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# APV, Unlevered cost of capital, Debt=equity ratio

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A firm has a cost of equity of 13.8% and a pre-tax cost of debt of 8.5%. The debt-equity ratio is .60 and the tax rate is .34. What is the firm's unlevered cost of capital?
a. 8.83%
b. 12.30%
c. 13.97%
d. 14.08%
e. 14.60%

Your firm has a pre-tax cost of debt of 7% and an unlevered cost of capital of 13%. Your tax rate is 35% and your cost of equity is 15.26%. What is your debt-equity ratio?
a. .43
b. .49
c. .51
d. .54
e. .58

A project has a NPV, assuming all equity financing, of \$1.5 million. To finance the project, debt is issued with associated flotation costs of \$60,000. The flotation costs can be amortized over the project's 5 year life. The debt of \$10 million is issued at 10% interest, with principal repaid in a lump sum at the end of the fifth year. If the firm's tax rate is 34%, calculate the project's APV.

#### Solution Preview

A firm has a cost of equity of 13.8% and a pre-tax cost of debt of 8.5%. The debt-equity ratio is .60 and the tax rate is .34. What is the firm's unlevered cost of capital?
a. 8.83%
b. 12.30%
c. 13.97%
d. 14.08%
e. 14.60%

Solution: - Computation of Firms unlevered cost of capital

Re = Ra + (D/E) (Ra - Rd) (1 - Tc)

0.138 = x + (0.6) (x - 0.085) (1 -0.34)
0.138 = x + 0.396x-0.03366
0.138 = 1.396x - ...

#### Solution Summary

The firm's unlevered cost of capital for a cost of equity of 13.8% and a pre-tax cost of debt being 8.5% is determined.

\$2.19

## Suppose Lucent Tech. has an equity cost of 10 %, market capitalization of \$10.8 billion, an enterprise value of \$14.4 billion. Suppose Lucent debt cost of capital is 6% and its marginal tax rate is 35%.a) What is Lucent's WACC? b) Lucent maintains a constant debt-equity ratio, what is the value of a project with average risk and the following expected free cash flows? Year 0 1 2 3 FCF -100 50 100 70c) If Lucent maintains its debt-equity ratio, what is the debt capacity of the project in part (b)? Question 9Consider Lucent in the above problem 5 a) What is Lucent's unlevered cost of capital? b) What is the unlevered value of the project? c) What are the interest tax shields from the project? What is their present value? d) Show that the APV of Lucent's project matches the value computed using WACC method.Question 10Consider Lucent in the above problem 5 . a) What is the free cash flow to equity for this project? b) What is its NPV computed using the FTE method? How does it compare with the NPV based on the WACC method?

Question 5

Suppose Lucent Tech. has an equity cost of 10 %, market capitalization of \$10.8 billion, an enterprise value of \$14.4 billion. Suppose Lucent debt cost of capital is 6% and its marginal tax rate is 35%.

a) What is Lucent's WACC?
b) Lucent maintains a constant debt-equity ratio, what is the value of a project with average risk and the following expected free cash flows?
Year 0 1 2 3
FCF -100 50 100 70

c) If Lucent maintains its debt-equity ratio, what is the debt capacity of the project in part (b)?

Question 9

Consider Lucent in the above problem 5

a) What is Lucent's unlevered cost of capital?
b) What is the unlevered value of the project?
c) What are the interest tax shields from the project? What is their present value?
d) Show that the APV of Lucent's project matches the value computed using WACC method.

Question 10

Consider Lucent in the above problem 5
.
a) What is the free cash flow to equity for this project?
b) What is its NPV computed using the FTE method? How does it compare with the NPV based on the WACC method?

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