Chapter 11
THE COST OF
CAPITAL
© 2000 South-Western College Publishing
COST OF CAPITAL
The return an investor receives on debt, preferred stock,
or common equity is a cost to the company
Costs are returns adjusted for taxes and transactions cost
Overall cost is a weighted average of these
Component Costs
TM 11-1 Slide 1 of 2
CAPITAL STRUCTURE
The mix of capital components in use
Component
Debt
Preferred Stock
Equity
Total Capital
$000
$30,000
$10,000
$60,000
$100,000
%
30%
10%
60%
100%.
RELATED CONCEPTS
The Target Capital Structure
Raising Money in the Proportions of the Capital Structure
TM 11-1 Slide 2 of 2
THE WEIGHTED AVERAGE CALCULATION THE WACC
A firm's overall cost of capital is the average of the costs of its
separate sources weighted by the proportion of each source used
Example of Calculation
Capital
Component
Debt
Preferred Stock
Common Stock
Value
$60,000
$50,000
$90,000
$200,000
Weight Cost
.30
x 9% = 2.70%
.25
x 11% = 2.75%
.45
x 14% = 6.30%
1.00
WACC = 11.75%
TM 11-2
CAPITAL STRUCTURE AND COST - BOOK
VS MARKET VALUES
A Source of Confusion:
Both capital structure and component costs can be viewed in terms of either the
book or market values of the underlying capital
1. CAPITAL STRUCTURE
Initial Capital Structure - Book and Market Values Equal
$
Equity
10,000 shrs x $10
= $100,000
Debt
100 bonds x $1,000
= $100,000
Total
$200,000
%
50%
50%
100%
Now imagine that stock price increases to $12, while interest rates climb driving
the price of the bonds down to $850
-Book Values Don't Change-
TM 11-3 Slide 1 of 3
Market-Value-Based Capital Structure
Equity 10,000 shrs x $12
Debt
100 bonds x $850
Total
$
%
= $120,000 58.5%
= $ 85,000 41.5%
$205,000 100.0%
(From Tables 11-1 and 2)
2. COMPONENT RETURNS
• Every security has a return on the money initially invested to buy it
and a current return that's available to new investors in the
secondary market.
• For example, a bond pays its coupon rate on the original investment
of its face value and the market yield to a new buyer.
TM 11-3 Slide 2 of 3
3. THE APPROPRIATE PERSPECTIVE FOR THE WACC
CALCULATION
Book Values - Existing Capital - Already Committed
Market Values - New Capital - Next Year's Projects
IRR and NPV Evaluate Newly Proposed Projects
Therefore, Market Values Are Appropriate
4. THE CUSTOMARY APPROACH
Structure: Maintain the existing structure based on market prices,
or
strive for a target structure based on market prices.
Component Costs: Based on market prices
TM 11-3 Slide 3 of 3
CALCULATING THE WACC
Three Steps
1. Develop a market value based capital structure.
2. Adjust market returns to reflect
component costs of capital.
3. Calculate WACC.
TM 11-4
STEP ONE:
DEVELOPING MARKET VALUE BASED CAPITAL STRUCTURES
EXAMPLE 11-2
Debt: Two thousand bonds were issued five years ago at a coupon rate of
12%. They had thirty year terms and $1,000 face values. They are now
selling to yield 10%.
Preferred Stock:
Four thousand shares of preferred are outstanding
each of which pays an annual dividend of $7.50. They originally sold to yield
15% of their $50 face value. They're now selling to yield 13%.
Equity:
200,000 shares of common stock are outstanding currently selling
at $15 per share.
TM 11-5 Slide 1 of 3
SOLUTION:
Debt:
Pb
= PMT[PVFAk,n] + FV[PVFk,n]
= $60[PVFA5,50] + $1,000[PVF5,50]
= $60(18.2559) + $1,000(.0872)
= $1,182.55
Market Value = $1,182.55 x 2,000 = $2,365,100
Preferred Stock:
Pp 
Market Value
Dp
k

$7.50
 $57.69
.13
= $57.69 x 4,000
= $230,760
TM 11-5 Slide 2 of 3
Common Equity:
Market Value = $15.00 x 200,000 = $3,000,000
Market Value Based Weights:
Debt
Preferred
Equity
$
$2,365,100
230,760
3,000,000
$5,595,860
%
42.3%
4.1%
53.6%
100.0%
TM 11-5 Slide 3 of 3
STEP TWO:
CALCULATING COMPONENT COSTS OF CAPITAL
Adjustments To Investor's Returns Reflect The Effect
Of Financial Markets and Taxes
Taxes Reduce the Effective Cost of Debt
kd(1-T)
Flotation Costs Increase the Effective Cost of a Component
Component
Investor's return
k
cost of
=

(1  f )
(1  f )
capital
TM 11-6
ILLUSTRATIONS
DEBT: Cost of debt = kd (1 - T)
EXAMPLE 11-3
Blackstone Inc. has bonds outstanding which yield 8% to investors buying
them now. The marginal tax rate is 37%
SOLUTION:
Cost of debt = kd (1 - T)
= .08 (1-.37)
= 5.4%
PREFERRED STOCK:
Cost of
Dp
kp
Preferred 

(1  f )Pp (1  f )
Stock
EXAMPLE 11-4
Francis Corporation's preferred stock yields new investors 9%. Flotation
costs are 11%.
SOLUTION:
Cost of
kp
9%


 10.1%
Preferred
(1  f ) 1 .11
Stock
TM 11-7
COMMON EQUITY - RETAINED EARNINGS:
No Adjustments:
Internally Generated and Not Tax Deductible
The CAPM Approach - The Required Rate of Return
kX = kRF + (kM - kRF)bX
The Dividend Growth Approach - The Expected Rate of Return
D0 ( 1  g )
ke 
g
P0
The Risk Premium Approach
ke = kd + rpe
COMMON EQUITY - NEW STOCK:
Cost of New Equity
D0 ( 1  g )
ke 
g
(1  f )P0
EXAMPLE 11-8
Periwinkle Inc.'s last annual dividend was $1.65, its stock sells for
$33.60, and it is expected to grow at 7.5%.
SOLUTION:
Cost of
$1.65(1.075 )

 .075  13.5%
new
(.88 )$33.60
Equity
TM 11-8 Slide 2 of 2
THE MARGINAL COST OF CAPITAL (MCC)
A graph showing how the WACC changes as a firm raises more capital
during a planning period, usually a year
A Typical MCC Schedule
WACC
WACC
Total
Capital
Raised
The MCC breaks upward when the cost of a capital component increases.
The first break usually occurs when retained earnings runs out and outside
equity is raised at higher cost.
TM 11-9
ILLUSTRATION OF MCC CONSTRUCTION
Capital
Structure
Weights
Capital
Component
Cost
With equity from RE
Debt
Equity
.4
.6
x
x
8% = 3.2%
10% = 6.0%
WACC = 9.2%
.4
.6
x
x
8% = 3.2%
12% = 7.2%
WACC = 10.4%
With equity from new stock
Debt
Equity
If expected RE = $3M and the capital structure is 60% equity, the first break
in the WACC occurs at $3M / .60 = $5M
Table 11-4 (modified)
WACC
10.4%
WACC
9.2%
$5M
$10M
Figure 11-1 The Brighton Company
The Marginal Cost of Capital (MCC) Schedule
TM 11-10 Slide 2 of 2
COMBINING THE MCC AND THE INVESTMENT
OPPORTUNITY SCHEDULE (IOS)
WACC
Project
IRRs
IOS
A
MCC
WACC=10.4%
B
C
9.2%
D
E
$5M
$10M
Figure 11-2 The Marginal Cost of Capital (MCC) Schedule and
The Investment Opportunity Schedule (IOS)