Question

Consider a project with free cash flows in one year of $ 133 495 in a weak market or $ 199 139 in a strong​ market, with each outcome being equally likely. The initial investment required for the project is $ 90 000​, and the​ project's unlevered cost of capital is 15 %. The​ risk-free interest rate is 9 %. ​(Assume no taxes or distress​ costs.) a. What is the NPV of this​ project? b. Suppose that to raise the funds for the initial​ investment, the project is sold to investors as an​ all-equity firm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this waylong dashthat ​is, what is the initial market value of the unlevered​ equity? c. Suppose the initial $ 90 000 is instead raised by borrowing at the​ risk-free interest rate. What are the cash flows of the levered equity in a weak market and a strong market at the end of year​ 1, and what is its initial market value of the levered equity according to​ MM?

Answer 1

All financials below are in $

Initial investment, C₀ = 90,000

Cash flow in year 1, in up state = C_1u = 199,139 with probability p = 0.5

Cash flow in year 1, in down state = C_1d = 133,495 with probability 1 - p = 1 - 0.5 = 0.5

Unlevered cost of capital, K_u = 15%

a. What is the NPV of this​ project?

NPV = - C₀ + [p x C_1u + (1 - p) x C_1d] / (1 + K_u) = - 90,000 + [0.5 x 199,139 + 0.5 x 133,495] / (1 + 15%) =  54,623.48

b. Suppose that to raise the funds for the initial​ investment, the project is sold to investors as an​ all-equity firm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this waylong dashthat ​is, what is the initial market value of the unlevered​ equity?

Initial market value of the unlevered​ equity = [p x C_1u + (1 - p) x C_1d] / (1 + K_u) = [0.5 x 199,139 + 0.5 x 133,495] / (1 + 15%) =  144,623.48

c. Suppose the initial $ 90 000 is instead raised by borrowing at the​ risk-free interest rate. What are the cash flows of the levered equity in a weak market and a strong market at the end of year​ 1, and what is its initial market value of the levered equity according to​ MM?

Debt to be paid off in year 1, D₁ = D₀ x (1 + risk free rate) = 90,000 x (1 + 9%) =  98,100

The cash flows of the levered equity in a weak market at the end of year​ 1 = C_L1u = C_1u - D₁ = 199,139 - 98,100 =  101,039
with probability p = 0.5

The cash flows of the levered equity in a strong market at the end of year​ 1 = C_L1d = C_1d - D₁ = 133,495 - 98,100 =   35,395  
with probability 1 - p = 1 - 0.5 = 0.5

In the absence of taxes, according to​ MM, value of the firm is independent of capital structure.

Hence, V_U = 144,623.48 = V_L = D₀ + E₀

Hence, initial market value of the levered equity, E₀ = 144,623.48 - D₀ = 144,623.48 - 90,000 =  54,623.48