Question

Consider a project with free cash flows in one year of $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 MM proposition II, the firm's equity cost of capital will be closest to:A) 45%B) 30%C) 25%D) 35%

Answer 1

Answer:

Option (D) is correct.

Explanation:

Expected cash flow in year 1 : C1 = (0.5 × 90,000) + (0.5 × 117,000)

                                                       = 103,500

Discount rate, r = Project's WACC = 15%

Hence, Value of the project today = Vp = C1 ÷ (1 + r)

                                                                  = 103,500 ÷ (1 + 15%)

                                                                  = $90,000

Value of equity today : Ve0 = Vp - Debt

                                               = 90,000 - 60,000

                                               = 30,000

Value of equity in year 1 = Project cash flows - Debt × (1 + interest rate)

Weak economy = 90,000 - 60,000 × (1 + 5%)

                          = 27,000

Strong economy = 117,000 - 60,000 × (1 + 5%)

                            = 54,000

Expected value of equity in year 1 : Ve1 = (0.5 × 27,000)  + (0.5 × 54,000)

                                                                   = 40,500

Hence, Levered cost of equity, Ke = (Ve1 ÷ Ve0) - 1

                                                         = (40,500 ÷ 30,000 ) - 1

                                                         = 35%