Cost of Capital

Dr Bryan Mills

Risk and Return

% return

% risk

Order of risk

• Treasury bills and gilts (risk free)

• Loan Notes – But ranked from AAA to BBB – with specialist

‘junk bonds’ being BB and less

• Equity

Dividend Valuation Model

• Share price must be equal to or less than future cash flows:

nnn

i

PD

i

D

i

DP

)1(...

)1()1( 22

11

0

• We can assume that D’s growth will be constant. (geometric progression).

ggD

KgK

D

gK

gDP e

ee

0

1

0

0100 P

D g

P

)1(or

)1(

Assumptions

• Uses next year’s dividend so must be ex div

• Fixed rate of growth

• Dividends paid in perpetuity

• Share price is discounted future cashflowP

Time

P0

Cum Div

Dividend Stream

Dividend growth:

• Either old dividend divided by new dividend and answer looked up on discount factor table for that number of years or;

n

nD

Dg

101

Example:

• If a company now pays 32p and used to pay 20p 5 years ago what is the rate of growth?

• 20(1+g)n = 32• (1+g)n = 32• 20• 1 + g = (1.60)1/5• 1 + g = 1.1• growth is 10%

Gordon’s Growth Model• Balance sheet asset value of £200, a profit of £20 in the year and a

dividend pay out of 40% (in this case £8) we would expect the new balance to be £212 (old + retained profit).

• If the ARR and retention policy remain the same for the next year what will the dividend growth be?

• Profit as a % of capital employed is £20/£200 = 10%• Next year has the same ARR then:• 10% X £212 = £21.20 is our new profit• as the dividend is 40% this equates to:• 40% X £21.20 = £8.48• Which represents a growth of (8.48-8)/8 = 6%

• Which could have been found much quicker (!) by:

• g = rb, g = 10% X 60%, g = 6%

Test

• Share price is £2, dividend to be paid soon is 16p, current return is 12.5% and 20% is paid out – what is cost of equity?

• g is rb – refer back to DVM for cost of equity

Portfolio theory

Investment A

Investment B

Time

Rat

e of

Ret

urn

Rat

e of

Ret

urn

Time

Combined effect (Portfolio Return)

Systematic risk

15-20

Portfolio Risk

Number of securities

Systematic (Market) Risk

Unsystematic (unique) Risk

CAPM

Rf

Rm

Return

1 Systematic Risk

Security Market Line (SML)

• Rf = Risk Free therefore = 0

• Rm = Market Portfolio (max diversification - all systematic) therefore = 1

• SML can be written as an equation:

• Rj = Rf + j(Rm - Rf)

• Called CAPM

Ry

Market Return Rm

Slope = >1

Ry

Market Return Rm

Slope = <1

Test

• Paying a return of 9%, gilts are at 5.5% and the FTSE averages 10.5% - what is the beta – and what does this value mean?

Aggressive and Defensive Shares

• If the risk free rate is 10% and the market index has been adjusted upward from 16% to 17% what will be the effect on shares with Betas of 1.4 and 0.7 accordingly?

• Shares with Betas greater than 1 are aggressive - they are over-sensitive to the market

• Shares with Betas less than 1 are defensive - they are under-sensitive to the market

• Assumptions of CAPM • perfect capital market• unrestricted borrowing at the risk free rate• uniformity of investor expectations• forecasts based on a single time period

• Advantages of CAPM:• provides a market based relationship between risk and return• demonstrates the importance of systematic risk• is one of the best methods of calculating a company's cost of

equity capital• can provide risk adjusted discount rates for project appraisal

• Limitations of CAPM: • avoids unsystematic risk by assuming a diversified

portfolio - how reliable is this?• Only looks at return in the most simple of ways (rate of

return not split into growth, dividends, etc.)• Only based on one-period• Can be difficult to estimate Rf Rm • Does not work well for investments that have low betas,

seasonality, low PE ratios - partly because it overstates the rate of return needed for high betas and understates the rate needed for low betas

Irredeemable Securities:

• In this case the company never returns the principal but pays interest in perpetuity.

•

• An equation we have seen before with I (interest) replacing the dividend (D)

• Note that tax relief relates to the company and not the market value

od P

tI

K

IP

)1(Kor d0

Redeemable Securities:

• Debenture priced at £74 with a coupon of 10% (remember this is 10% of £100). The interest has just been paid and there are four years until the redemption (at par) and final interest are paid.

• IRR of cashflows

Year Cashflow Discount Factor PV

(74.00) 1.00 (74.00)

1 10.00 0.87 8.70

2 10.00 0.76 7.56

3 10.00 0.66 6.58

4 110.00 0.57 62.89

NPV 11.73

@15%

Year Cashflow Discount Factor PV

(74.00) 1.00 (74.00)

1 10.00 0.82 8.20

2 10.00 0.67 6.72

3 10.00 0.55 5.51

4 110.00 0.45 49.65

NPV (3.92)

@22%

IRR = original % +

Lowest % 0.15

Difference in % 0.07

Higher return 11.73

Range between high and low 15.649

Higher Divided by Range 0.7493

Times by Difference 0.0524

Return pa 20%

range

returnhigher %Difference

Interesting point:

• Debt redeemable at current market price has the same cost (and formula) as irredeemable debt

Others

• Convertible– Redemption value is higher of cash

redemption or future value of shares

• Non-tradable debt– ‘normal’ loans – just use (1-t)

• Preference sahres– Not really debt but use D/P

WACC

• Step by Step Approach:

• Calculate weights for each source of capital (source/total)

• Estimate cost of each source Multiply 1 and 2 for each source

• Add up the result of 3 to get combined cost of capital

DE

D)C-(1k

DE

Ek W taxdgeg

ACC

WACC

0

Cost of Cap %

XGearing

Cost of equity

WACC

Cost of debt

Market Value of firm

0

£

XGearing

Market value of equity

Market value

• MV of company = Future Cash Flows

• WACC