Cost of Capital

Dr Bryan Mills

% return

Risk and 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:

P

0  ( 1

D

1 

i

) 1  ( 1

D

2 

i

) 2  ...



D n

( 1  

i

)

P n n

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

geometric progression)

.

P

0 

D

0

K

( 1  

g g

) 

e K e D

1 

g

or

K e



D

0 ( 1 

g

) P 0  g  D 1 P 0 

g

Assumptions

• Uses next year’s dividend so must be

ex div

• Fixed rate of growth • Dividends paid in perpetuity • Share price is discounted future cashflow P Dividend Stream Cum Div P 0 Time

Dividend growth:

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

or

; 1 

g

  

D

0

D



n

  1

n

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

Rat e of Ret urn Rat e of Ret urn

Portfolio theory

Investment A

Investment B Time Combined effect (Portfolio Return) Time

Portfolio Risk

Systematic risk

Unsystematic (unique) Risk Systematic (Market) Risk 15-20

Number of securities

Retur n R m R f

CAPM

Security Market Line (SML) 1 Systematic Risk 

• Rf = Risk Free therefore  = 0 • Rm = Market Portfolio (max diversification - all systematic) therefore  = 1 • SML can be written as an equation: • R j = R f +  j (R m • Called CAPM - R f )

R y

Slope =  >1 Market Return

R y R m

Slope =  <1 Market Return

R m

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.

P

0 

I K d

or K d 

I

( 1 

P o t

) • 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

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 1 2 3 4 Cashflow (74.00) 10.00

10.00

10.00

110.00

Discount Factor 1.00

0.87

0.76

0.66

0.57

Year 1 2 3 4 Cashflow (74.00) Discount Factor 1.00

10.00

10.00

10.00

110.00

0.82

0.67

0.55

0.45

PV (74.00) 8.70

7.56

6.58

62.89

11.73

NPV @15% NPV @22% PV (74.00) 8.20

6.72

5.51

49.65

(3.92)

IRR = original % +   Difference % higher return range   Lowest % Difference in % Higher return Range between high and low Higher Divided by Range Times by Difference

Return pa

0.15

0.07

11.73

15.649

0.7493

0.0524

20%

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 W

ACC

 k eg E   E  D k dg (1 E C tax )  D  D

Cost of Cap % 0

WACC

Cost of equity WACC Cost of debt X Gearing

£

Market Value of firm

0 X Gearing Market value of equity

Market value

• • MV of company = Future Cash Flows WACC