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Ch 10: The Cost of Capital
WACC = wdrd(1 - T) + wpsrps + wcers
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The Cost of Capital: Preliminaries
 What is it?
 Why we care?
The Cost of Capital: Three Component Costs
 The Costs of Debt
 The Cost of Preferred Stock
 The Cost of Common Stock
The Weighted Average Cost of Capital
Flotation Cost Adjustment
Risk-Adjusted Cost of Capital
Divisional and Project Costs of Capital
Other Issues
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Cost of Capital: Georgia Pacific Co.
“On a market-value basis, our
debt-to-capital ratio was 47
percent. By employing this capital
structure, we believe that our
weighted average cost of capital is
nearly optimized – at
approximately 10 percent …..”
from Georgia Pacific Co. Annual Report
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The Cost of Capital
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Simply speaking, it refers to the opportunity cost
that a firm incurs in raising capital to finance new
projects.
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Opportunity cost: The return investors could earn on
alternative investments of equal risk.
Ways to finance new project
o
o
“GE issued 6% 20-year bonds and borrowed capital from JP
Morgan to invest on new technology for its electronic division.”
“eBay paid 0.39 share to acquire each of the approximately 68
million fully diluted shares of PayPal. Based on eBay's closing
price Thursday of $51.90 in 4 p.m. on the Nasdaq Stock
Market trading, the deal was valued at $1.4 billion.” (from
WSJ, October 14, 2002)
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The Cost of Capital
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Depends on the risk associated with the firm’s
activities
What the firm must pay for capital in the
capital markets
Equal to the equilibrium rate of return
demanded by investors in the capital markets
for securities of that degree of risk
Minimum rate of return required on new
investments
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Why Cost of Capital is Important
 We
know that the return earned on assets
depends on the risk of those assets
 Our cost of capital provides us with an
indication of how the market views the risk of
our assets
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Why Cost of Capital is Important
 We
need to earn at least the required return to
compensate our investors for the financing
they have provided
 Knowing our cost of capital can also help us
determine our required return for capital
budgeting projects
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What types of long-term capital do
firms use?
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Debt
 Long-term
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debt
Equity
 Preferred
 Retained
stock
earnings and/or
Common stock
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WACC: Individual Components
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Typically, the WACC has three
component costs including:
 Cost of Debt
 Cost of Preferred Stock
 Cost of Common Equity
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Cost of Debt, rd(1-T)
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An investor requires return, rd, from investment
on bonds.
- return to an investor = cost to the company.
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Cost of Debt = YTM(1-T)
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Use the market price of the bonds to find YTM,
or YTC if the bonds sells at a premium and
likely to be called.
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The cost of debt is NOT the coupon rate. Use
the current interest rate on new debt, not the
coupon rate on existing debt.
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Example: A 15-year, 12% semiannual
bond sells for $1,153.72. What’s rd?
0
1
2
30
i=?
...
60
-1,153.72
INPUTS
30
N
OUTPUT
60
-1153.72 60
I/YR
PV
PMT
5.0% x 2 = rd = 10%
60 + 1,000
1000
FV
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Cost of Debt: Example
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Should we focus on before-tax or after-tax
capital costs? Only after-tax cost is relevant
because the interest on debt is tax-deductible.
 r d AT = rd BT(1-T)
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Interest is tax deductible, so
rd AT
= rd BT(1 - T)
= 10%(1 - 0.40) = 6%.
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Cost of Preferred Stock, rps
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Preferred dividends are expected to be
paid every period forever (perpetuity
concept)
Flotation costs for preferred stocks are
significant, so are reflected. Use net price.
Preferred dividends are not tax-deductible,
so no tax adjustment. Just rps.
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Cost of Preferred Stock Example :
What’s the cost of preferred stock when
Pp = $113.10; Dividend = $10 per year;
Flotation cost = $2 per share?
rps 
D ps
Pp
$10

$113.10  $2
 0.090
 9.0%.
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Cost of Common Stock, rs
What are the two ways of common equity
financing?
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Companies can issue new shares of
common stock.
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Companies can retain and reinvest
earnings.
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Why is there a cost for reinvesting
earnings?
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Earnings can be reinvested or paid out as dividends.
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After a firm generates earnings, who owns that money?
The shareholders.
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But when the firm retain earnings it is not giving the
money to the shareholders. In a way, the firm is investing
the money for shareholders in their company.
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Those shareholders want some return on that money the
firm is keeping. How much return do they expect?
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They want the same amount as if they had gotten the
retained earning in the form of dividends, and bought
more stock in the company. THAT is the cost of retained
earnings.”
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Continued
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Thus, there is an opportunity cost if
earnings are reinvested.
The shareholders could buy similar
stocks and earn rs, or company could
repurchase its own stock and earn rs.
So, rs, is the cost of reinvested earnings
and it is the cost of equity.
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Three ways to determine the
cost of common stock, rs:
1. CAPM: rs = rRF + (rM - rRF)b
= rRF + (RPM)b.
2. DCF: rs = D1/P0 + g.
3. Bond-Yield-Plus-Risk Premium:
rs = rd + RP.
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What’s the cost of equity
based on the CAPM?
rRF = 7%, RPM = 6%, b = 1.2.
rs = rRF + (rM - rRF )b.
= 7.0% + (6.0%)1.2 = 14.2%.
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What’s the DCF cost of equity, rs?
Given: D0 = $4.19;P0 = $50; g = 5%.
D0 1  g 
D1
rs 
g
g
P0
P0
$4.19105
. 

 0.05
$50
 0.088  0.05
 13.8%.
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Find rs using the own-bond-yieldplus-risk-premium method.
(rd = 10%, RP = 4%.)
rs = rd + RP
= 10.0% + 4.0% = 14.0%
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Here RP = the firm’s judgmental risk premium
This RP  CAPM RPM.
Produces ballpark estimate of rs. Useful check.
Ad hoc and subjective approach – suitable for
privately-held firms
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What’s a reasonable final estimate
of rs?
Method
CAPM
DCF
rd + RP
Average
Estimate
14.2%
13.8%
14.0%
14.0%
One of survey studies shows that the CAPM approach
is by far the most widely used method, although most of
firms use more than one approach.
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What’s the WACC?
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We can use the individual costs of capital that we have
computed to get our “average” cost of capital for the
firm.
This “average” is the required return on our assets,
based on the market’s perception of the risk of those
assets
The weights are determined by how much of each type
of financing that we use
Suppose we have a target capital structure calling for
30% debt, 10% preferred stock, and 60% common
equity. T=40%.
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WACC Calculation: Final Stage
WACC
= wdrd(1 - T)
+ wpsrps + wcers
= 0.3(10%)(1-0.4) + 0.1(9%) + 0.6(14%)
= 1.8%
+ 0.9%
+ 8.4%
= 11.1%.
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Determining the Weights for the WACC
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The weights are the percentages of the
firm that will be financed by each
component.
If possible, always use the target
weights for the percentages of the firm
that will be financed with the various
types of capital.
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Estimating Weights for the
Capital Structure
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If you don’t know the targets, it is better to
estimate the weights using current market
values than current book values.
If you don’t know the market value of debt,
then it is usually reasonable to use the book
values of debt, especially if the debt is shortterm.
(More...)
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A comprehensive example: IBM
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IBM needs an estimate of the weighted average of cost
of capital for their firm. The firm has just paid a dividend
of $1.27, a current stock price of $20.00, and an
expected growth rate in dividends of 10%. The IBM’s
beta is 1.25. The risk free rate is 5% and the expected
return on the market portfolio is 13%. The company has
bonds outstanding with a par value of $1,000, coupon
rate of 8% paid semiannually, and 5 years until maturity.
These bonds are selling in the market of $852.80. IBM
also carries preferred stocks on its balance sheet. The
preferred stocks sell for $35 per share and they pay a
dividend of $3 per share. IBM faces 30% marginal tax
rate, and has a target capital structure of 40% debt, 10%
preferred stock, and 50% equity.
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IBM example, Continued
1.
2.
3.
4.
Calculate the cost of debt.
Calculate the cost of common stock,
using Dividend Discount Model and
Capital Asset Pricing Model (CAPM).
Take an average.
Calculate the cost of preferred stock.
Calculate the weighted average of cost
of capital.
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IBM example, Continued
IMB currently considers producing a new mainframe
computer. The financial analysts of the company
agree that this new project will carry the same level
of risk as the average risk of the company. The new
investment will require $1,000,000 and expected
cash inflows will be $250,000 annually for five years
(net of tax). Should IBM take on this project?
 Compute Net Present Value (NPV) using the cost of
capital we just computed.
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WACC Estimates for Some Large
U. S. Corporations (by Stern Stewart)
Company
Intel
General Electric
Motorola
Coca-Cola
Walt Disney
AT&T
Wal-Mart
Exxon
H. J. Heinz
BellSouth
WACC
12.9%
11.9
11.3
11.2
10.0
9.8
9.8
8.8
8.5
8.2
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What factors influence a company’s WACC?
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Factors the firm cannot control
 Market conditions, especially interest rates and
tax rates.
 Market risk premium
Factors the firm can control
 The firm’s capital structure and dividend policy.
 The firm’s investment policy. Firms with riskier
projects generally have a higher WACC.
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Flotation costs
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One may argue that the firm incurs additional
cost in raising debts. For example, hiring
investment bankers.
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Flotation cost = commissions and fees paid to
investment bankers and other incidental costs
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Flotation costs: Can flotation cost be
large enough for the issuing company
to consider it in evaluating new
projects?
Source: IPO Prospectus
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Flotation costs
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Flotation cost for bond financings is often small
because most of bonds are privately placed, so
ignore it. Most of equity is raised internally as
retained earnings. In these cases, there are no
flotation costs.
However, if companies issue debt or new stock
to the public, then flotation costs can be large.
So omitting it in calculating the WACC may
distort a true WACC.
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Adjusting for Flotation costs:
Cost of Debt
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Example: Coupon rate=10% annually
paid coupons, par=$1,000, YTM=10%,
and PB=$1,000.
Suppose F(flotation cost) = 1% of the
value of the issue.
Since the firm should pay 1% of $1,000
to the investment bankers, the net
proceed is $990. Now use a financial
calculator
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Adjusting for Flotation costs:
Cost of Debt
INPUTS
10
N
OUTPUT
-990
100
1000
PV
PMT
FV
I/YR
10.11%
After-tax cost of debt= rd(1-T)
=10.11%(1-40%) = 6.07%
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Why is the cost of internal equity from
reinvested earnings cheaper than the
cost of issuing new common stock?
1. When a company issues new common
stock they also have to pay flotation
costs to the underwriter.
2. Issuing new common stock may send a
negative signal to the capital markets,
which may depress stock price.
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Adjusting for Flotation costs:
Cost of New Common Stock, re
Estimate the cost of new common equity: P0=$50,
D0=$4.19, g=5%, and F=15%.
D0 (1  g )
re 
g
P0 (1  F )
$4.191.05 

 5 .0 %
$501  0.15 
$4.40
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 5.0%  15.4%.
$42.50
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Adjusting for Flotation costs:
Cost of Preferred Stock
Estimate the cost of preferred stock: Pn=$100
Dps=$5, g=5%, and F=10%.
rps 
Dps
Pn (1  F )
$5

$100 1  0.10 
$5

 5.6%.
$90
Risk-adjusted cost of capital:
Should the company use the composite
WACC as the hurdle rate for each of its
new projects?
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NO! The composite WACC reflects the risk of an
average project undertaken by the firm. Therefore,
the WACC only represents the “hurdle rate” for a
typical project with average risk.
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Different projects have different risks. The project’s
WACC should be adjusted to reflect the project’s
risk.
Using the WACC as our discount rate is only
appropriate for projects that are the same risk as the
firm’s current operations.
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Example
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Suppose you are a financial analyst of “Headache Free,
Co.,” a leading pain relief drug manufacturer. You are
about to report the WACC of the company to be 10%.
The CEO of the company just announced that the
company will invest in anti-AIDS drug research. Would
you recommend that the company use the same 10% as
a hurdle rate for anti-AIDS research project?
No! The anti-AIDS research project is potentially riskier
than the average of typical projects for a pain relief drug
company. Should use a higher rate than 10%.
Company WACC ≠ Individual Project WACC
≠ Divisional Project WACC
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General Electric and its subsidiaries
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Divisional Cost of Capital
Rate of Return
(%)
13.0
Project H
11.0
10.0
9.0
7.0
0
WACC
Division H’s WACC
Project L
Composite WACC
for Firm A
Division L’s WACC
RiskL
Risk Average
RiskH
Risk
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What procedures are used to determine
the risk-adjusted cost of capital for a
particular project or division?
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Estimate what the cost of capital would be
if the project/division were a stand-alone
firm. This requires estimating the project’s
beta.
Subjective adjustments to the firm’s
composite WACC.
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Example
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Assumptions:
 Target debt ratio = 10%.
 rd = 12%.
 rRF = 7%.
 Tax rate = 40%.
 betaDivision = 1.7.
 Market risk premium = 6%
 No preferred stock financing.
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Beta = 1.7, so division has more market
risk than average.
Division’s required return on equity:
rs = rRF + (rM – rRF)bDiv.
= 7% + (6%)1.7 = 17.2%.
WACCDiv. = wdrd(1 – T) + wcrs
= 0.1(12%)(0.6) + 0.9(17.2%)
= 16.2%.
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How does the division’s WACC
compare with the firm’s overall WACC?
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Division WACC = 16.2% versus company
WACC = 11.1% (PRETEND that we calculated
company WACC of 11.1% earlier.)
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“Typical” projects within this division would be
accepted if their returns are above 16.2%.
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What if it is below 16.2% but still above 11.1%?
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Subjective Approach
 Consider
the project’s risk relative to the firm
overall
 If the project is more risky than the firm, use a
discount rate greater than the WACC
 If the project is less risky than the firm, use a
discount rate less than the WACC
 You may still accept projects that you
shouldn’t and reject projects you should
accept, but your error rate should be lower
than not considering differential risk at all
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Subjective Approach: Example
Risk Level
Discount Rate
Very Low Risk
WACC – 8%
Low Risk
WACC – 3%
Same Risk as Firm
WACC
High Risk
WACC + 5%
Very High Risk
WACC + 10%
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Three Mistakes to Avoid
1.
When estimating the cost of debt, use the current
interest rate on new debt, not the coupon rate on
existing debt.
2.
When estimating the risk premium for the CAPM
approach, don’t subtract the current long-term T-bond
rate from the historical average return on common
stocks.
3.
Use the target capital structure to determine the
weights. If you don’t know the target weights, then use
the current market value of equity, and never the book
value of equity. If you don’t know the market value of
debt, then the book value of debt often is a reasonable
approximation, especially for short-term debt.
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Some Problems in Cost of Capital
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Privately owned firms or Small business
 Firms whose stock is not traded
Measurement problems
 Difficult to estimate accurate input data such as
CAPM input variables and growth rate for Dividend
Discount Model
Costs of capital for projects of differing riskiness
 It is often difficult to estimate the level of risk for new
project.
Capital structure weights
 Difficult to estimate target capital structure
Judgments must be exercised.
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Costs of Capital for various industries by
Value Line
Our cost of capital provides us with an
indication of how the market views the
risk of our assets!
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Summary
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The cost of capital is the minimum return
demanded by investors.
The cost of capital indicates how the market
views the risk of the firm’s assets or investments.
WACC includes three component costs.
The flotation cost can be significant.
The firm DOES incur opportunity cost when it
retains and reinvest earnings.
Overall firm-level WACC ≠ Individual project
WACC