12-1
Review
• In capital budgeting, we discount the cash flows of a
project to find the NPV
• In stock valuation, we discount the cash flows
(dividends) of a stock to find the stock price
• In bond valuation, we discount the cash flows
(interests and par value) of a bond to find the bond
price
• What discount rate to be used?
– The expected/required rate of return of the capital
providers
– Depends on the riskiness (market risk, beta) of
the cash flows to the capital providers
1
12-2
Sources and cost of Capital
• Sources
– Common stock/share or equity (S or E)
– Preferred stock/share (P)
– Bond or debt (B or D)
• Cost of capital
– A weighted (market value) average of
• Cost of equity, rS
• Cost of preferred stock, rP
• After-tax cost of debt, (1-TC)rB
2
12-3
Sources and cost of Capital
Current Assets
Current Liabilities
Cost of Goods Sold
Debts
Interests
Taxes
Preferred Stocks
Preferred Stock Dividends
Long-term Assets
Common Stocks
Earnings to Common Stocks
Public Assets
Government
3
12-4
WACC
 S 
 P 
 B 
rWACC = 
  rS + 
  rP + 
  rB  (1 − TC )
S +P+B
S +P+B
S +P+B
• Why WACC?
– An investment requires $100 today and pays
$111 in one year
– You withdraw $80 from your bank account
which pays 10% per year and borrow $20 from
the bank at 15% interest rate
– What discount rate should be used?
4
Cost of Preferred Stock (Perpetual Debt)
• Preferred stock
DP
DP
PP =
 rP =
rP
PP
• Perpetual debt
I
I
PB =  rB =
rB
PB
(YTM)
5
12-6
Cost of Debt
• Zero-coupon bond
1
T
F
F
PB =
 rB =   − 1
T
(1 + rB )
 PB 
(YTM)
• Coupon bond
I
I
I
PB =
+
+
+
2
3
(1 + rB ) (1 + rB )
(1 + rB )
I
F
....+
+
T
(1 + rB )
(1 + rB )T
(YTM)
6
The Cost of Equity Capital
Firm with
excess cash
Pay cash dividend
Shareholder
invests in
financial
asset
A firm with excess cash can either pay a
dividend or make a capital investment
Invest in project
Shareholder’s
Terminal
Value
Because stockholders can reinvest the dividend in risky financial assets,
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk.
7
Cost of Equity (Constant Growth Model)
• Dividend valuation model
𝐷1
𝑟𝑆 =
+𝑔
𝑃0
• Only works for stocks that have constant growth
• Have to estimate the growth rate, g
8
12-9
The Cost of Equity (CAPM)
𝑟𝑆 = 𝑟𝒇 + β𝑠 (𝑟𝑀 − 𝑟𝒇 )
• Suppose a stock has a beta of 1.5, the market
return is 16% and the risk-free rate is 6%
𝑟𝑆 = 0.06 + 1.5(0.16 − 0.06) = 0.21
• If this company is 100% equity financed, rWACC =
rS. So we use 21% to calculate NPV for any
projects that have similar risk of existing assets.
9
12-10
IRR
Project
The Cost of Equity (CAPM)
Good
A
projects
21%
B
6%
C
SML
Bad projects
Firm’s risk (beta)
1.5
An all-equity firm should accept a project whose IRR exceeds
the cost of equity capital and reject projects whose IRRs fall
short of the cost of capital.
10
Estimation of Beta
𝐶𝑜𝑣(𝑅𝑖 , 𝑅𝑀 ) σ𝑖𝑀
β𝑖 =
= 2
𝑉𝑎𝑟(𝑅𝑀 )
σ𝑀
• Most analysts argue that betas are generally stable
for firms remaining in the same industry.
• That’s not to say that a firm’s beta can’t change.
– Changes in product line, technology or
financial leverage
• If you believe that the operations of the firm are
similar to the operations of the rest of the industry,
you should use the industry beta. Don’t forget
about adjustments for financial leverage.
11
12-12
Determinants of Beta
• Business Risk
– Cyclicity of Revenues
– Operating Leverage
• Financial Risk
– Financial Leverage
12
12-13
Cyclicity of Revenues
• Highly cyclical stocks have high betas.
– Empirical evidence suggests that retailers and automotive
firms fluctuate with the business cycle.
– Transportation firms and utilities are less dependent upon the
business cycle.
• Note that cyclicity is not the same as variability—
stocks with high standard deviations need not have
high betas.
– Movie studios have revenues that are variable, depending
upon whether they produce “hits” or “flops,” but their
revenues are not especially dependent upon the business
cycle.
13
Operating Leverage
• The degree of operating leverage measures how
sensitive a firm (or project) is to its fixed costs.
• Operating leverage increases as fixed costs rise and
variable costs fall.
• Operating leverage magnifies the effect of cyclicity
on beta.
• The degree of operating leverage is given by:
Change in 𝐸𝐵𝐼𝑇
%Δ𝐸𝐵𝐼𝑇
𝐸𝐵𝐼𝑇
𝐷𝑂𝐿 =
൙Change in Sales =
%Δ𝑆
Sales
14
Operating Leverage
$
Total
costs
Fixed costs
 EBIT
 Volume
Fixed costs
Volume
Operating leverage increases as fixed costs rise
and variable costs fall.
15
12-16
Operating Leverage
EBIT in millions
5.00
With FC
4.00
3.00
No FC
Break-even point
Advantage to
fixed costs
2.00
1.00
0.00
500
(1.00)
Disadvantage
to fixed costs
1,000
1,500
Sales in quantity
16
Financial Leverage
• Operating leverage refers to the sensitivity to the
firm’s fixed costs of production.
• Financial leverage is the sensitivity of a firm’s
fixed costs of financing.
• The degree of financial leverage is given by:
Change in 𝐸𝑃𝑆
%Δ𝐸𝑃𝑆
𝐸𝑃𝑆
𝐷𝐹𝐿 =
൙Change in 𝐸𝐵𝐼𝑇 =
%Δ𝐸𝐵𝐼𝑇
𝐸𝐵𝐼𝑇
17
12-18
Financial Leverage
EPS
10.00
Debt
8.00
6.00
Break-even
point
No Debt
Advantage
to debt
4.00
2.00
0.00
(2.00)
1,000
Disadvantage
to debt
2,000
3,000
EBIT in
dollars, no
taxes
18
Financial Leverage and Beta
– A (the risk of the assets) is determined by the
business risk (and operating leverage)
– S (the risk of the equity) increases when B/S
increase (higher financial leverage)
• Financial leverage always increases the equity
beta relative to the asset beta
𝐵
𝛽𝑠 = 𝛽𝐴 + (1 − 𝑇𝐶 )(𝛽𝐴 − 𝛽𝐵 )
𝑆
19
12-20
The Firm versus the Project
• Any project’s cost of capital depends on the use to
which the capital is being put—not the source.
• Therefore, it depends on the risk of the project and not
the risk of the company.
20
12-21
Project
IRR
Capital Budgeting & Project Risk
The SML can tell us why:
Hurdle
rate
SML
Incorrectly accepted
negative NPV projects
𝑅𝒇 + β𝐹𝐼𝑅𝑀 (𝑅𝑀 − 𝑅𝒇 )
rf
FIRM
Incorrectly rejected
positive NPV projects
Firm’s risk (beta)
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value.
21
12-22
Liquidity and the Cost of Capital
• The cost of trading an illiquid stock reduces the
total return that an investor receives.
• Investors thus will demand a high expected return
when investing in stocks with high trading costs.
• This high expected return implies a high cost of
capital to the firm.
22
12-23
Liquidity and the Cost of Capital
Liquidity
An increase in liquidity, i.e., a reduction in trading costs,
lowers a firm’s cost of capital.
23
12-24
Liquidity and Adverse Selection
• There are a number of factors that determine the
liquidity of a stock.
• One of these factors is adverse selection.
• This refers to the notion that traders with better
information can take advantage of specialists who
have less information.
• The greater the heterogeneity of information, the
wider the bid-ask spreads, and the higher the
required return on equity.
24
12-25
What the Corporation Can Do
• A stock split would increase the liquidity of the shares.
• Companies can also facilitate stock purchases through
the Internet.
• Direct stock purchase plans and dividend reinvestment
plans handled on-line allow small investors the
opportunity to buy securities cheaply.
• The companies can also disclose more information,
especially to security analysts, to narrow the gap
between informed and uninformed traders. This should
reduce spreads.
25
12-26
Summary and Conclusions
• The expected return on any capital budgeting project
should be at least as great as the expected return on a
financial asset of comparable risk. Otherwise the
shareholders would prefer the firm to pay a dividend.
• A project’s required return depends on the project’s .
• A project’s  can be estimated by considering
comparable industries or the cyclicity of project
revenues and the project’s operating leverage.
• If the firm uses debt, the discount rate to use is the
rWACC.
• In order to calculate rWACC, the cost of equity and the
cost of debt applicable to a project must be estimated.
26
12-27
Textbook Exercises
• Chapter 13
– 10, 11, 16, 19, 20, 23
27