diligently”? Acting diligently means when he will provide professional services then he will comply all required standards and regulations. 58. State the safeguards against the threat. Safeguard that may eliminate such threats to an acceptable level fall into two broad categories: Safeguard created by the profession, legislation or regulation. Safeguard in the work environment. 59. State the objectives of corporate governance. There are four broad objectives which are discussed below: The corporate perspective on corporate governance. The public policy perspective on corporate governance. The stakeholder perspective on corporate governance. The stewardship perspective on corporate governance.

60. What are the symptoms of a serious conflict of interest? There is no standard way in which a serious conflict of interest becomes apparent. It may become evident by: Financial collapse without warning. Directors are trying to disguise true financial statements from shareholders. Disputes over director’s remuneration. Decision taken by the board of director for their own interest without thinking about shareholder.



61. What are the concerns of good governance?

Good practice in corporate governance is concerned with: Openness and transparency. Integrity and accountability. Reducing the potentials for conflicts. Reconcile the interest of shareholder and directors as far as possible.

62. How can an ethical culture be promoted? An ethical culture can be promoted by a combination of: Ethical leadership from the board of directors. Code of ethics or business conduct. Policies and procedures to support ethical behavior.

63. What are the attributes of ethical leadership?

The attributes of ethical leadership are as under: Openness. Courage. Ability to listen. Honesty. Fair mindedness

64. Define Demand. Which factors affect the demand for a product? The amount of a particular economic good or service that a consumer or group of consumers will want to purchase at a given price.

Price of the good Price of complementary goods Price of substitutes Consumer's income Consumer's taste for the good Consumer's expectations about future prices Advertising Taxation 65. What factors shift demand curve? changes in price of related goods e.g. substitutes and complements change in income e.g. normal goods/inferior goods changes in tastes Changes in expectations. 66. Define supply. Which factors influence supply? The total amount of a good or service available for purchase; along with demand, one of the two key determinants of price.

Factors influence on supply: The Income The expectations of people The customers' satisfaction The number of people buying something The price of the product



67. Define Equilibrium price.

The market price at which the supply of an item equals the quantity demanded.

68. Price elasticity of demand. Factors affecting the Price Elasticity of Demand.

The price elasticity of demand measures the responsiveness of quantity demanded to a change in price, with all other factors held constant.

Availability of substitutes. Degree of necessity. Proportion of the purchaser's budget consumed by the item. Time period. Permanent or temporary price change. Price points.

69. What is centralization? What are the ways of centralization? What factors affecting centralization?

Definition: The process of transferring and assigning decision-making authority to lower levels of an organizational hierarchy.

Way of centralization: (i)Geographically. (ii)By authority.

Factors affecting centralization: Leadership. Size of activity diversification. Extent of activity diversification. Effectiveness of communication. Geography of location.

70. Define crisis management. Describe the types of crisis. How crisis can be managed?

Crisis management is the task for creating and implementing a business plan that can be implemented quickly in the face of a crisis. Types of crisis: Lerbinger categorized seven types of crises Natural disaster Technological crises Confrontation Malevolence Organizational Misdeeds Workplace Violence Rumors Crisis can be managed by the following ways: Crisis prevention. Contingency planning. Effective action in the event of crisis.



71. What are the qualities of good information (ACCURATE)? A Accurate C Complete C Cost-beneficial U User-targeted R Relevant A Authoritative T Timely E Easy to use

72. How data or information is processed? To be effective, information processing should meet the following CATIVA criteria: C Completeness A Accuracy T Timeliness I Inalterability V Verifiability A Assessibility

73.Write Short Notes: Management Governance Power Authority Responsibility Accountability Delegation Fiduciary relationship

Balance Scorecard Perpetual inventory methods

Management information system (MIS)

i) Management: Getting things done through other people. ii) Governance: The system by which businesses are directed and controlled. iii) Power: The ability to get things done. iv) Authority: The right to do something and expect it to be done. v) Responsibility: The obligation a person has to fulfill a task which s/he has been given. vi) Accountability: Liability for the task s/he has been given. vii) Delegation: Responsibility is to be delegated among subordinate to get things done. viii) Balance Scorecard: Balanced scorecard methodology is an analysis technique designed to

translate an organization's mission statement and overall business strategy into specific, quantifiable goals and to monitor the organization's performance in terms of achieving these goals.

Input (Data)

Processing Output (information)



ix) Management information system (MIS): Management Information Systems (MIS) are processes used by companies to provide management with the best information for decision making.

x) Fiduciary relationship: A fiduciary relationship exists when a person claims to act in the best interests of, or in behalf of, another, and the other accepts that trust.

xi) Perpetual inventory methods: An accounting method of maintaining up-to-date inventory records that accurately reflect the level of goods on hand.

1. Nikko Ltd. has revenue of Taka 1,600,000 cost of sales Taka 900,000 and expenses of

Taka 350, 000. Requirement: GP margin, Net margin and Mark-up on cost of sales.

Answer to the above question

(i) GP Margin = Revenue - Cost of Goods Sold x 100 Revenue

= 1,600,000-9,00,000 x 100

1,600,000

= 43.75%

(ii) Net Margin = Net Profit x 100 Revenue

= 3,50,000

x 100 1,600,000

= 21.87%

Note: Where net profit =Revenue-COGS-Operating Expenses

(iii) Mark-up on cost on sale = Gross margin x 100 1- Gross Margin

= .4375 x 100 1- .4375 = 77.77% 2. Profit is usually measured initially in CUs in absolute terms:

Revenue 100,000.00 Cost of sales (58,000.00) Gross profit 42,000.00 Expenses (24,000.00) Net profit 18,000.00 Requirement: GP margin, Net margin and Mark-up on cost of sales.

Math for Business Finance



Answer to the above question 42,000.00 a.Gross margin: Gross profit/ Revenue = 100,000.00 = 42 %

18000.00 b.Net margin: Net profit/ Revenue = 100,000.00 = 18 %

42,000.00 c.Markup : Gross profit/ cost of sales = 58,000.00 = 72% 3. Gridlock ltd has revenue of CU 1.6m, cost of CU 0.9m and expenses of

CU0.35m.Calculate the following: a.Gross margin b.Net margin c.Markup on cost of sales

Answer to the above question a. Gross margin: (1.6-0.9)/1.6X 100% = 43.75% b.Net margin: (1.6-0.9-0.35)/1.6 X 100% = 21.87% c.Markup on cost of sales (gross profit/cost of sales): (1.6-0.9)0.9 X 100% = 77.78%

4. ABC limited has Taka100, 000 which can be invested@10% p.a in FDR.Alternatively, the fund can be invested now to receive back Taka125,000 in 12 months time because of risk issue, the company expects 12% return on it. What would be your suggestion as an advisor?


PV=FV / (1+i)n =125000/ (1+.12)1 =Tk.1,11,607

Since the present value of the investment is more than the amount invested, we say it has a positive NPV of (1,11,607-1,00,000)=Tk.11,607.This NPV is higher than(1,10,000-1,00,000)=Tk.10,000. Generally the project with higher NPV should be accepted so the investment in the 12 months project should be accepted. 5.Enron Limited has the following data in their financial statements of 2009: Ordinary shares @Tk.100 per shareTk.150,000 Dividend Tk.45,000 Market price per shareTk.200 Earnings per share Tk.17 From the above information please calculate the followings: i) Dividend per share ii)

Dividend cover iii)P/E Ratio iv)Dividend yield.




i) Dividend per share = Sum of dividend over a period Share outstanding for the period

= 45,000 1,500 = 30

(ii)Dividend cover = Earnings per share Dividend per share

= 17 30 = .57

ii) P/E Ratio = Market Value per share Earnings per share

= 200 17 = 11.76

iii) Dividend Yield = Dividend per share X 100 Current price per share = 30 X 100 200 = 15%

6. How can we calculate (i) Inventory turnover ratio; ii) Return on capital employed iii) Current ratio iv) Quick ratio; v)Debt Equity ratio; vi)Gearing ratio vii)Interest cover and vii) Asset- turnover.


i) Inventory Turnover Ratio = Cost of goods sold

Average or Current year Inventory

(ii)ROCE = EBIT Total Asset – Current Liabilities

iii) Current Ratio = Current Asset Current Liabilities

iv) Quick Ratio = Current Asset-Inventory Current Liabilities

v) Debt Equity Ratio = Total Liabilities Shareholder Equity

vi) Gearing Ratio = Non-current Liabilities Shareholder’s equity + Non-current Liabilities

vii) Interest cover Ratio = PBIT Finance Cost

viii) Asset turnover = Revenue Capital employed(total asset-current liabilities)



FURLONG LTD INCOME STATEMENTFOR THE YEAR ENDED 31 DECEMBER

2008 2007Revenue 3,095,576.00 1,909,051.00Cost of Sales 2,402,609.00 1,441,950.00Gross Profit 692,967.00 467,101.00Other Income 2 744.00 2,782.00Operating Income 693,711.00 469,883.00Administrative Expenses 1 333,466.00 222,872.00Finance Cost 18,115.00 21,909.00Profit before Tax 3 342,130.00 225,102.00Tax 74,200.00 31,272.00Profit for the Year 267,930.00 193,830.00Dividend per Share 1.40 1.00Earning per Share 12.80 9.30

FURLONG LTD BALANCE SHEETASSETSNon-Current AssetsTangible non-current assets 802,180 656,071 Current Assets:Inventory 64,422 86,550 Receivable 4 1,002,701 853,441 Cash & Cash Equivalent 1,327 68,363 Total Assets 1,870,630 1,664,425 EQUITY AND LIABILITIESEquityOrdinary Share Tk. 10 per Share 5 210,000 210,000 Share Premium Account 48,178 48,178 Retained Earnings 630,721 393,791 Non-Current liabilities10% loan notes 2004/2009 100,000 100,000 Current Liabilities 6 881,731 912,456 Total Equity and Liability 1,870,630 1,664,425

1.DepreciationDepreciation Charged 151,107 120,147 2.Other IncomeReceivable on short-term deposit 744 2,782 3.Finance CostPayable on short-term borrowings 8,115 11,909 Payable on loan notes 2004/2009 10,000 10,000

18,115 21,909

YearParticulars Notes

NOTES TO THE FINANCIAL STATEMENTS

7. From the following information-Calculate ratio analysis.



2008 20074.ReceivablesTrade Receivables 905,679 807,712 Prepayments and accrued income 97,022 45,729 Total Receivables 1,002,701 853,441

5.Called-up Share CapitalAuthorised ordinary shares of Tk.10 each 1,000,000 1,000,000 Issued and fully paid ordinary shares Tk.10 each 210,000 210,000

6.Current LiabilitiesTrade Payables 627,018 545,340 Accruals and Deffered income 81,279 280,464 Tax 173,434 86,652

881,731 912,456

YearParticulars

Profitability measures: Profit before interest and tax(PBIT) Particulars Year-2008 Year-2007 Profit before tax 3,42,130 2,25,102 Finance Cost 10,000 10,000 PBIT 3,52,130 2,35,102

Growth (in %) = 3,52,130-2,35,102 X 100 = 50%. 2,35,102 Return on capital employed(ROCE)

Particulars Year-2008 Year-2007

ROCE = 3,52,130 X 100 2,35,102 X 100 9,88,899 751,969 = 35.6% = 31.3%

Gross margin


Gross margin = 6,92,967 X 100 4,67,101 X 100 30,95,576 19,09,051 = 22.4% = 24.5%

ROCE = PBIT Capital employed

*Capital employed=Equity +long-term liabilities Or =Total asset less current liabilities

Gross margin = Gross profit X 100 Revenue



Net margin


Net margin = 3,52,130 X 100 2,35,102 X 100 30,95,576 19,09,051 = 11.4% = 12.3%

Liquidity and solvency measures: Short-term liquidity: Current ratio


Current ratio = 10,68,450 10,08,354 8,81,731 9,12,456 = 1.21:1 = 1.10:1

Quick ratio


Quick ratio = 10,68,450-64,422 10,08,354-86,550 8,81,731 9,12,456 = 1.14 = 1.01

Long-term liquidity: Debt ratio


Debt ratio

=

8,81,731+1,00,000

X100

9,12,456+1,00,000

X 100 18,70,630 16,64,425 = 52% = 61%

Gearing ratio


Gearing ratio

=

1,00,000

X100

1,00,000

X 100 8,88,899 +1,00,000 651969 +1,00,000 = 10% = 13%

Net margin = PBIT X 100 Revenue

Current ratio = Current Assets

Current Liabilities

Quick ratio = Current Assets less inventory

Current Liabilities

Debt ratio = Total current & Non-current Liabilities

Total Assets

Gearing ratio = Non-current Liabilities Shareholder’s equity + Non-current Liabilities



Interest cover


Interest Cover

=

3,52,130

2,35,102

18,115 21,909 = 19.4 times = 10.7 times

Efficiency and working capital management measures:

Asset turnover


Asset turnover

=

30,95,576

19,09,051

18,70,630-8,81,731 16,644,25-9,12,456 = 3.13 times = 2.54 times

Inventory turnover Ratio

Receivable collection period

Payables payment period

Interest cover = PBIT Finance Cost

Asset turnover = Revenue Capital employed(total asset-current liabilities)

Inventory turnover Ratio = Cost of Sales Average Inventory

*Inventory=Opening+Closing/2

Inventory turnover Ratio = 24,02,609 (86,550+64,422)/2

= 31.8 times


Inventory turnover Period = Inventory X 365 Inventory X 365 Cost of Sales Cost of Sales

= 64,422 X 365 86,550 X 365 24,02,609 14,41,950 = 9.8 days =21.9 days

Receivable collection period = Trade Receivables X 365 days Revenue from credit sales


Receivable collection Period = 9,05,679 X 365 8,07,712 X 365 30,95,576 19,09,051 = 106.8 days =154.4 days

Payables payment period = Trade Payables X 365 days Cost of sales Particulars Year-2008 Year-2007

Payables payment period = 627018 X 365 5,45,340 X 365 24,02,609 14,41,950 = 95.3 days =138.0 days



Length of Cash Operating Cycle

Investor measures:

Dividend cover


Dividend cover

=

12.8p

9.3p

1.4p 1.0p = 9.1 times = 9.3 times

Assuming the company’s current share price is 54p and 85p at the end 2007 and 2008 respectively what would be the P/E Ratio and Dividend yield? Price earnings ratio Particulars Year-2008 Year-2007

P/E Ratio Current share price/Earnings per share = 85p/12.8p 54p/9.3P = 6.6:1 = 5.8:1

8. Following are the financial statements of XYZ Limited:

Income Statement of XYZ Limited For the year ended 31 Dec. 2009

Particulars 2009 2008 Revenue 30,95,576 19,09,051 Cost of Sales 24,02,609 14,41,950 Gross Profit 6,92,967 4,67,101 Other Income 744 2,782 Administration Expenses 3,33,466 22,2,872 Finance Cost 18,115 21,909 Profit before tax 3,42,130 2,25,102 Tax 74,200 31,272 Profit for the year 2,67,930 1,93,830 Dividend per share 1.40 1.00 Earnings per share 12.76 9.23 Market price per share 100 75

Particulars Year-2008 days

Year-2007 days

Inventory turnover period 9.8 21.9 Less. Payable payment period 95.3 138.0 Add. Receivable collection period 106.8 154.4 Length of Cash Operating Cycle 21.3 38.3

Inventory turnover period – payables payment period + receivable collection period

Dividend cover = Earnings per share Dividend per share



Balance Sheet of XYZ Limited As at Dec. 2009

From the above please calculate the followings: a) Current Ratio, b) Quick Ratio, c) Asset Turnover Ratio, d) ROCE, e) Debt Equity Ratio, f) Gearing Ratio, g) P/E Ratio, h) Dividend yield, i) Dividend cover and j) Interest cover.

Answer to the above question:

Particulars 2009 2008 Assets: Non-current Assets: Tangible Asset 8,02,180 6,56,071 Current Assets: Inventory 64,422 86,550 Receivables 10,02,701 853,441 Cash in Hand 1327 68,363 Total Current Assets 10,68,450 10,08,354 Total Assets 18,70,630 16,64,425 Equity and Liabilities Equity: Ordinary Share @Tk.10 each 2,10,000 2,10,000 Share Premium Account 48,178 48,178 Retained Earnings 6,30,721 3,93,791 Non-current Liabilities 10% Loan Notes 1,00,000 1,00,000 Current Liabilities 8,81,731 9,12,456 Total Equity and Liabilities 18,70,630 16,64,425

2009 2008 a)Current Ratio Current Assets 10,68,450 10,08,354 Current Liabilities 8,81,731 9,12,456 1.25:1 1.11:1 b) Quick Ratio Current Assets less inventory 10,04,028 921,804 Current Liabilities 8,81,731 9,12,456 1.14:1 1.01:1 c) Asset Turnover Ratio Revenue 30,95,576 19,09,051 Capital Employed 9,88,899 7,51,969 3.13 times 2.54 times d) ROCE PBIT 3,52,130 2,35,102 Capital Employed 9,88,899 7,51,969 35.61% 31.26% e) Debt Equity Ratio Total current + Non-current liabilities 9,81,731 10,12,456 Total Assets 18,70,630 16,64,425

52.46% 60.81% f) Gearing Ratio Non-current liabilities 1,00,000 1,00,000 Equity + Non-current liabilities 9,88,899 7,51,969



9. Apollo Drinks and Beverages Ltd. operates many outlets throughout the country. Some

of the vending machines in one of its outlets provide very little revenue, so the company is considering removing the machines and installing equipment to dispense soft ice cream. The equipment would cost Taka 80,000 and have an eight-year useful life. Incremental annual revenues and costs associated with the sale of ice cream would be as follows:

The vending machines can be sold for Tk.5,000 scrap values. The company will not purchase equipment unless it has a payback of three years or less. Should the equipment be purchased? Required:

i. Compute the net annual cash inflow. ii. Compute the payback period.

Answer to for i

Net Annual Cash Flow: Operating Income + Depreciation =20,000 + 10,000 =30,000

10.11% 13.31% g) P/E Ratio Market price per share 100 75 Earnings per share 12.76 9.23 7.83 8.12 h) Dividend yield Dividend per share 1.40 1.00 Market price per share 100 75 1.40% 1.33% i) Dividend cover Earnings per Share 12.76 9.23 Dividend per share 1.40 1.00 9.11 times 9.23 times j)Interest cover PBIT 3,52,130 2,35,102 Finance Cost 18,115 21,909 19.44 times 10.73 times

Particulars Taka Sales 1,50,000 Less. Cost of ingredients 90,000 Contribution margin 60,000 Less. Fixed expenses: Salaries 27,000 Maintenance 3,000 Depreciation 10,000 Total fixed expenses 40,000 Net operating income 20,000



Answer to for ii

Year Cash flow Cumulative cash flow

Balancing amount

0 -80,000 -80,000 1 35,000 35,000 -45,000 2 30,000 65,000 -15,000 3 30,000

Therefore, Payback period=2+ (15,000/30,000) =2.6 years

10. You are advised to calculate the Break Even Point from the following data:

Answer for b:

Break-even point:

In units = 1,50,000 10,000 -7,000

= 50 units In volume

= 1,50,000

1-(7,000/10,000) = Tk. 5,00,000

11. Product a currently sells for Tk.5, and demand at this price is 1,700 units. If the price fell to Tk.4.60, demand would increase to 2,000 units. Product B currently sells for Tk.8 and demand at this price is 9,500 units. If the price fell to Tk.7.50, demand would increase to 10,000 units.

In each of these cases, calculate: a) The price elasticity of demand (PED) for the price changes given; and b) The effect on total revenue, if demand is met in full at both the old and the new prices,

of the change in price.


(a) Product A: At price Tk.5

Change in quantity = Present Quantity- Previous Quantity

X 100 Previous Quantity

= 2000-1700 X 100 1700

= 17.64%(rise)

Particulars Taka Fixed Costs Monthly Lease Rent 100,000 Insurance 50,000 Total Monthly fixed costs 150,000 Variable Costs Materials 3,000 Labour 4,000 Total Variable Costs 7,000 Selling Price 10,000



Change in price = Present price- Previous price X 100 Previous price

= 4.60-5 X 100 5

= -8%(fall)

PED = Change in Quantity X 100 Change in Price

= 17.64 %

-8 %

= -2.20

Demand is elastic and a fall in price should result in such a large increase in quantity demanded that total revenue will rise. Impact after fall in price:

Revenue at old Price (Tk. 5 x 1700) Tk.8,500

Revenue at new Price (Tk.4.60 x 2,000) Tk.9,200

Increase in Total Revenue Tk.700

(b) Product B:

At price Tk.8

Change in quantity = Present Quantity- Previous Quantity

X 100 Previous Quantity

= 10000-9500 X 100 9500

= 5.26%(rise)

Change in price = Present price- Previous price X 100 Previous price

= 7.50-8 X 100 8

= -6.25%(fall)

Therefore,PED = Change in Quantity X 100 Change in Price

= 5.26 %

-6.25 % = -0.85

Demand is inelastic and a fall in price should result in only a relatively small increase in quantity demanded that total revenue will fall. Impact after fall in price:

Revenue at old Price (Tk. 8 x 9500) Tk.76,000

Revenue at new Price (Tk.7.50 x 10,000) Tk.75,000

Increase in Total Revenue (Tk.1000)



12. The following three companies have current asset financing structures which may be considered as aggressive, average and defensive:

Balance Sheet Particulars Aggressive Average Defensive Non-current Assets 50,000 50,000 50,000 Current Assets 50,000 50,000 50,000 100,000 100,000 100,000 Equity(Tk.1 per Share) 30,000 50,000 50,000 Long-term debt(average cost 10% p.a)

- 20,000 40,000

Current Liabilities(average cost 3% p.a) 70,000 30,000 10,000 100,000 100,000 100,000

Income Statement Particulars Aggressive Average Defensive PBIT 15,000 15,000 15,000 Less. Finance Cost (2,100) (2,900) (4,300)

12,900 12,100 10,700 Tax@30% (3,870) (3,630) (3,210) Net profit for the period 9,030 8,470 7,490

Requirement: Calculate current ratio and earnings per share for each company and comments on their strengths and weakness.

Answer to the above question:

Particulars Aggressive Average Defensive Current ratio 0.71:1 1.66:1 5:1 Earnings per share Tk.0.30 Tk.0.16 Tk.0.14

Aggressive It has a short-term credit than equity in it’s structure, returns a higher profit but at the cost of greater risk revealed in its relatively poor current ratio.

Average There is less risk here than in the aggressive company, as shown by the healthy current ratio, but considerably less return as well as seen in the EPS.

Defensive This is a low risk and low return company.

13.Calculate EOQ from the following information: Reagent costs Taka100 per Litre. 2000 Ltr.are to be used per annum and holding cost Tk.5 per Ltr. Each order placed costs Taka 200 against overhead.

EOQ = √ 2 x A x Cp Ch

A = Demand for the year Cp = Cost to place a single order Ch = Cost to hold one unit inventory for a year

EOQ =

√ 2 x 2000 x 200 5

= =

√ 8,00,000 5

400 kgs.



14.Following are opening and closing data of Apon Aloy Ltd.’s balance sheet and income statement for the year 2009. Calculate approximate length of the cash operating cycle.

Answer to the above question: Cash Operating Cycle=Inventory Turnover Period + Receivable collection period – Payable Payment Period

Inventory Turnover period Average Inventory X 365 COGS

= 6,50,000 X 365 60,00,000 = 39.54 days

Receivable Collection Period = Average Trade Receivables X 365 Credit Sales

= 8,50,000 X 365 10,000,000 = 31.02 days

Payable payment Period = Average Trade Payables X 365 COGS

= 2,25,000 X 365 6,000,000 = 13.68 days

Therefore, Cash Operating Cycle = (39.54 + 31.02-13.68) =56.88 days 15.Calculate Economic Value Addition from the following information’s:

Answer to the above question EVA= PBIT after tax – (Capital employed x Rate of cost of Capital)

2008 2007 2,77,930 – (9,88,899 x .12) 2,03,830– (7,51,969 x .12) =1,59,262 =1,13,594

As EVA increased by Tk.45,668 or 40% thus the business performance has improved.

Particulars 1 Jan 31 Dec Taka Taka

Accounts Receivable 800,000 900,000 Accounts payable 200,000 250,000 Inventory 600,000 700,000 Credit Sales 10,000,000 Cost of Goods Sold 6,000,000

Particulars 2008 2007 Taka Taka

PBIT after tax 2,77,930 2,03,830 Capital employed 9,88,899 7,51,969 Cost of Capital 12%



15.Calculate the Length of Cash Operating Cycle from the following information’s:

Sales 36,00,000 Average Receivable 3,06,000 Gross Margin 25% Inventories: Finished goods Work in progress Raw Materials

2,00,000 3,50,000 1,50,000

Average Payables 1,30,000 Inventory levels are constant Raw materials represent 60% of total production cost

Answer to the above question Cash Operating Cycle= (Inventory turnover period+ Receivable collection period-Payable payment period). Cost of Sales= (36,00,000 x .25)= Tk.27,00,000

Inventory turnover period= Average Inventory X 365 Cost of Sales

Raw Material= 1,50,000 X 365 27,00,000 x .60 = 34 days

Finished Goods & WIP= 5,50,000

X 365 27,00,000 = 74 days

Receivable collection period = Average Receivables X 365 Credit Sales

= 3,06,000 X 365 36,00,000 = 31 days

Payable payment period = 1,30,000 X 365 27,00,000 x .60 = 29 days

Therefore, Cash Operating Cycle= (108 days +31days-29 days) =110 days. 16.Voltar Company manufactures and sells a telephone answering machine. The

company's contribution format income statement for the most recent year is given below:

Particulars Total Per unit Percent of sales

Sales $1,200,000 $60 100% Less variable expenses 900,000 45 ?% Contribution margin 300,000 15 ?% Less fixed expenses 240,000 Net operating income $60,000 Requirement: a) Calculate break even point both in units and sales dollars.



b) To earn a minimum profit of $90,000. How many units will have to be sold to meet the target profit figure?

Margin of safety of safety both in dollars and percentage form

Answer to the above question for a

Sales = Variable expenses + Fixed expenses +Profit $60Q = $45Q + $240,000 + $0 $15Q = $240,000 Q = $240,000 / 15 per unit Q = 16,000 units; or at $60 per unit, $960,000

Answer to the above question for b

Sales = Variable expenses + Fixed expenses + Profits $60Q = $45Q + $240,000 + $90,000 $15Q = $3330,000 Q = $3330,000 / $15 Per unit Q = 22,000 Units

Answer to the above question for b

Margin of safety = Total sales – Break even sales* = $1,200,000 – $960,000 = $240,000 Margin of safety percentage = Margin of safety in dollars / Total sales = $240,000 / $1,200,000 = 20% *The break even sales have been calculated as follows: Sales = Variable expenses + Fixed expenses + Profit $60Q = $45Q + $240,000 + $0** $15Q = $240,000 Q = $240,000 / $15 per unit Q = 16,000 units; or at $60 per unit. $960,000 17.What Does Payback Period Mean?

The length of time required to recover the cost of an investment. Calculated as:

Payback Period All other things being equal, the better investment is the one with the shorter payback period. For example, if a project costs $100,000 and is expected to return $20,000 annually, the payback period will be $100,000 / $20,000, or five years. There are two main problems with the payback period method: 1. It ignores any benefits that occur after the payback period and, therefore, does not measure profitability. 2. It ignores the time value of money. Because of these reasons, other methods of capital budgeting like net present value, internal rate of return or discounted cash flow are generally preferred.



Present Value 18. Suppose you are depositing an amount today in an account that earns 5% interest,

compounded annually. If your goal is to have $5,000 in the account at the end of six years, how much must you deposit in the account today?

Answer to the above question The following information is given:

future value = $5,000 interest rate = 5% number of periods = 6

Present value = future value / (1 + interest rate) number of periods PV = FV/ (1 + r)t Inserting the known information, PV = $5,000 / (1 + 0.05)6 PV = $5,000 / (1.3401) PV = $3,731 Present Value Annuity 19. Suppose you determine that you can pay $5,000 per year on a loan. If the loan is for a period of

six years and the interest charged is 5% per year, how much can you borrow?

Answer to the above question The following information is given:

periodic cash flow = $5,000 interest rate = 5% number of cash flows = 6

We want to solve for the present value.

Using notation, such that:

CF = periodic cash flow PV = future value r = interest rate T = number of cash flows

PV = CF ((1- (1/ (1 + r) T)) / r) Inserting the known information, PV = $5,000 (5.0757) PV = $25,378



Future Value 20. Suppose you are depositing an $5,000 today in an account that earns 5% interest,

compounded annually. What will be the balance in the account at the end of six years if you make no withdrawals?


The following information is given: present value = $5,000 interest rate = 5% number of periods = 6

We want to solve for the future value. Future value = present value (1 + interest rate)number of periods FV = PV (1 + r)t Inserting the known information, FV = $5,000 (1 + 0.05)6 FV = $5,000 (1.3401) FV = $6,701

Future Value Annuity 21. Suppose you want to deposit an equal amount each year, starting in one year, in an account

that earns 5% interest, compounded annually. If your goal is to have $5,000 in the account at the end of six years, how much must you deposit in the account each year (for a total of six deposits)?


The following information is given: future value = $5,000 interest rate = 5% number of cash flows = 6

We want to solve for the cash flow. Using notation, such that: CF = periodic cash flow FV = future value r = interest rate T = number of cash flows

FV = CF (((1 + r) T) - 1) / r) Inserting the known information, $5,000 = CF (6.8019) CF = $5,000 / 6.8019 = $735



Problem: 22-

ABC Company Ltd is considering a long-term capital investment project called ZIP. The project will require an investment of Tk.1,20,000 and it will have a useful life of 4 years. Annual net income for ZIP is expected to be as follows:

Year-1 12,000 Year-2 10,000 Year-3 8,000 Year-4 6,000 Total 36,000

Depreciation is computed by the straight-line method with no salvage value. The company’s cost of capital is 12%. Requirement: (i)Compute annual rate of return. (ii)Compute payback period. (iii)Compute Net Present Value (iv)Should the project be accepted?


(i)Annual rate of return: Average expected annual return/Average investment =(36,000/4) / (1,20,000/2) =9,000/60,000 =.15 or 15%. (ii)Payback period: Cost of capital investment / Annual cash inflow Annual depreciation (1,20,000/4)=30,000

Year Cash Inflow Cumulative cash inflow

1 12,000 +30,000 42,000 2 10,000+30,000 82,000 3 8,000+30,000 1,20,000 4 6,000+30,000 1,56,000

Therefore, Payback period=3 years (iii) Net Present Value: Year Discount Rate Cash Flow Present Value 1 .89286 42,000 37,500 2 .79719 40,000 31,888 3 .71178 38,000 27,048 4 .63552 36,000 22,879 1,19,315

Capital Investment 1,20,000 Negative net present value (685)

(iv)The annual rate of return 15% is good. However the payback period is 75% of the project’s useful life and net present value is negative. The recommendation is to reject the project.



Table A-1 Future Value Interest Factors for One Dollar Compounded at k Percent for n Periods: FVIF k,n = (1 + k) nPeriod 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 20%

1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.22 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.21 1.2321 1.2544 1.2769 1.2996 1.3225 1.3456 1.443 1.0303 1.0612 1.0927 1.1249 1.1576 1.191 1.225 1.2597 1.295 1.331 1.3676 1.4049 1.4429 1.4815 1.5209 1.5609 1.7284 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5181 1.5735 1.6305 1.689 1.749 1.8106 2.07365 1.051 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.6851 1.7623 1.8424 1.9254 2.0114 2.1003 2.48836 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.8704 1.9738 2.082 2.195 2.3131 2.4364 2.9867 1.0721 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.828 1.9487 2.0762 2.2107 2.3526 2.5023 2.66 2.8262 3.58328 1.0829 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.3045 2.476 2.6584 2.8526 3.059 3.2784 4.29989 1.0937 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.999 2.1719 2.3579 2.558 2.7731 3.004 3.2519 3.5179 3.803 5.1598

10 1.1046 1.219 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 2.8394 3.1058 3.3946 3.7072 4.0456 4.4114 6.191711 1.1157 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531 3.1518 3.4785 3.8359 4.2262 4.6524 5.1173 7.430112 1.1268 1.2682 1.4258 1.601 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384 3.4985 3.896 4.3345 4.8179 5.3503 5.936 8.916113 1.1381 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523 3.8833 4.3635 4.898 5.4924 6.1528 6.8858 10.69914 1.1495 1.3195 1.5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.3104 4.8871 5.5348 6.2613 7.0757 7.9875 12.83915 1.161 1.3459 1.558 1.8009 2.0789 2.3966 2.759 3.1722 3.6425 4.1772 4.7846 5.4736 6.2543 7.1379 8.1371 9.2655 15.40716 1.1726 1.3728 1.6047 1.873 2.1829 2.5404 2.9522 3.4259 3.9703 4.595 5.3109 6.1304 7.0673 8.1372 9.3576 10.748 18.48817 1.1843 1.4002 1.6528 1.9479 2.292 2.6928 3.1588 3.7 4.3276 5.0545 5.8951 6.866 7.9861 9.2765 10.761 12.468 22.18618 1.1961 1.4282 1.7024 2.0258 2.4066 2.8543 3.3799 3.996 4.7171 5.5599 6.5436 7.69 9.0243 10.575 12.375 14.463 26.62319 1.2081 1.4568 1.7535 2.1068 2.527 3.0256 3.6165 4.3157 5.1417 6.1159 7.2633 8.6128 10.197 12.056 14.232 16.777 31.94820 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 4.661 5.6044 6.7275 8.0623 9.6463 11.523 13.743 16.367 19.461 38.33821 1.2324 1.5157 1.8603 2.2788 2.786 3.3996 4.1406 5.0338 6.1088 7.4002 8.9492 10.804 13.021 15.668 18.822 22.574 46.00522 1.2447 1.546 1.9161 2.3699 2.9253 3.6035 4.4304 5.4365 6.6586 8.1403 9.9336 12.1 14.714 17.861 21.645 26.186 55.20623 1.2572 1.5769 1.9736 2.4647 3.0715 3.8197 4.7405 5.8715 7.2579 8.9543 11.026 13.552 16.627 20.362 24.891 30.376 66.24724 1.2697 1.6084 2.0328 2.5633 3.2251 4.0489 5.0724 6.3412 7.9111 9.8497 12.239 15.179 18.788 23.212 28.625 35.236 79.49725 1.2824 1.6406 2.0938 2.6658 3.3864 4.2919 5.4274 6.8485 8.6231 10.835 13.585 17 21.231 26.462 32.919 40.874 95.39630 1.3478 1.8114 2.4273 3.2434 4.3219 5.7435 7.6123 10.063 13.268 17.449 22.892 29.96 39.116 50.95 66.212 85.85 237.37635 1.4166 1.9999 2.8139 3.9461 5.516 7.6861 10.677 14.785 20.414 28.102 38.575 52.8 72.069 98.1 133.176 180.314 590.66836 1.4308 2.0399 2.8983 4.1039 5.7918 8.1473 11.424 15.968 22.251 30.913 42.818 59.136 81.437 111.834 153.152 209.164 708.80240 1.4889 2.208 3.262 4.801 7.04 10.286 14.974 21.725 31.409 45.259 65.001 93.051 132.782 188.884 267.864 378.721 * 50 1.6446 2.6916 4.3839 7.1067 11.467 18.42 29.457 46.902 74.358 117.391 184.565 289.002 450.736 700.233 * * *

Table A-2 Future Value Interest Factors for a One-Dollar Annuity Compouned at k Percent for n Periods: FVIFA k,n = [(1 + k) n - 1 ] / kPeriod 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 20%

1 1 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.22 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1 2.11 2.12 2.13 2.14 2.15 2.16 2.23 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.31 3.3421 3.3744 3.4069 3.4396 3.4725 3.5056 3.644 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.641 4.7097 4.7793 4.8498 4.9211 4.9934 5.0665 5.3685 5.101 5.204 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.2278 6.3528 6.4803 6.6101 6.7424 6.8771 7.44166 6.152 6.3081 6.4684 6.633 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 7.9129 8.1152 8.3227 8.5355 8.7537 8.9775 9.92997 7.2135 7.4343 7.6625 7.8983 8.142 8.3938 8.654 8.9228 9.2004 9.4872 9.7833 10.089 10.405 10.73 11.067 11.414 12.9168 8.2857 8.583 8.8923 9.2142 9.5491 9.8975 10.26 10.637 11.028 11.436 11.859 12.3 12.757 13.233 13.727 14.24 16.4999 9.3685 9.7546 10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.579 14.164 14.776 15.416 16.085 16.786 17.519 20.799

10 10.462 10.95 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937 16.722 17.549 18.42 19.337 20.304 21.321 25.95911 11.567 12.169 12.808 13.486 14.207 14.972 15.784 16.645 17.56 18.531 19.561 20.655 21.814 23.045 24.349 25.733 32.1512 12.683 13.412 14.192 15.026 15.917 16.87 17.888 18.977 20.141 21.384 22.713 24.133 25.65 27.271 29.002 30.85 39.58113 13.809 14.68 15.618 16.627 17.713 18.882 20.141 21.495 22.953 24.523 26.212 28.029 29.985 32.089 34.352 36.786 48.49714 14.947 15.974 17.086 18.292 19.599 21.015 22.55 24.215 26.019 27.975 30.095 32.393 34.883 37.581 40.505 43.672 59.19615 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772 34.405 37.28 40.417 43.842 47.58 51.66 72.03516 17.258 18.639 20.157 21.825 23.657 25.673 27.888 30.324 33.003 35.95 39.19 42.753 46.672 50.98 55.717 60.925 87.44217 18.43 20.012 21.762 23.698 25.84 28.213 30.84 33.75 36.974 40.545 44.501 48.884 53.739 59.118 65.075 71.673 105.93118 19.615 21.412 23.414 25.645 28.132 30.906 33.999 37.45 41.301 45.599 50.396 55.75 61.725 68.394 75.836 84.141 128.11719 20.811 22.841 25.117 27.671 30.539 33.76 37.379 41.446 46.018 51.159 56.939 63.44 70.749 78.969 88.212 98.603 154.7420 22.019 24.297 26.87 29.778 33.066 36.786 40.995 45.762 51.16 57.275 64.203 72.052 80.947 91.025 102.444 115.38 186.68821 23.239 25.783 28.676 31.969 35.719 39.993 44.865 50.423 56.765 64.002 72.265 81.699 92.47 104.768 118.81 134.841 225.02622 24.472 27.299 30.537 34.248 38.505 43.392 49.006 55.457 62.873 71.403 81.214 92.503 105.491 120.436 137.632 157.415 271.03123 25.716 28.845 32.453 36.618 41.43 46.996 53.436 60.893 69.532 79.543 91.148 104.603 120.205 138.297 159.276 183.601 326.23724 26.973 30.422 34.426 39.083 44.502 50.816 58.177 66.765 76.79 88.497 102.174 118.155 136.831 158.659 184.168 213.978 392.48425 28.243 32.03 36.459 41.646 47.727 54.865 63.249 73.106 84.701 98.347 114.413 133.334 155.62 181.871 212.793 249.214 471.98130 34.785 40.568 47.575 56.085 66.439 79.058 94.461 113.283 136.308 164.494 199.021 241.333 293.199 356.787 434.745 530.312 * 35 41.66 49.994 60.462 73.652 90.32 111.435 138.237 172.317 215.711 271.024 341.59 431.663 546.681 693.573 881.17 * * 36 43.077 51.994 63.276 77.598 95.836 119.121 148.913 187.102 236.125 299.127 380.164 484.463 618.749 791.673 * * *

Present Value and Future Value Tables



Present Value and Future Value TablesTable A-3 Present Value Interest Factors for One Dollar Discounted at k Percent for n Periods: PVIF k,n = 1 / (1 + k) nPeriod 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 20%

1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.885 0.8772 0.8696 0.8621 0.83332 0.9803 0.9612 0.9426 0.9246 0.907 0.89 0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.69443 0.9706 0.9423 0.9151 0.889 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7312 0.7118 0.6931 0.675 0.6575 0.6407 0.57874 0.961 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.735 0.7084 0.683 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.48235 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.713 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.40196 0.942 0.888 0.8375 0.7903 0.7462 0.705 0.6663 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.33497 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.547 0.5132 0.4817 0.4523 0.4251 0.3996 0.3759 0.3538 0.27918 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.582 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269 0.305 0.23269 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843 0.263 0.193810 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3522 0.322 0.2946 0.2697 0.2472 0.2267 0.161511 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.2366 0.2149 0.1954 0.134612 0.8874 0.7885 0.7014 0.6246 0.5568 0.497 0.444 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 0.2076 0.1869 0.1685 0.112213 0.8787 0.773 0.681 0.6006 0.5303 0.4688 0.415 0.3677 0.3262 0.2897 0.2575 0.2292 0.2042 0.1821 0.1625 0.1452 0.093514 0.87 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.232 0.2046 0.1807 0.1597 0.1413 0.1252 0.077915 0.8613 0.743 0.6419 0.5553 0.481 0.4173 0.3624 0.3152 0.2745 0.2394 0.209 0.1827 0.1599 0.1401 0.1229 0.1079 0.064916 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 0.1883 0.1631 0.1415 0.1229 0.1069 0.093 0.054117 0.8444 0.7142 0.605 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929 0.0802 0.045118 0.836 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.212 0.1799 0.1528 0.13 0.1108 0.0946 0.0808 0.0691 0.037619 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.031320 0.8195 0.673 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.124 0.1037 0.0868 0.0728 0.0611 0.0514 0.026121 0.8114 0.6598 0.5375 0.4388 0.3589 0.2942 0.2415 0.1987 0.1637 0.1351 0.1117 0.0926 0.0768 0.0638 0.0531 0.0443 0.021722 0.8034 0.6468 0.5219 0.422 0.3418 0.2775 0.2257 0.1839 0.1502 0.1228 0.1007 0.0826 0.068 0.056 0.0462 0.0382 0.018123 0.7954 0.6342 0.5067 0.4057 0.3256 0.2618 0.2109 0.1703 0.1378 0.1117 0.0907 0.0738 0.0601 0.0491 0.0402 0.0329 0.015124 0.7876 0.6217 0.4919 0.3901 0.3101 0.247 0.1971 0.1577 0.1264 0.1015 0.0817 0.0659 0.0532 0.0431 0.0349 0.0284 0.012625 0.7798 0.6095 0.4776 0.3751 0.2953 0.233 0.1842 0.146 0.116 0.0923 0.0736 0.0588 0.0471 0.0378 0.0304 0.0245 0.010530 0.7419 0.5521 0.412 0.3083 0.2314 0.1741 0.1314 0.0994 0.0754 0.0573 0.0437 0.0334 0.0256 0.0196 0.0151 0.0116 0.004235 0.7059 0.5 0.3554 0.2534 0.1813 0.1301 0.0937 0.0676 0.049 0.0356 0.0259 0.0189 0.0139 0.0102 0.0075 0.0055 0.001736 0.6989 0.4902 0.345 0.2437 0.1727 0.1227 0.0875 0.0626 0.0449 0.0323 0.0234 0.0169 0.0123 0.0089 0.0065 0.0048 0.001440 0.6717 0.4529 0.3066 0.2083 0.142 0.0972 0.0668 0.046 0.0318 0.0221 0.0154 0.0107 0.0075 0.0053 0.0037 0.0026 0.000750 0.608 0.3715 0.2281 0.1407 0.0872 0.0543 0.0339 0.0213 0.0134 0.0085 0.0054 0.0035 0.0022 0.0014 0.0009 0.0006 *

Table A-4 Present Value Interest Factors for a One-Dollar Annuity Discounted at k Percent for n Periods: PVIFA = [1 - 1/(1 + k)n] / kPeriod 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 20%

1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.885 0.8772 0.8696 0.8621 0.83332 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.808 1.7833 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257 1.6052 1.52783 2.941 2.8839 2.8286 2.7751 2.7232 2.673 2.6243 2.5771 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.2459 2.10654 3.902 3.8077 3.7171 3.6299 3.546 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.855 2.7982 2.58875 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522 3.2743 2.99066 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.2305 4.1114 3.9975 3.8887 3.7845 3.6847 3.32557 6.7282 6.472 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.033 4.8684 4.7122 4.5638 4.4226 4.2883 4.1604 4.0386 3.60468 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 4.9676 4.7988 4.6389 4.4873 4.3436 3.83729 8.566 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.759 5.537 5.3282 5.1317 4.9464 4.7716 4.6065 4.03110 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.8892 5.6502 5.4262 5.2161 5.0188 4.8332 4.192511 10.368 9.7868 9.2526 8.7605 8.3064 7.8869 7.4987 7.139 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337 5.0286 4.327112 11.255 10.575 9.954 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.4206 5.1971 4.439213 12.134 11.348 10.635 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.5831 5.3423 4.532714 13.004 12.106 11.296 10.563 9.8986 9.295 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 6.0021 5.7245 5.4675 4.610615 13.865 12.849 11.938 11.118 10.38 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474 5.5755 4.675516 14.718 13.578 12.561 11.652 10.838 10.106 9.4466 8.8514 8.3126 7.8237 7.3792 6.974 6.6039 6.2651 5.9542 5.6685 4.729617 15.562 14.292 13.166 12.166 11.274 10.477 9.7632 9.1216 8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 6.0472 5.7487 4.774618 16.398 14.992 13.754 12.659 11.69 10.828 10.059 9.3719 8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 6.128 5.8178 4.812219 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.6036 8.9501 8.3649 7.8393 7.3658 6.938 6.5504 6.1982 5.8775 4.843520 18.046 16.351 14.877 13.59 12.462 11.47 10.594 9.8181 9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 6.2593 5.9288 4.869621 18.857 17.011 15.415 14.029 12.821 11.764 10.836 10.017 9.2922 8.6487 8.0751 7.562 7.1016 6.687 6.3125 5.9731 4.891322 19.66 17.658 15.937 14.451 13.163 12.042 11.061 10.201 9.4424 8.7715 8.1757 7.6446 7.1695 6.7429 6.3587 6.0113 4.909423 20.456 18.292 16.444 14.857 13.489 12.303 11.272 10.371 9.5802 8.8832 8.2664 7.7184 7.2297 6.7921 6.3988 6.0442 4.924524 21.243 18.914 16.936 15.247 13.799 12.55 11.469 10.529 9.7066 8.9847 8.3481 7.7843 7.2829 6.8351 6.4338 6.0726 4.937125 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.8226 9.077 8.4217 7.8431 7.33 6.8729 6.4641 6.0971 4.947630 25.808 22.396 19.6 17.292 15.372 13.765 12.409 11.258 10.274 9.4269 8.6938 8.0552 7.4957 7.0027 6.566 6.1772 4.978935 29.409 24.999 21.487 18.665 16.374 14.498 12.948 11.655 10.567 9.6442 8.8552 8.1755 7.5856 7.07 6.6166 6.2153 4.991536 30.108 25.489 21.832 18.908 16.547 14.621 13.035 11.717 10.612 9.6765 8.8786 8.1924 7.5979 7.079 6.6231 6.2201 4.9929

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