Costofcap Approach

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Optimal Capital StructureThe Cost of Capital Approach

P.V. Viswanath

Based on Damodarans Corporate Finance


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Cost of Capital Approach

We have already seen that

FCFF = EBIT(1-t)(Capital ExpendituresDep)

Change in Noncash Working Capital

The Value of the firm is the sum of the discountedpresent 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 pickthe 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 firmsasset beta.

Compute the firms levered beta for different debt ratiolevels and use this to figure out the cost of equity capital atthe different debt ratio levels.


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Cost of debt capital

Estimate the firms dollar debt and interest exp at each debtratio.

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-freerate to get the pre-tax cost of debt.

Apply the marginal tax rate to get the after-tax cost of debt, keepingin 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 agencycosts are going to increase as the debt ratio goes up and asthe bond rating goes down.

To keep a limit on these costs, the firm might want to put aconstraint on the lowest bond rating allowed.

Use normalized operating income to estimate bond ratingsso that temporarily depressed income does not yield anoverly low optimal debt ratio.

Lower estimates of operating income for higher debt ratiosdue to indirect bankruptcy costs.


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Example

Problem 12, Chapter 19 from Damodaran, CorporateFinance, Theory and Practice

You have been asked by JJ Corporation, a California-basedfirm that manufactures and services digital satellite

television systems, to evaluate its capital structure. Theycurrently have 70 million shares outstanding trading at $10per share. In addition, it has 500,000 ten-year convertiblebonds, with a coupon rate of 8%, trading at $1000 perbond. JJ Corporation is rated BBB, and the interest rate onBBB straight bonds is currently 10%. The beta for thecompany is 1.2, and the current risk-free rate is 6%. The taxrate is 40%.



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 ofthe 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%.



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 previoussection.



Cost of equity after borrowing

JJ Corporation is proposing to borrow $250 millionto 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 inthe bond rating to B, which currently carries an interestrate of 11%.

c. What will be the firm's cost of equity after thisadditional borrowing?



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%.



WACC after borrowing

d. What will the firm's weighted average cost of

capital be after this additional borrowing?

Solution: The WACC =



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 annualsavings 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 (netincrease 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.

Costofcap Approach

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