Solutions Guide: Please do not present as your own. This is only meant as a
solutions guide for you to answer the problem on your own. I recommend doing
this with any content you buy online whether from me or from someone else.
Suppose Lucent Technologies has an equity cost of capital of 10%, market capitalization
of $ 10.8 billion, and an enterprise value of $ 14.4 billion. Suppose Lucent’s debt cost of
capital is 6.1% and its marginal tax rate is 35%.
a. What is Lucent’s WACC?
b. If 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)?
10.8
14.4  10.8
10% 
6.1%(1  0.35)  8.49%
14.4
14.4
a.
rwacc 
b.
Using the WACC method, the levered value of the project at date 0 is
VL 
50
100
70


 185.86
1.0849 1.08492 1.08493
Given a cost of 100 to initiate, the project’s NPV is 185.86 – 100 = 85.86.
c.
Lucent’s debt-to-value ratio is d = (14.4 – 10.8) / 14.4 = 0.25. The project’s debt capacity is equal
to d times the levered value of its remaining cash flows at each date:
Year
FCF
VL
D = d*VL
0
–100
185.86
46.47
1
50
151.64
37.91
2
100
64.52
16.13
3
70
0
0.00
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 the WACC method.
a. rU 
10.8
14.4  10.8
10% 
6.1%  9.025%
14.4
14.4
50
100
70


 184.01
2
1.09025 1.09025 1.090253
b.
VU 
c.
Using the results from problem 5(c):
Year
FCF
VL
D = d*VL
Interest
Tax Shield
0
–100
185.86
46.47
1
50
151.64
37.91
2.83
0.99
2
100
64.52
16.13
2.31
0.81
3
70
0
0.00
0.98
0.34
The present value of the interest tax shield is
PV(ITS) 
d.
0.99
0.81
0.34


 1.85
1.09025 1.090252 1.090253
VL  APV  184.01  1.85  185.86
This matches the answer in 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?
a. Using the debt capacity calculated in problem 5, we can compute FCFE by adjusting FCF for aftertax interest expense (D*rD*(1 – tc)) and net increases in debt (Dt – Dt-1):
Year
D
FCF
After-tax Interest Exp.
Inc. in Debt
FCFE
b.
NPV  53.53 
0
46.47
1
37.91
2
16.13
3
0.00
-$100.00
$0.00
$46.47
-$53.53
$50.00
-$1.84
-$8.55
$39.60
$100.00
-$1.50
-$21.78
$76.72
$70.00
-$0.64
-$16.13
$53.23
39.60 76.72 53.23


 $85.86
1.10 1.102 1.103