The Cost of Capital
March 15, 2004
• D e b t
Sources of capital
– B ank loans
– B ond issues
– C onvertible bonds
– D elaying payment on accounts payable
• P referred equity
• Common equity
– C ommon stock issues
– R etained earnings
Effect of taxes on the cost of capital
• I nterest payments are a deductible expense, but returns to stockholders (i.e., dividends, retained earnings) are not.
• => For every dollar of return paid on equity, the firm must earn 1/(1- ) dollars of income before taxes; for every dollar of interest paid, the firm need only only earn one dollar of income before taxes.
• T he effective ‘after-tax’ c ost of debt = (1- ) r b
• T he after-tax cost of equity is r s
• Q uestion: Why don’t firms rely exclusively on debt to raise capital?
Other questions
• W hat determines the ‘capital structure’ of the company -- i.e., the proportions of the different types of financing that it uses?
• W hat other factors affect the relative cost of the different types of financing? For a given type of financing, do all projects and companies have access to capital at the same cost?
The relationship between investment risk and expected returns
• Each class of financing is perceived by investors to be associated with a different level of risk
– B onds
– P referred stock
– C ommon stock
• T he require d rat e o f return is the minimum rate of return necessary to induce in vestors to buy or hold a security
– F or any given security, the required rate of return, r, equals the riskless rate of interest, R F , plus a risk premium,
r = R F+
The relationship b etween risk and required r ate of return
R equired rate of return (%)
A
= K A - R F
K B = 1 1.0
Capital Market Line (CML) k = R F +
= 6.0 + .5
}
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
B B F
= K - R
- - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - -
{
K A = 8.0 R F = 6.0
0
Risk(
(4%) (10%)
Source: W eston and Brigham
Nuclear Energy Economics and Policy analysis
The effect of rising interest rate on the required rate of return
Required rate of return (%)
CML : k = 8.0 + .5
2
k B 2 =13
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
CML : k = 6.0 + .5
1
- - - - - - - - - - - - - - - - - - -
k A 2 =10 - - - - - - - - - - R F 2 = 8
R F 1 = 6
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
4% 10% Risk ( ) Source: W eston and Brigham
Nuclear Energy Economics and Policy analysis
The Eff ect of Changing In v estor A ttitudes on the R equired R ate of R eturn
Required rate of return (%)
CML 2
= 6.0 + .7
(pessimistic)
k B2 =13
k B1 =1 1
k A2 =8.8
k A1 =8.0
R F =6
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - -
- - - - - - - - - - - - -
- - - - - - - - - - - - -
CML 1 = 6 .0 + .5
(optimistic)
4% 10% Risk ( )
Source: Weston and Brigham
Nuclear Energy Economics and Policy analysis
Source s o f risk
• M acroeconomic risks
– I nterest rates
– T ax policies
• I ndustry-specific business risks
– T echnological uncertainties
– M arket uncertainties
– C ompetitor uncertainties
• F irm-specific business risks
– M anagerial performance
• F inancial risks
– E ffect of degree of financial ‘leverage’ (debt-to-equity ratio)
Effec t o f financia l leverag e o n th e cos t o f capital
E x a m pl e (f r o m W e s t o n a n d Bri g h a m):
C o n s i d e r thr e e firm s i n t h e s a me in d u s t r y th a t a r e id e n tic a l e x c e pt f o r t h e i r f i na n c ial p o lic i es . F i rm A : N o deb t ( 0 % l e ve r a g e )
F i rm B : 5 0 % deb t fi n a n c e
F i rm C : 7 5 % deb t fi n a n c e
FI R M A
T o tal as s e ts
$200
To t a l d e b t
Ne t w o r t h of equ i t y in v e s t ors
T o tal lia b iliti e s (c la i m s )
$ 0
$200
$200
FI R M B
T o tal as s e ts
$200
T o tal d e b t ( 6 %) Ne t w o r t h of equ i t y in v e s t ors
T o tal lia b iliti e s
$100
$100
$200
FI R M C
T o tal as s e ts
$200
T o tal d e b t ( 6 %) Ne t w o r t h of equ i t y in v e s t ors
T o tal lia b iliti e s
$150
$50
$200
Stockholder Returns under V arious Leverage and Economic Conditions
Economic Conditions
Level
|
2% |
5% |
6% |
8% |
1 1% |
14% |
|
$4 |
$10 |
$12 |
$16 |
$22 |
$28 |
|
Firm A: Leverage Factor 0% |
|||||
Rate of return on assets before interest and taxes
Earning s before interest and taxes (EBIT)
V ery poor poor Indifference
Normal Good V ery Good
|
EBIT |
$4 |
$10 |
$12 |
$16 |
$22 |
$28 |
|
Less: I nterest expense |
0 |
0 |
0 |
0 |
0 |
0 |
|
T axable I ncome |
$4 |
$10 |
$12 |
$16 |
$22 |
$28 |
|
T axes (50%) a |
2 |
5 |
6 |
8 |
1 1 |
14 |
|
A vailable to common stock |
$2 |
$5 |
$6 |
$8 |
$11 |
$14 |
|
Percent return on net worth |
1% |
2.5% |
3% |
4% |
5.5% |
7% |
|
Firm B: Leverage Factor 50% |
||||||
|
EBIT |
$4 |
$10 |
$12 |
$16 |
$22 |
$28 |
|
Less: I nterest expense |
6 |
6 |
6 |
6 |
6 |
6 |
|
T axable i ncome |
$(2) |
$4 |
$6 |
$10 |
$16 |
$22 |
|
T axes (50%) a |
(1) |
2 |
3 |
5 |
8 |
1 1 |
|
A vailable to common stock |
$(1) |
$2 |
$3 |
$5 |
$8 |
$1 1 |
|
Percent return on net worth |
-1% |
2% |
3% |
5% |
8% |
11% |
|
Firm C: Leverage Factor 75% |
||||||
|
EBIT |
$4 |
$10 |
$12 |
$16 |
$22 |
$28 |
|
|
Less: I nterest expense |
9 |
9 |
9 |
9 |
9 |
9 |
|
|
T axable i ncome |
$(5) |
$1 |
$3 |
$7 |
$13 |
$19 |
|
|
T axes (50%) a |
(2.5) |
.5 |
1.5 |
3.5 |
6.5 |
9.5 |
|
|
A vailable to common stock |
$(2.5) |
$ .5 |
$ 1.5 |
$ 3.5 |
$ 6.5 |
$ 9.5 |
|
|
Percent return on net worth |
-5% |
1% |
3% |
7% |
13% |
19% |
|
a The tax calculation assumes that losses are carried back and result in tax credits
Nuclear Energy Economics and Policy analysis
Rate of return on net worth (after corporate income taxes)
20
C: Debt/assets = 75 percent
15
10
B: Debt/assets = 50 percent
5
3
A: Debt/assets = 0 percent
0
5 6
1 0
15
20
Rate of return on assets (before corporate income taxes)
-5
Nuclear Energy Economics and Policy Analysis
The required return on equity increases with the leverage ratio (i.e., debt-to-equity ratio)
Re t u r n o n e q u i t y
B u s i n e s s r i sk p r em iu m Ri s k f r e e r e t u r n
Lev er a g e r a t i o
There is, in general, a degree of leverage at which the cost of capital is minimized
A f t e r t a x c o s t of c a p i t a l
Co s t o f e q u i t y
C o m pos i t e co s t of c a p i t a l
Co s t o f d e b t
Lev er a g e
ra t i o
Note: the more stable the industry is , the higher the optimal le verage ratio (i.e., the greater the use of debt)
Margina l cos t o f capita l fo r a give n firm *
|
Marginal cost of capital |
|
|
(%) |
|
|
New capital ($) |
|
C o st o f c a pi t a l a n d I R R
Ma r g i n a l c o s t of c a p i t a l
IR R
C u m u la t i v e in v e s t me n t or b o r r o w i n g a m t .
*At each stage, the capit a l structurei s c hosen to mi ni mi ze the cost of capital
Co mplicat ions :
1. Determination of optim al capital structure/ marginal co st of capital curve is co m p lex.
2. Effect of capital rationing. Firm s ma y be unwilling to operate at th e intersection:
• U n c ertainties in projections ma y cau s e firm to ‘play it safe’
• E xpectation of better investment opportunities in future years ma y cause firm s to stop short of intersection point.