How Much Does It Cost to Raise Capital? Or
How Much Return Do Security-Holders Require
a Company to Offer to Buy Its Securities?
Lecture: 5 - Capital Cost and Structure
THREE TOPICS COVERED
I.
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.
II.
Capital Structure Theory - What Percent of Capital
Should Be Raised Through Selling Stock, Bonds
and Preferred?
III.
Consider Fixed Costs in a Firm’s Risk
a. Business or Operating Risk
b. Financial Risk
Calculating a Firm’s Marginal (Weighted) Cost of
Capital
Lecture: 5 - Capital Cost and Structure
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
combine.
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
Lecture: 5 - Capital Cost and Structure
After-Tax Cost of Debt - Debt has a cost advantage because
interest payments are a tax deductable
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, solve for ? in the bond pricing equation
BNP
= I(PVA?,n) + PAR(PV?,n)
where, BNP is the Net Proceeds From Bond Issuance
(Gross Proceeds Minus Flotation Costs)
An Example of Calculating the After-Tax Cost of
Debt
Lecture: 5 - Capital Cost and Structure
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 = I(PVA?,n) + M(PV?,n)
($1000 - $30) = 100(PVA?,10) + 1000(PV?,10)
( M  B NP )
n
M .6( B NP  M )
I
Approximation =
=
(1000  970)
10
1000.6(970  1000)
100 
= [100+3]/[1000-18] = 10.5%
After Tax
ki = 10.5%(1 - .4) = 6.3%
After-Tax Cost of Preferred Stock
Lecture 5 - Capital Cost and Structure
After-Tax Cost of Preferred Stock
General Formula
Kps = Divps/Pnp
= Dividends on Preferred / Net Proceeds per Share
Example:
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?
Kps
= Divps/Pnp
= 10/90 = .1111 = 11.11%
Note:
No adjustment is made for taxes because
dividends are paid after-tax.
Calculating the After-Tax Cost of Common Stock
Lecture 5 - Capital Cost and Structure
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
Lecture 5 - Capital Cost and Structure
After-Tax Cost of Common Stock - Internally Generated
1. DCF - Constant Growth Method
ks
= D1/P0 + g = D0(1 + g)/P0 + g
where D1 = next year’s dividend
P0 = present stock price
g = growth in dividends
2. CAPM
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
Lecture 5 - Capital Cost and Structure
DCF METHOD
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 + 5 = 25%
CAPM METHOD
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%
BOND YIELD PLUS RISK PREMIUM METHOD
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
Lecture 5 - Capital Cost and Structure
After-Tax Cost of Common Stock - Externally Generated
1. DCF - Constant Growth Method
ks = D1/PNP + g
where PNP = net proceeds per share
Example:
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).”
Lecture 5 - Capital Cost and Structure
Marginal Cost of Capital
MCC = Wdebtki + Wpskps + Wsks
Example:
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)
MCC
= .5(6.3%) + .1(11.11%) + .4(25%)
= 14.26%
(Externally Generated Common)
MCC
= .5(6.3%) + .1(11.11%) + .4(25.8%)
= 14.58%
Calculating Capital Structure Weights From
Market Prices If Firm Has No Target Weights
Lecture 5 - Capital Cost and Structure
FIRM SECURITIES VALUES
Common stock = 1,000,000 shares * $50/share= 50 mm
Debt
= 50,000 bonds * $950/bond
= 47.5 mm
Preferred
= 100,000 shares * $90/share = 9 mm
106.5 mm
Figure the Weights?
Weights
Ws
Wd
Wps
= 50/106.5 = 47%
= 47.5/106.5 = 45%
= 9/106.5 = 8%
MCC
= .45(6.30) + .08(11.11) + .47(25)
= 2.84 + .89 + 11.75
= 15.48
Note: You may need to make adjustments for projects that
are not average risk projects such as projects for different
divisions.
Capital Structure Refers a Firm’s Various
Sources of Long-Term Financing as a
Proportion of Total Capital
Lecture: 5 - Capital Cost and Structure
Manager’s Goal: Increase EPS Through Leverage, But by
Enough to Offset the Increase in Risk so
that Stock Price Increases.
Two Capital Structure Theories of Leverage
a. Traditional - Share Price will Increase with
Leverage up to a Point (Too Much Risk)
b. Net Operating Income Theory - Any Increase
in Leverage and EPS will be Offset by
Increased Risk (Assuming No Taxes)
Leaving the Share Price Unchanged.
Illustration using the constant growth model.
P = D1/ (ks - g)
Increasing leverage may increase D1 and g but
will increase beta (risk) so that ks will increase.
Theoretically, P stays the same because the
positive effect of the increase in D1 and g is just
offset by the negative effect of the ks increase.
Traditional Theory - As Debt is Added, D/E
Rises But kavg Falls Because Debt has Lower
Cost. Eventually kE and kD Rise Due to Rising
Bankruptcy Probabilities, Pushing kavg Up
Lecture: 5 - Capital Cost and Structure
Ke
Cost of
Capital
Kavg
minimum
Kd
optimal
Debt to Equity Ratio
Net Operating Income Theory - (Modigliani and Miller)
No optimal capital structure and no advantage of debt over
equity financing. kavg stays constant no matter what the debt
level. Unlike in the graph above, the kavg line would be flat
with no minimum kavg (assumes no taxes).
Net Operating Income Theory - Modigliani and
Miller With Corporate Taxes Changes the
Theory’s Implications
Lecture: 5 - Capital Cost and Structure
REMEMBER: The Value of the Firm Is the Discounted
Value of It’s After-Tax Cash Flows Going to
Bondholders and Stockholders.
Without Income Taxes - income goes to
1. stockholders
2. bondholders
With Income Taxes - income goes to
1. stockholders
2. bondholders
3. government.
Because interest paid on debt is tax deductable we can
reduce the amount going to the government (and increase
the amount going to bondholders and stockholders) by
increasing the amount of debt in the capital structure.
Lecture: 5 - Capital Cost and Structure
Initial Capital
Structure
Increase Debt
Financing
S
S
B
G
B
G
S is the portion of EBIT paid to Stockholders
B is the portion of EBIT paid to Bondholders
G is the portion of EBIT paid to Government
Value of the Levered Firm With Corporate
Taxes Is the Value of the Unlevered Firm Plus
the Present Value of the Debt’s Tax Shield
Lecture: 5 - Capital Cost and Structure
Assume no growth in EBIT. The unlevered firm’s value, is
Vu =
EBIT (1- T)
k su
where EBIT = earnings before interest and taxes
T = corporate tax rate
ksu = the unlevered cost of equity capital
Then the value of the levered firm, VL is
VL = VU + (present value of the tax shield from debt)
VL = VU + (tax rate)(value of debt) = VU + (T)(B)
When there is a difference in personal tax rates on bond
and stock income then adjust the equation above to
VL
= VU + [1 - (1 - T)(1 - Ts)/(1 - TB)]B
where
T
Ts
TB
B
= corporate tax rate
= stock tax rate
= bond tax rate
= face value of bonds
Because bondholders demand the same after tax rate of
return as stockholders (assuming equal risk), if TB > Ts,
then interest rates on bonds must be higher than stock
returns so that after tax returns will be equal. This reduces
the advantage of debt.
Lecture: 5 - Capital Cost and Structure
Example: SI Inc. is an all-equity firm that generates EBIT of
$3 million per year. Its cost of equity capital is 16
percent, its marginal corporate tax rate is 35
percent, and it has 1 million shares outstanding.
a What is SI’s market value?
b. If SI issues $4 million of debt and uses it to buy
back some shares, what will be its new market
value and new equity value?
c. Show that the change in per-share value goes
up even though total equity decreases.
a. Vu = $3,000,000(1 - .35) / .16 = $12,187,500
b. VL = $12,187,500 + (.35)($4,000,000)=$13,587,500
equity = $13,587,500 - $4,000,000 = $9,587,500
c. Before buyback, share price= $12,187,500/1,000,000
= 12.187
After buyback of $4,000,000/12.187 = 328,218 shares
we get a new price of
P =$9,587,500/(1,000,000 - 328,218) = 14.27
Fixed Operating Costs Produce Operating
Leverage and Fixed Financing Costs Produce
Financial Leverage But Leverage Creates Risk
Lecture: 5 - Capital Cost and Structure
Business Risk - Factors Affecting:
a. Sensitivity of Sales to Business Cycle
b. Firm Size and Industry Competition
c. Operating Leverage (Proportion of Fixed
to Variable Operating Costs in Total Costs)
d. Input Price Variability
e. Ability to Adjust Output Prices
Degree of Operating Leverage
DOL = % Change in EBIT / % Change in Sales
= [Sales - Variable Costs] / EBIT
= 1 + Fixed Cost / EBIT
Lecture: 5 - Capital Cost and Structure
Financial Risk - Factors Affecting:
a. Variability of Shareholder EPS
b. Financial Risk Increases with Leverage
Degree of Financial Leverage
DFL = % Change in EPS / % Change in EBIT
= EBIT / [EBIT - I - L - d/(1 - T)]
where, I = Interest, L = Lease Payments, and
d = preferred dividends (Grossed Up by [1 - T]
because there is No Tax Deduction)
Degree of Combined Leverage: Operating and Financial
DCL = DOL x DFL
= % Change in EPS / % Change in Sales
= [Sales - Variable Costs] / [EBIT - I - L -d/(1 - T)]
Note: The larger is DCL, the larger the firm’s return
variance .
Leverage - DOL, DFL, and DCL
“DOL - As sales rise, fixed cost per unit falls. DFL - Fixed
Cost Financing causes EPS to fluctuate. DCL - Combined
effects of operating and financial leverage.”
Lecture 5 - Capital Cost and Structure
Example:
Clark Comp. has the following income statement in
millions.
Sales
Variable Costs
Revenues Before Fixed Costs
Fixed Costs
EBIT
Interest
EBT
Taxes (30%)
EAT
50
24
26
13
13
3
10
3
7
a) Calculate DOL, DFL, and DCL.
b) If sales increase by 20%, by what % will EAT increase
and to what amount?
a. DOL
= (50-24)/13
= 2.0
DFL
= 13/(13-3) = 1.3
DCL
= 2 x 1.3 = 2.6
b. EAT % Increase = .20 x 2.6 = .52 = 52%
EAT Amount Increase = 7 x 1.52 = $10.64