Chapter 17-Cost of Capital

8/13/2019 Chapter 17-Cost of Capital

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1. The overall approach

How do we find a suitable discount rate?

- weigh the costs of each type of long term

finance

- Weighted Average Cost of Capital (WACC)



1. The overall approach

Traded debt Non-traded debt

Irredeemable Redeemable Convertible Bank loans

Debt

Sources of long-term finance

Prefer

ence sharesE

quity



2. Estimating the cost of capital

Key ideas in estimating cost of capital

A. Cost of a debt or equity instrument is:

- The rate that discounts the future streams of cash-flows to

- The present price of the instrument

B. The cost of debt or equity instrument is implicit in the price.

C. To evaluate cost of a debt or equity instruments we will use

- prices

- streams of cash-flows (interest, dividends etc.)



2. Estimating the cost of equity

COST OF EQUITY – 2 models

A. The Dividend Valuation Model (DVM)

- constant dividends

- constant growth in dividends

B. The Capital Asset Pricing Model (CAPM)




The Dividend Valuation Model (DVM)

The cost of equity finance is the return the investors expect to

achieve on their shares.

Assumptions:

- Stream of cash-flows is the stream of dividends paid out by

the company

- Dividends will be paid in perpetuity

- Dividends will be constant or growing at a fixed rate





Assuming constant dividends

Where:

D = the constant dividend from year 1 to infinity

P0 = share price now (year 0)

r e = shareholders’ required return, expressed as decimal

00 P

Dr

r

D P

ee





Assuming constant growth in dividends

Where:

g = constant rate of growth in dividends

D1

= the dividend to be received in one year

D0 (1+g) = the dividend just paid adjusted for one year’s growth



g r

D

g r

g D P

ee

10

0

)1(





Assuming constant growth in dividends

Where:

g = constant rate of growth in dividends

D1

= the dividend to be received in one year

D0 (1+g) = the dividend just paid adjusted for one year’s growth



g P

D g

P

g Dr

e

0

1

0

0 )1(





Ex-dividend (ex-div) vs Cum-dividend price

Cum-div

Ex-div

Dividend

declared

Share goes

ex-div

Dividend

paid

Share goesex-div





Use ex-dividend (ex-div) price

In some question the cum-dividend price is

given and a dividend is due shortly

Cum div share price – Dividend due = Ex div share price





Estimating annual growth

- extrapolating based on past dividend patterns

- assuming growth is dependent on the level of

earnings retained in the business





Estimating growth (g) from past dividends

Also known as geometric average.

1

1

0

n

ago yearsn Dividend

D g





The earnings retention model (Gordon’s growth model)

where:

r = the accounting rate of return

b = earnings retention rate

r b g



3. Estimating the cost of preference shares

Use DVM since preference shares pay constant dividend

Where:

D = the constant dividend from year 1 to infinity


K p = cost of preference share

0

0

P

D K

K

D P p

p



4. Estimating the cost of debt

Types of debt

Traded debt Non-traded debt

Irredeemable Redeemable Convertible Bank loans

Loan notes – bonds – loan stock – marketable debt– used interchangeably




Cost of irredeemable debt

Cost of debt to company.

Where:

I = annual interest starting in one year’s time

MV = market value of the loan note now (year 0 )

K d (1-T) = post-tax cost of debt to the company

T = corporate taxation

MV

T I T K

d

)1()1(




Cost of redeemable debt

The company will:

- pay interest for a number of years and then

- repay the principal (sometimes at a premium or a discount

to the original loan).

Expected cahs-flow stream:

- interest paid to redemption;

- repayment of principal.

Market price = PV of interest and redemption payment




Cost of redeemable debt

Cost of redeemable debt to the company - the IRR of the following

MV Price paid to invest in debt instrument (x)

T 1-n Interest received × (1-T) xTn Capital repayment x




Cost of redeemable debt at current market price

Use the formula for irredeemable debt

MV T I T K d )1()1(




Cost of convertible debt

A form of loan note that allows the investor to choose between

taking the redemption proceeds or converting the loan note

into a pre-set number of shares.

Method:

(1) Calculate the value of the conversion option (estimated value

of shares on option date);

(2) Compare the conversion option with the cash option. Assume

all investors will choose the option with the higher value.

(3) Calculate the IRR of the flows as for redeemable debt




Cost of non-tradeable debt

Includes bank loans and other non-tradeable fixed interest loans

Simply adjust for tax relief

Cost to company = I×(1-T)




Weighted Average Cost of Capital (WACC)

1. Calculate weights for each source of capital

2. Estimate cost of each source of capital

3. Multiply the proportion of each source in the total sources of

capital by the cost of that source4. Sum the results of step 3 to get the WACC

V d and V e = the market values of debt and equity

K e = the cost of equity

K d (1-T) = the (post-tax) cost of debt

)1( T K

V V

V K

V V

V WACC d

d e

d e

d e

e




The average is known as Weighted Average Cost of Capital (WACC)

Choice of weights

- Book values (BVs)

- Market values (MVs)

Whenever possible choose market values



7. Cost of equity – Capital Asset Pricing Model (CAPM)

A. CAPM relies on the following assumptions:

- Investors would require a rate of return at leastequal to the risk-free rate

- To compensate for any extra-risk taken, theyrequire a premium



7. Estimating the cost of equity – the Capital Asset Pricing Model

Capital Asset Pricing Model (CAPM)

Shows how the minimum required rate of return on a quoted

security depends on its risk.

premium Risk return free Risk returnquired Re

CAPM - works out a formula for the risk premium




B. CAPM relies on the following assumptions (continued)

- Investors are risk averse;

- Investors deal with risk by way of diversification ;

- Invest in companies whose returns are negatively correlated

- Eliminate company specific risk (unsystematic risk)

- Only face the systematic risk (market risk)




Reducing risk by combining investments - Diversification

Total

portfolio

risk

No. of securities

Systematic risk

(Market risk)

Unsystematic risk

(firm specific risk)

15-20

securities

1 security




C. CAPM relies on the following assumptions (continued)

- Investors judge investments by the correlation of their returns with the

average market return

)(Re f m f R R Rreturnquired

Rf = risk-free rate of return

Rm = average return on the market

β = relative level of systematic risk (relative to the market)





Interpretation of beta

β is a measure of the systematic risk of an investment relative to that

of the market.

β >1 – the investment is riskier than the average

- returns have same direction as average market returns but change quicker

0< β < 1 – the investment is less risky than the average- returns have same direction as average market returns but change quicker

β = 0 – the investment is risk free

- no volatility in returns in respect to the average market returns





Useful in calculating risk-adjusted cost of equity for projects with risk

profiles that are different than the current risk profile of the

business.

Find a beta factor – by reference to the beta factor of a similar

company operating in the new business are

CAPM – gives you beta and the required rate of return

- this helps compute the cost of equity

But if the project is financed with both equity and debt we need to

weigh the cost of the two sources of finance

Chapter 17-Cost of Capital

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