f9 formulas

ACCA F9 Formula Sheets June 2014

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CHAPTER 2 INVESTMENT APPRAISAL TECHNIQUES

Total Profit= Total Cash inflows – Depreciation

PV= Present Value

FV= Future Value

R= Rate of interest or Cost of Capital

N= No. of years

(

)

L= lower discount rate

H= Higher discount rate

NL= NPV at lower discount rate

NH= NPV at higher discount rate


2

CHAPTER 3 ADVANCED DISCOUNTING CASH FLOW TECHNIQUES

Fisher Effiect

(1+m) = (1+r) (1+i)

r= Real discount rate

m= Money discount rate

i= Inflation rate

Calculating NPV when dealing with cash flows

Pro Forma ( Big 5)

1. NTR (inflows and outflows from trading)

2. Tax Payable (NTR tax rate)

3. Tax Allowance (Require separate working)

4. Investment

5. Residual Value

(Change in discount rate)


3

Expected Value = EV = px

p= Probability if an outcome

x= The value of an outcome

CHAPTER 5 COST OF CAPITAL

Cost of Equity: Calculated in two ways:

1)

PO= Ex-div market price of share ( Ex-div means dividend has just paid)

d= Constant dividend pa

Ke= Cost of Equity

( Cash inflow from the dividends is normally perpetuity)

D1= dividend to be paid on one year time

G= Constant rate of growth in dividends

Estimating growth of dividends= Two methods

A. √

– 1

Do= current dividend

Dn- dividend n years ago


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B. Gordon’s growth model= g = rb

R= return on invested funds

B= proportion of funds retained

2) CAPM= Rf + (Rm-Rf) β

Ke= Required return from individual security

Rf= Risk free rate of interest

Rm= Return on market portfolio

B= Beta factor of individual security

Irredeemable debt with tax= ke =

I= Interest paid

T= marginal rate of tax

P0= ex interest (similar to ex div)

Redeemable Debt with tax

Technique:

Columnar approach

Identify the cash flows

Discount at 5% and 10%

Use the IRR formula

Relevant cash flows would be:

YEAR CASH FLOW

0 Market value of loan note P0

1 to n Annual interest payments I (1-T)

N Redemption value of loan RV

Weighted Average Cost of Capital (WACC) =

+


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CHAPTER 6 Capital structure and risk adjusted WACC

Cost of capital and shareholder wealth= Market Value=

WACC and shareholder wealth= Market Value=

Converting geared beta of sector into geared beta of investing company

STEPS:

1) Equity Beta (Proxy Company_ Same Industry)

2) Degear (Equity β → Asset β):

Convert the geared beta of sector company to ungeared beta of sector company by

removing the gearing risk.

Ba=

( Data from sector company)

3) Regear (Asset β → Equityβ):

Convert the ungeared beta (above) into geared beta of investing company.

Be=

(Data from investment company)

4) Use CAPM formula to calculate cost of equity

Ke= Rf + (Rm – Rf) β

CHAPTER 7 Ratio Analysis

Profitability Ratios

ROCE=

ROE=

______________________________________________________________________________


6

Gearing Ratos

Operational grearing=

Equity Gearing=

Capital or Total Gearing=

Interest Cover=

Stock Market Ratios

Earning per share (EPS)=

PE Ratio=

→ [ ]

PE Ratio=

→ [ ]

Dividend Cover=

→ [ ]

Dividend Cover=

→ [ ]

Dividend Yield=

→ [ ]

Dividend Yield=

→ [ ]


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CHAPTER 8 RAISING EQUITY FINANCE

Theatrical Ex-Rights Price (TERP)=

Value of rights= TERP – Issue price

Value of rights + Issue price of new share = Total paid by third party

Calculate change in share price after new investment made

Tip: Most likely examiner gives PE ratio and earnings and from that you have to calculate the required

price

STEPS

1. Calculate the earnings

2. Calculate the earnings per share

3. Calculate the share price after the investment

4. Calculate the change in share price

= Difference between TERP and final share price

CHAPTER 9 WORKING CAPITAL MANAGEMENT

Operating Cycle

Inventory turnover period=

Receivable turnover period=

Average payable period=

Operating Cycle= ( Inventory days + Receivable days) – Payable days


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Liquidity Ratio

Current Ratio =

Acid Test Ratio =

_____________________________________________________________________________________

Cost of Financing= Receivables Interest rate

_____________________________________________________________________________________

Discount for early settlement

(Ex.4 – pg.257)

STEPS

1) Calculate the receivable balance for those who continue with existing terms

= £10m 60%

= £1800,000

2) Calculate the receivable balance for those who pay after 30 days

= £10m 40%

= £328,767

3) Calculate the interest rate cost of these

= (£1800,000 0.06) + (£328,767 0.06)= £147,726

4) Calculate the cost of discount

= £10m 40% 0.5%= £20,000

So, Total Cost of finance= £127,726 + £20,000= £147,726

Decision: Compare it with financing cost of receivables. Choose the lower cost.


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Calculation of order quantity that minimizes the costs (using table)

Pro Forma

Average Stock ( Order quantity 2)

No. of orders PA (Total demand Order quantity)

_____________________________________

£

Total annual holding costs (Avg. stock holding cost/unit)

Total annual ordering costs (No. of orders Cost/order)

Calculation of order quantity that minimizes the costs (using formula)

Q= √

Q= Economic Order Quantity

Co= Cost per order

D= Annual demand

Ch= Cost of holding one unit for one year

Managing Cash

There are 3 areas associated with managing cash:

1) Miller –Orr model

It involves upper and lower limits of cash.

Difference between upper and lower limit is called Spread

Calculating the spread:

Spread= (

)

Transaction costs= Cost of investing as limits are reached

Variance= Measure of uncertainty. It is square of standard deviation of cash balance.

Interest Rate= Rate of interest per day

Calculations for exams point of view

Setting the lower limit: Always given in exams

Setting the upper limit: Lower limit + Spread

Return Point: lower limit + 1/3 of spread


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2) Baumol Model

Using EOQ model to manage the cash

(same formula as previously studied)

Q= √

Q= Economic Order Quantity

Co= Cost per order

D= Annual demand

Ch= Cost of holding one unit for one year

3) Cash Budget

(Using Example on pg.270)

Reqd. Calculate the material purchased for two months

STEPS

A) Calculate sale units for each month ( Sales Revenue / Unit Selling price)

B) Calculate production units (sale units + cl.stock – op.stock = Production units)

C) Calculate cost of raw material used (raw material cost + cl.stock – op.stock= Material

purchased). State in which month payments are made- usually after a month.

D) Calculate all relevant overheads.

Per forma for cash budget

RECEIPTS

Sales

SUB TOTAL

PAYMENTS

Material

Labor

Fix OH

Var OH

Expenses

Purchase cost

SUB TOTAL

NET CASH FLOW ( Receipts – Payments)

Bal b/d

Bal c/d


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CHAPTER 11 VALUATION

BUSINESS AND ASSETS VALUATION (for exam purpose mean valuing shares or debts). There are 3

methods:

1) Asset Basis

Net Assets= Total Assets – Total Liabilities

2) Dividend Valuation Model (DVM)

This could be used to calculate MV of company or value of a share

P0=

PO= Ex div share price

D0= Current dividend that has just been paid

G= Dividend growth

Ke= Cost of capital

Ke= CAPM formula= Rf + β(Rm-Rf)

G=

= √

– 1

So, Market Value = Share Price (P0) Total no. of shares


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3) Income/Earnings Based Method: There are 2 ways of doing this:

1.1) PE Ratio

Recall previously used formulas:

PE Ratio=

→ [ ]

PE Ratio=

→ [ ]

EPS=

This can be used to value shares in unquoted companies as:

Value per Share= EPS P/E Ratio

Value of Company= PAT P/E Ratio

1.2) Earnings Yield: Inverse of PE Ratio

Earnings Yield=

It could be used ro value the shares or market capitalization of a company by:

Price per share=

Value of Company=


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2) Present value of free cash flows

Used to calculate NPV & Market price.

Method:

A) Identify free cash flows

Operating Cash flows (e-g inflow and outflow from material, labour)

Revenue from sales of assets

= Trading cash flows

Tax payable at trading cash flows

Tax relief

Synergy (advantage) from merger

Capital investment

= Free Cash Flows

B) Select suitable time horizon: The question may specify the time horizon or it maybe

perpetuity.

C) Identify Suitable discount rate: It may have to be calculated e-g by use of WACC or

CAPM. If it is perpetuity we use dividend growth model

D) Finally calculate the present value of cash flows over time horizon less value of any

debt.

Valuation of Debt

Assume Debt= £100 Always

1) Irredeemable of Debt

MV=

If you are given taxation details then:

MV=

MV= Market price of debenture now (Yr0)

I= Annual interest starting in one year tme

R= Debt holder required return


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2) Redeemable Debt

The market value is the present value of future cash flows which include:

Interest payments for years in issue

Redemption value

3) Convertible Debt

With convertible debt the holder have option at conversion date to either

Convert to shares

Retain the debt until redemption

Choose the option which is higher

The market value is present value of future cash flows which include:

Interest payments

Conversion/Redemption value

Floor Value= PV of interest + PV of redemption money

4) Preference Shares

Recall formula for cost of capital formula:

Ke/kp=

This could be re-arranged for preference shares as

P0=

D= Constant annual preference dividend

P0= Ex-div market value of share

Kp= Cost of preference shares


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CHAPTER 12 RISK

Impact of Purchasing Power Parity (PPP)

=

Impact of Interest Rate Parity (IRP)

=

International Fisher Effect

Recall this formula when dealing with DCF & inflation

(1+m)= (1+r) (1+i)

This formula could be re-arranged for calculating the real interest rate:

R=

M= Interest rate

I= Inflation rate

Spot Rate with spread

$: = 1.3990-1.4010

[

]

If converting first currency second currency = DIVIDE

If converting second currency first currency = MULTIPLY

If company is buying first currency ($) LOWER RATE

If company is selling first currency ($) HIGHER RATE


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Questions including forward discount

STEPS:

1) Calculate the forward rate ( Spot rate + Forward discount)

2) Multiply or divide

3) Use buy rate or sell rate

f9 formulas

Documents

money discount rate

real discount rate

inflation rate

cost of capital cost

cost of equity ke

higher discount rate

dividend cover

expected value