Exercises
1. Weighted average cost of capital (LO1) United Business Forms’ capital structure is as follows:
Debt
Preferred stock
Common equity
35%
15
50
The after-tax cost of debt is 7 percent; the cost of preferred stock is 10 percent; and the cost of common
equity (in the form of retained earnings) is 13 percent. Calculate United Business Forms’ weighted
average cost of capital.
Solution
United Business Forms
Debt (Kd)
Preferred stock (Kp)
Common equity (Ke) (retained earnings)
Weighted average cost of capital (Ka)
Cost
(after-tax)
7.0%
10.0
13.0
Weighted Cost
Weights
35%
15
50
2.45%
1.50
6.50
10.45%
2. Lloyd Enterprises has a project which has the following cash flows:
Year
Cash Flow
0
-$200,000
1
50,000
2
100,000
3
150,000
4
40,000
5
25,000
The cost of capital is 10 percent.
a) What is the projects NPV?
b) What is the project's discounted payback?
1
Solution
a) NPV= -200,000 + 50,000/1.10 + 100,000 / (1.10)2 + 150,000/(1.10)3 + 40,000/(1.10)4 + 25,000 /(1.10)5 =
-200,000+ 45,454.54 +82,644.63 +112,697.2 +27,320.54 +15,523.03=83,639.96
b)
Discounted payback
0
r = 10%
CFs -200,000
1
2
3
50,000
100,000
150,000
40,000
25,000
50,000
1.1
100,000
(1.1)2
150,000
(1.1)3
40,000
(1.1)4
25,000
(1.1)5
27,320.54
15,523.03
Discounted
CFs -200,000
45,454.55 82,644.63 112,697.22
Discounted CF
Cumulative CF
0
-200,000.00
-200,000.00
1
45,454.55
-154,545.45
2
82,644.63
-71,900.82
Payback
3
112,697.22
+40,796.40
4
27,320.54
+68,116.94
5
15,523.03
+83,639.97
Payback period = 2 years +
3.
4
5
$71,900.82 = 2.638 years.
$112,697.22
Le Grand Bâillement SA is currently valued at €900 million but management wants to completely pay
off its perpetual debt of €300 million. Le Grand Bâillement is subject to a 30 per cent marginal tax rate.
If Le Grand Bâillement pays off its debt, what will be the total value of its equity?
Solution:
Le Grand Bâillement will be worth €900 million less the present value of the tax shield on its
current debt. The present value of the tax shield is
€300 000 000 × 0.3 = €90 000 000
Therefore, Le Grand Bâillement will be worth €810 million after the recapitalisation and since it
will be an all-equity firm, that will be the value of the equity.
2