The Cost of Capital
Chapter 12
Cost of Capital
 The firm’s average cost of funds, which is
the average return required by the firm’s
investors
 What must be paid to attract funds
The Logic of the Weighted
Average Cost of Capital
 The use of debt impacts a fim’s ability to
use equity, and vice versa, so the
weighted average cost must be used to
evaluate projects, regardless of the
specific financing used to fund
a particular project
Basic Definitions
 Capital component
 types of capital used by firms to raise
money
 kd = before tax interest cost
 kdT = kd(1-T) = after tax cost of debt
 kps = cost of preferred stock
 ks = cost of retained earnings
 ke = cost of external equity (new stock)
Basic Definitions
 WACC = weighted average cost of capital
 Capital structure
 combination of different types of capital
used by a firm
After-Tax Cost of Debt
 The relevant cost of new debt—its yield
to maturity (YTM)
 Taking into account the tax deductibility
of interest
 Used to calculate the WACC
 kdT = bondholders’ required rate of
return minus tax savings
 kdT = kd - (kd  T) = kd(1-T)
Cost of Preferred Stock
 Rate of return investors require on the
firm’s preferred stock
 the preferred dividend divided by the net
issuing price
k ps 
Dps
NP

Dps
P0 - Flotation costs
Cost of Retained Earnings
 Rate of return investors require on the
firm’s common stock
D̂1
k Three
 g  k̂ s
s  ksolutions:
RF  RP 
P0
1. CAPM
2. Bond yield plus risk premium
3. Discounted cash flow (DCF)
The CAPM Approach
k s  k RF  k M - k RF  β s
The Bond-Yield-PlusPremium Approach
 Estimate a risk premium above the bond
interest rate
 Judgmental estimate for premium
 “Ballpark” figure only
k s  Bond yie ld  Risk premium
 10%  4%  14%
The Discounted Cash Flow
(DCF) Approach
 Price and expected rate of return on a
share of common stock depend on the
dividends expected on the stock
P0 

D̂1
1  k s 
1

D̂2

1  k s 
2
 1  k 
t 1
D̂t
t
s

D̂
1  k s 

DCF Approach
 Internal equity, ks
 based on the fact that investors demand the
firm use funds that are retained to earn an
appropriate rate of return
D̂1
ks 
g
P0
Cost of Newly Issued
Common Stock
 External equity, ke
 based on the cost of retained earnings
 adjusted for flotation costs (the expenses of
selling new issues)
D̂1
D̂1
ke 
g
g
NP
P0 1  F 
Target Capital Structure
 Optimal capital structure
 percentage of debt, preferred stock, and
common equity that will maximize the
price of the firm’s stock
Weighted Average Cost of
Capital, WACC
 A weighted average of the component costs
of debt, preferred stock, and common
equity
 Proportion   After - tax    Proportion   Cost of    Proportion   Cost of  
 
  
 
  
 


 
of

cost
of

of
preferred

preferred

of
common

common
 
  
 
  
 













debt   debt   
stock   stock    equity   equity  


Wd

k dT

Wps

k ps

Ws

ks
Marginal Cost of Capital
 MCC
 the cost of obtaining another dollar of new
capital
 the weighted average cost of the last dollar
of new capital raised
MCC Schedule
 Marginal cost of capital schedule
 a graph that relates the firm’s weighted
average of each dollar of capital to the total
amount of new capital raised
 reflects changing costs depending on
amounts of capital raised
MCC Schedule
 Weighted Average Cost of Capital (WACC) (%)
WACC3=11.5%
11.5 WACC2=11.0%
11.0 -
10.5 -
WACC1=10.5%
New Capital Raised
(millions of dollars)
100
150
Break Point
 BP
 the dollar value of new capital that can be
raised before an increase in the firm’s
weighted average cost of capital occurs
Break
Total amount of lower costcapital of a giventype

Point Proportion of this type of capital in the capital structure
MCC Schedule
 Weighted Average Cost of Capital (WACC) (%)
WACC3=11.5%
11.5 -
WACC2=11.0%
11.0 -
10.5 -
WACC1=10.5%
BPRE
BPDebt
New Capital Raised
(millions of dollars)
100
150
MCC Schedule
 Schedule and break points depend on
capital structure used
MCC Schedule
 Weighted Average Cost of Capital (WACC) (%)
Smooth, or Continuous,
Marginal Cost of Capital
Schedule
WACC
0-
Dollars of New Capital Raised
Combining the MCC and
Investment Opportunity Schedules
 Use the MCC schedule to find the cost of
capital for determining whether a project
should be purchased
 Investment Opportunity Schedule (IOS)
 graph of the firm’s investment
opportunities ranked in order of the
projects’ rates of return
Combining the MCC and
Investment Opportunity Schedules
Percent
12.0 -
ReturnC = 12.0%
ReturnB = 11.6%
ReturnD = 11.5%
11.5 -
ReturnE = 11.3%
WACC2=11.0%
11.0 10.5 -
WACC3=11.5%
MCC
IRRA = 10.8%
WACC1=10.5%
Optimal Capital
Budget - $139
20
40
60
80
IOS
100 120 140 160 180
New Capital Raised and invested (millions of dollars)
End of Chapter 12
The Cost of
Capital