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Optimal Capital Structure
The Cost of Capital Approach
P.V. Viswanath
Based on Damodaran’s Corporate Finance
Cost of Capital Approach
 We have already seen that

FCFF = EBIT(1-t) – (Capital Expenditures – Dep) –
Change in Noncash Working Capital
 The Value of the firm is the sum of the discounted
present values of FCFF plus current cash.
 If we can assume that the cashflows are unaffected
by the choice of financing mix, then

Max Firm Value = Min WACC
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Cost of Equity Capital
 We compute WACC at different debt/capital ratios and pick
the lowest WACC.
 Three inputs needed:



Cost of equity
After-tax cost of debt
Weights on debt and equity
 Start with the current equity beta and compute the firm’s
asset beta.
 Compute the firm’s levered beta for different debt ratio
levels and use this to figure out the cost of equity capital at
the different debt ratio levels.
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Cost of debt capital
 Estimate the firm’s dollar debt and interest exp at each debt
ratio.
 At each debt ratio,




compute a financial ratio(s) such as the interest coverage ratio
(EBIT/Interest expenses) to measure default risk;
use that ratio(s) to estimate a synthetic bond rating for the firm.
Add on a default spread based on the estimated rating to the risk-free
rate to get the pre-tax cost of debt.
Apply the marginal tax rate to get the after-tax cost of debt, keeping
in mind that the marginal tax rate might decrease as we increase the
amount of debt-related income deductions for tax purposes.
 Weight the costs of debt and equity based on the proportions
used of each type.
 Choose the debt ratio that minimizes the WACC.
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Interest Coverage Ratios and Spreads
If interest coverage ratio is
>
≤ to
Rating is
Spread is
-100000
0.199999
D
20.00%
0.2
0.649999
C
12.00%
0.65
0.799999
CC
10.00%
0.8
1.249999
CCC
8.00%
1.25
1.499999
B-
6.00%
1.5
1.749999
B
4.00%
1.75
1.999999
B+
3.25%
2
2.2499999
BB
2.50%
2.25
2.49999
BB+
2.00%
2.5
2.999999
BBB
1.50%
3
4.249999
A-
1.00%
4.25
5.499999
A
0.85%
5.5
6.499999
A+
0.70%
6.5
8.499999
AA
0.50%
8.50
100000
AAA
0.35%
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Constrained Approach
 The unconstrained approach is problematic because agency
costs are going to increase as the debt ratio goes up and as
the bond rating goes down.
 To keep a limit on these costs, the firm might want to put a
constraint on the lowest bond rating allowed.
 Use normalized operating income to estimate bond ratings
so that temporarily depressed income does not yield an
overly low optimal debt ratio.
 Lower estimates of operating income for higher debt ratios
due to indirect bankruptcy costs.
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Example
 Problem 12, Chapter 19 from Damodaran, Corporate
Finance, Theory and Practice
 You have been asked by JJ Corporation, a California-based
firm that manufactures and services digital satellite
television systems, to evaluate its capital structure. They
currently have 70 million shares outstanding trading at $10
per share. In addition, it has 500,000 ten-year convertible
bonds, with a coupon rate of 8%, trading at $1000 per
bond. JJ Corporation is rated BBB, and the interest rate on
BBB straight bonds is currently 10%. The beta for the
company is 1.2, and the current risk-free rate is 6%. The tax
rate is 40%.
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Debt-Equity Ratio computation
 a. What is the firm's current debt-equity ratio?
 Solution: The market value of the common stock is 70m. x
$10 = $700m.
The 500,000 convertible bonds would sell at a yield of 10%
if they were straight. Hence the straight bond component of
the convertibles =

Since the convertibles trade at $1000 per bond, the equity
component = $124.63 per convertible bond.
Hence total equity = 700+124.63(0.5m.) = 762.32m.
The market value of the debt component of the convertibles
= 875.37(0.5) = 437.69m.
Hence the debt-equity ratio = 437.69/762.32 = 57.41%.
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WACC Computation
 b. What is the firm's current weighted average cost
of capital?
 Solution: The required rate of return on the equity,
using the CAPM is .06 + 1.2(0.055) = 12.6%.
 The WACC =
(.5741/1.5741)(1-0.4)10% + (1/1.5741)12.6%
= 10.192%, using the data from the previous
section.
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Cost of equity after borrowing
 JJ Corporation is proposing to borrow $250 million
to use for the following purposes:




Buy back $100 million
Pay $100 million in dividends
Invest $50 million in a project with a NPV of $25
million.
The effect of this additional borrowing will be a drop in
the bond rating to B, which currently carries an interest
rate of 11%.
 c. What will be the firm's cost of equity after this
additional borrowing?
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Cost of equity after borrowing
 Solution: After this borrowing, the market value of equity
will be $762.32m - $200m + $25m. = $586.5m. The market
value of debt will be 437.69+250=687.69m.
 Hence the debt-equity ratio will be 1.17.
The unlevered beta =
Hence the levered beta will be equal to 0.89(1+(1-0.4)1.17)
= 1.52.
 Hence, the cost of equity = .06+1.52(0.055) = 14.36%.
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WACC after borrowing
 d. What will the firm's weighted average cost of
capital be after this additional borrowing?
 Solution: The WACC =
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Value of firm after borrowing
 e. What will the value of the firm be after this additional
borrowing?
 Solution: The original firm value was $1200. The WACC
has decreased from 10.192% to 10.17%; hence the annual
savings in financing costs equal (1200)(.10192-.1017).
 Discounting these at the new cost of capital of 10.17%, we
get (762.32+437.68)(.10192-.1017)/(0.1017) = $2.36m.
 New Firm Value= $ 1,200 (original firm value) + $ 50 (net
increase in capital after capital structure changes)+ $ 25
(NPV of new project) + $ 2.36 (increase in firm value due to
capital structure change) = $ 1277.36 million.
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