Suppose that USB Corp has $100m invested in 8% risk-free bonds that mature in one-year. The company also has $80m in debt outstanding that will also mature in a year. USB shareholders are considering selling the $100m in debt and investing in a project that has a 60% chance of returning $200m and a 40% chance of returning $2m. Agency costs: Given the pay-offs of the project, what does the per cent 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

To calculate the expected value of equity without the project, we need to subtract the debt from the assets and divide the sum by the number of outstanding shares. Therefore, the expected value of equity without the project is:

Equity without project = ($100m x 1.08 - $80m) / 1 = $28m

To calculate the expected value of equity with the project, we need to consider the payoffs of the project and the probability of success. Therefore, the expected value of equity with the project is:

Equity with project = ($200m x 0.6 + $2m x 0.4) / 1 = $120m

Now, we need to find the probability of success that makes the expected value of equity with the project equal to the expected value of equity without the project. Mathematically, we can express this as:

Equity with project = Equity without project
$120m = $28m
($200m x p + $2m x (1 - p)) = $28m
p = 0.167 or 1/6

Therefore, the per cent chance of success that makes the expected value of equity with the project equal to the expected value of equity without the project is 1/6 or 16.7%, which corresponds to answer D.

Suppose That USB Corp Has $100m Invested in 8% Risk-Free