Agency costs: 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?

Question

Quizplus · Accepted Answer

In order for the expected value of equity with the project to be equal to the expected value of equity without the project, the agency cost needs to be zero.

To calculate the agency cost, we need to compare the expected value of equity with the project to the expected value of equity without the project.

Let P be the percent chance of success of the project. Then, the expected value of equity with the project is:

(0.6P - 0.4)($3,000,000) = $1,800,000P - $1,200,000

The expected value of equity without the project is simply:

$1,200,000

Setting these two equal and solving for P, we get:

$1,800,000P - $1,200,000 = $1,200,000

$1,800,000P = $2,400,000

P = 4/6 = 2/3

The agency cost is:

$1,800,000(2/3) - $1,200,000 = $400,000/3

Therefore, in order for the agency cost to be zero, the percent chance of success needs to be:

$400,000/3 ÷ $3,000,000 = 1/6

Thus, the answer is D.

Agency Costs: Given the Payoffs of the Project, What Does