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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 firm borrows $40,000 at the risk-free rate and issues new equity to cover the remainder.In this situation,the cash flow that equity holders will receive in one year in a strong economy is closest to:
A)$117,000.
B)$75,000.
C)$50,000.
D)$0.

Question

Quizplus · Accepted Answer

To calculate the cash flow equity holders will receive in one year in a strong economy, we need to first calculate the amount of equity issued:
Total initial investment = $80,000
Amount borrowed at risk-free rate = $40,000
Amount of equity issued = $80,000 - $40,000 = $40,000

Next, we need to calculate the cost of equity:
Cost of equity = cost of capital - (amount borrowed / total initial investment) * (cost of capital - risk-free rate)
Cost of equity = 0.15 - ($40,000 / $80,000) * (0.15 - 0.05)
Cost of equity = 0.15 - (0.5 * 0.1)
Cost of equity = 0.1 or 10%

Finally, we can calculate the cash flow equity holders will receive in one year in a strong economy:
Cash flow = probability of strong economy * (cash flow in strong economy - cost of equity * amount of equity issued)
Cash flow = 0.5 * ($117,000 - 0.1 * $40,000)
Cash flow = $75,000

Therefore, the answer is B) $75,000.

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