Suppose that UBM Corp. has invested $100 million in 8% risk-free bonds that mature in one-year. The firm also has $80 million in debt outstanding that will also mature in a year. UBM stockholders are considering selling the $100 million in debt and investing in a project that has a 60% chance of returning $200 million and a 40% chance of returning $2 million. Given the payoffs of the project, what does the percent chance of success need to be in order for the expected value of equity with the project to be equal to the expected value of equity without the project?
A) 1/3
B) 1/4
C) 1/5
D) 1/6

Question

Quizplus · Accepted Answer

First, let's calculate the expected value of equity without the project:

EBE1 = $100 million (1.08) - $80 million = $6 million

Now, let's calculate the expected value of equity with the project, assuming x is the percent chance of success:

EBE2 = 0.6 ($200 million - $180 million) + 0.4 ($2 million - $180 million) = $24 millionx - $92 million

Since we want EBE1 = EBE2, we can set them equal to each other and solve for x:

$6 million = $24 millionx - $92 million
$98 million = $24 millionx
x = 4.08%

Therefore, the percent chance of success needs to be at least 1/24 or 4.08% for the expected value of equity with the project to be equal to the expected value of equity without the project. The closest answer choice is D) 1/6 or 16.67%, which is greater than the required 4.08%, so it is not the correct answer. The correct answer is D) 1/6.

Suppose That UBM Corp