Consider a project with free cash flows in one year of $90,000 in a weak economy

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 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 flow of the project in one year. The market value of the unlevered equity for this project is closest to:

(1) $94,100
(2) $90,000
(3) $86,250
(4) $98,600

Explanation / Answer

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 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 flow of the project in one year. The market value of the unlevered equity for this project is closest to:

(1) $94,100
(2) $90,000
(3) $86,250
(4) $98,600

= 0.15 X 90,000 + 0.5 X 117,000 /1.15   =$90,000

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