Cost of Capital Lecture

Goal of the Lecture:
Understand how much a
business must pay to raise the
capital it needs to fund
corporate investments.
How Much Does It Cost to Raise Capital?
How Much Return Do Security-Holders Require
a Company to Offer to Buy Its Securities?
Calculate the Costs (the k’s) of Various Securities in a
Company’s Capital Structure Using CAPM and Other
Methods and Combine to Get an Overall k.
Note: Required return, opportunity cost of capital,
and weighted average cost of capital (WACC) are
used interchangeably.
Calculating a Firm’s Marginal
(Weighted) Cost of Capital
A Firm’s Marginal Cost of Capital (MCC)
General Formula
MCC = Wdebtki + Wpskps + Wsks
where, Wdebt = weight of debt in firm’s capital structure
Wps = weight of preferred stock
Ws = weight of common stock
ki = after-tax cost of debt
kps = after-tax cost of preferred stock
ks = after-tax cost of common stock
Note: After tax costs are used because after-tax cash
flows are used for capital budgeting. To get MCC,
calculate the individual weights and costs and
Use MCC, if:
a. Project Risk is Average for the Firm
b. Proportions of Debt and Securities are Expected
to Stay Approximately Constant
Calculating the After-Tax Cost of Debt
After-Tax Cost of Debt - Debt has a cost advantage because
interest payments are a tax deductible
expense while dividends are not.
Ki = Kb(1 - T) = after-tax cost of debt
where, Kb = Before Tax Cost of Debt Financing
T = Marginal Corporate Tax Rate
To get Kb, use the Excel Rate function
[=Rate(n, I, Bnp, M)]
where, BNP is the Net Proceeds From Bond Issuance
(Gross Proceeds Minus Flotation Costs)
I is the coupon in dollars,
M is par value, usually $1000.
An Example of Calculating the
After-Tax Cost of Debt
Example: Suppose Firm A issues a 10 year bond that has
a$1000 Par; a coupon rate of 10% paid annually; flotation
costs are $30 per bond; and the marginal tax rate is 40%.
Find the before-tax and after-tax cost of debt.
Find before-tax cost
BNP = ($1000 - $30) = $970
I = 100
M = 1000
[=Rate(10, 100, -970, 1000)] => kb = 10.5%
( M  B NP )
M .6( B NP  M )
Approximation =
(1000  970)
1000.6( 970  1000)
100 
= [100+3]/[1000-18] = 10.5%
After Tax
ki = 10.5%(1 - .4) = 6.3%
n = 10
After-Tax Cost of Preferred Stock
After-Tax Cost of Preferred Stock
General Formula
Kps = Divps/Pnp
= Dividends on Preferred / Net Proceeds per Share
Suppose that Firm A issues a $100 Par Preferred
Stock with a $10 dividend and flotation costs are
$10/Share. What is the After-Tax Cost of the
Preferred Stock?
= Divps/Pnp
= 10/90 = .1111 = 11.11%
No adjustment is made for taxes because
dividends are paid after-tax.
Calculating the After-Tax Cost
of Common Stock
Two Methods to Raise Common Stock - Different Costs
1. Generate common stock internally by retaining
earnings - avoids flotation costs
2. Sell common shares to external investors
-must hire investment bankers and brokers and
issue prospectuses -> flotation costs
Three Methods to Calculate the Cost of Common Stock
1. Use the DCF growth model
2. Use the CAPM
3. Use the bond yield plus risk premium method
Note: As a final measure of the cost of equity you can
average the results from the three methods or
select the one that you believe is the most
precise given the situation.
Three Methods For Calculating the After-Tax
Cost of Internally-Generated Common Stock
After-Tax Cost of Common Stock - Internally Generated
1. DCF - Constant Growth Method
= D1/P0 + g = D0(1 + g)/P0 + g
where D1 = next year’s dividend
P0 = present stock price
g = growth in dividends
ks= krf + Bi(km - krf)
where, krf = risk-free rate (T-bill Rate),
km = expected market return (S&P 500)
Bi = stock i’s beta
3. Bond Yield Plus Risk Premium
ks = kb + Risk Premium
where kb = before-tax cost of debt
Examples of the Three Methods For
Calculating the After-Tax Cost of InternallyGenerated Common Stock
Suppose the Market Price of a stock is $50, its
dividend is $10, and it is expected to grow by
5%. What is ks?
ks = 10/50 + .05 = .25 = 25%
Suppose the T-bill rate is 10%, expected return
on the S&P 500 is 17.5% and beta is 2. Find ks.
ks = .10 + 2(.175 - .10) = .25 = 25%
Suppose a common stock is very risky and
should earn a 15% premium over its bonds
which have a yield to maturity of 10.36%. What
is ks?
ks = .1036 + .15 = .2536 = 25.36
Note: No adjustments for flotation costs.
One Method For Calculating the After-Tax Cost
of Externally-Generated Common Stock
After-Tax Cost of Common Stock - Externally Generated
1. DCF - Constant Growth Method
ks = D1/PNP + g
where PNP = net proceeds per share
Suppose a firm’s market price is $50, but the
flotation costs are $1/share, and the stock must
be issued at $1 below its market price. Its
dividend is $10 and it grows by 5%.
ks = 10/48 + .05
= .258 = 25.8%
MCC - Marginal Cost of Capital
“The cost of the last dollar of additional funds secured; the
firm’s opportunity cost of capital (equals WACC).”
Marginal Cost of Capital
MCC = Wdebtki + Wpskps + Wsks
From previous calculations of ki = 6.3%,
kps =11.11%, external ks = 25.8% and internal
ks = 25%. For capital structure, assume the firm
has a target of 50% Debt, 10% Preferred Stock,
and 40% Common Stock. What is the MCC?
(Internally Generated Common)
= .5(6.3%) + .1(11.11%) + .4(25%)
= 14.26%
(Externally Generated Common)
= .5(6.3%) + .1(11.11%) + .4(25.8%)
= 14.58%