Valuation analysis

ECN372 Corporate Finance 2, 2012/2013
Problem Set 5: Solutions

1. a) The face value of debt is given by:
0.5 × F + 0.5 × 40 = 60 ⇒ F = 80
The value of the firm is:
V = 0.5 × 150 + 0.5 × 40 = 95
The value of equity is:
E = 95 − 60 = 35
b) The value of debt:
D = 0.5 × 50 + 0.5 × (20 − 10) = 30
The value of the firm is:
V = 0.5 × 70 + 0.5 × (20 − 10) = 40
The value of equity is:
E = 40 − 30 = 10
c) If the firms were to merge then:
The value of debt:
D = 0.5 × (80 + 50) + 0.5 × (40 + 70 + 15 − 10) = 122.5
The value of the firm is:
V = 0.5 × (150 + 20 + 15) + 0.5 × (40 + 70 + 15 − 10) = 150
The value of equity is:
E = 150 − 122.5 = 27.5
Notice that the equity value without a merger is: 35 + 10 = 45. So the management of company X should not go ahead with the merger.
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d) Similar to question c, but the synergy is higher and now debt is safe. The value of debt:
D = 0.5 × 130 + 0.5 × 130 = 130
The value of the firm is:
V = 0.5 × (150 + 20 + 37) + 0.5 × (40 + 70 + 37) = 177
The value of equity is:
E = 177 − 130 = 47
The firm should go ahead with the merger.
2. a) Project A has an expected payoff equal to 85. Project B’s expected payoff is: 0.5 × 150 = 75
Project C’s expected payoff is:
0.1 × 350 + 0.9 × 25 = 57.5
b) With debt at face value 35 million due in one year, the value of equity for each of the three projects is:
EA = 85 − 35 = 50
EB = 0.5 × (150 − 35) = 57.5
EC = 0.1 × (350 − 35) = 31.5
Thus, equity holders prefer project B.
c) With debt at face value 120 million due in one year, the value of equity for each of the three projects is:
EA = 0
EB = 0.5 × (150 − 120) = 15
EC = 0.1 × (350 − 120) = 23
Thus, equity holders prefer project C.

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d) The expected agency cost for the firm from having 35 million in debt is:
V (projectA) − V (projectB) = 85 − 75 = 10
The expected agency cost for the firm from having 120 million in debt is:
V (projectA) − V (projectC) = 85 − 57.5 = 27.5

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