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:
Dn  Pn
D1
D2
P0 

 ... 
1
2
(1  i ) (1  i )
(1  i ) n
• We can assume that D’s growth will be
constant. (geometric progression).
D0 (1  g )
D0 (1  g )
D1
D1
P0 

or K e 
g 
g
Ke  g
Ke  g
P0
P0
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
P0
Time
Dividend growth:
• Either old dividend divided by new
dividend and answer looked up on
discount factor table for that number of
years or;
 D0
1  g  
 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
Portfolio theory
Rat
e
of
Ret
urn
Investment A
Investment B
Time
Rat
e
of
Ret
urn
Combined effect
(Portfolio Return)
Time
Systematic risk
Portfolio
Risk
Unsystematic
(unique) Risk
Systematic (Market)
Risk
15-20
Number of
securities
CAPM
Retur
n
Rm
Security
Market Line
(SML)
Rf
1 Systematic Risk

• 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
Slope = 
>1
Market Return
Ry
Rm
Slope = 
<1
Market
Return Rm
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.
I
I (1  t )
•
P 
or K 
0
Kd
d
Po
• 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
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
@22%
(3.92)
IRR = original % +

higherreturn
Difference
%


range


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%
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
WACC 
k eg  E
ED

k dg (1 - C tax )  D
ED
WACC
Cost of equity
Cost
of Cap
%
WACC
Cost of debt
0
X
Gearing
Market Value of firm
£
Market
value of
equity
0
X
Gearing
Market value
• MV of company = Future Cash Flows
•
WACC