Suppose Blank Company has only one project,as forecast above,and an unlevered cost of equity of 8%.If the company borrows $10,000 at 5% to make the investment,what is the return to equity holders if demand is weak?
A)8.0%
B)-37.5%
C)-58.6%
D)-35.3%
E)-12.5%

Question

Quizplus · Accepted Answer

First, we need to calculate the levered cost of equity using the formula: 
Levered Cost of Equity = Unlevered Cost of Equity + (Debt/Equity) * (Unlevered Cost of Equity - Pre-tax Cost of Debt)
= 8% + (10,000/10,000) * (8% - 5%)
= 8% + 3%
= 11%
Next, we need to calculate the net present value (NPV) of the project using the formula: 
NPV = CF1 / (1 + r) + CF2 / (1 + r)2 + ... + CFn / (1 + r)n - Initial Investment
= (-$4,000) / (1 + 11%) + $14,000 / (1 + 11%)2 + $18,000 / (1 + 11%)3 - $10,000
= -$3,023.22
Since the NPV is negative, the project is not profitable and equity holders would experience a loss. Therefore, the return to equity holders would be the unlevered cost of equity minus the after-tax cost of debt, multiplied by the debt-to-equity ratio: 
Return to Equity Holders = (Unlevered Cost of Equity - After-tax Cost of Debt) * (Debt / Equity)
= (8% - 5% * (1 - 0.35)) * (10,000 / 0)
= -35.3% (negative return indicates a loss)

Suppose Blank Company Has Only One Project,as Forecast Above,and an Unlevered