Use the information for the question(s)below.
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 flows of the project in one year.The market value of the unlevered equity for this project is closest to:
A)$94,100.
B)$90,000.
C)$86,250.
D)$98,600.

Question

Quizplus · Accepted Answer

To find the market value of the unlevered equity, we need to use the following formula:

Market Value of Unlevered Equity = Present Value of Free Cash Flows / Number of Shares

Since the project is being sold as an all-equity firm, there are no debt financing costs to be deducted from the cash flows. So, the Free Cash Flows to the Firm (FCFF) will be the same as Free Cash Flows to Equity (FCFE).

To calculate the present value of the expected cash flows, we need to find the expected cash flows and their probabilities first:

Expected Cash Flows = (0.5 * $90,000) + (0.5 * $117,000) = $103,500

Now, we can use the cost of equity as the discount rate since the project is being sold to investors as an all-equity firm. The cost of equity can be calculated using the following formula:

Cost of Equity = Risk-Free Rate + (Equity Beta * Equity Risk Premium)

Since no information is given about the equity beta or equity risk premium, we cannot calculate the cost of equity. However, we are given that the cost of capital for the project is 15%, which is the weighted average of the cost of equity and cost of debt. So, we can use this information and assume that the cost of equity is higher than the risk-free rate and lower than the cost of capital. Let's assume a cost of equity of 12% based on this information.

Using the above information, we can calculate the present value of the expected cash flows as follows:

PV of Expected Cash Flows = $103,500 / (1 + 0.12) = $92,410.71

Since the entire project is being sold to investors as an all-equity firm, the number of shares is equal to the total equity value divided by the price per share. So, we can calculate the market value of unlevered equity as follows:

Market Value of Unlevered Equity = $92,410.71 / 1 = $92,410.71

Therefore, the closest option to the calculated market value is $90,000, which is option B.

Use the Information for the Question(s)below