Question

Consider a project with free cash flows in one year is $90,000 in a weak economy or $117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is $80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%.  

Suppose that you borrow $60,000 in financing the project. According to the MM proposition II, the firm's equity cost of capital will be closest to:

a. 45%

b. 30%

c. 25%

d. 35%

Answer 1

First we will calculate the value of firms total cash flow :

PV(equity cash flows - unlevered) = [(0.5 * $90,000) + (0.5 * $117,000)] / 1.15 = $90,000

According to MM Proposition II, rE = rU + D/E (rU -rD)

where,

rE = Cost of Equity

rU = Cost of Capital / Project

D = Firms Debt

E = Firms Equity

rD = Cost of Debt

Here, the Debt portion is $60,000 (given) and value of firms total cash flow = $90,000 (as calculated above). So if we borrow $60,000, firms equity will be worth $30,000 ($90,000 - $60,000).

Therefore, rE = 0.15 + [$60,000 / ($90,000 - $60,000)]*(0.15 - 0.05) = 0.35 or 35% i.e option d.