Suppose​ Alcatel-Lucent has an equity cost of capital of 10.4 %​, market capitalization of $ 8.97 ​billion, and an enterprise value of $ 13 billion. Assume that​ Alcatel-Lucent's debt cost of capital is 7.4 %​, its marginal tax rate is 35 %​, the WACC is 8.6671​%, and it maintains a constant​ debt-equity ratio. The firm has a project with average risk. The expected free cash​ flow, levered​ value, and debt capacity are as​ follows:
Year 0 1 2 3
FCF ($ million) -100 50 101 74
189.21 155.61 68.10 0.00
58.66 48.24 21.11 0.00 ​
Thus, the NPV of the project calculated using the WACC method is $ 189.21 million minus $ 100 million equals $ 89.21 million.
a. What is​ Alcatel-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​ Alcatel-Lucent's project matches the value computed using the WACC method.