cost of capital, capm, gordon's growth, wacc and cost of debt
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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