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 $80,000 at the risk-free rate, then the cost of capital for the firm's levered equity is closest to:Group of answer choices15%.25%.95%.45%.
Question
Consider a project with free cash flows in one year of 117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is 80,000 at the risk-free rate, then the cost of capital for the firm's levered equity is closest to:Group of answer choices15%.25%.95%.45%.
Solution
To calculate the cost of capital for the firm's levered equity, we first need to calculate the expected free cash flows from the project. Given that the outcomes of 117,000 are equally likely, the expected free cash flow is the average of the two, which is $103,500.
Next, we need to calculate the present value of these expected cash flows, discounted at the project's cost of capital of 15%. The present value (PV) is calculated as follows:
PV = Expected Cash Flow / (1 + Cost of Capital)
Substituting the given values, we get:
PV = 90,000
Since the firm borrows the initial investment of $80,000 at the risk-free rate of 5%, the present value of this debt, discounted at the risk-free rate, is:
PV of Debt = Debt / (1 + Risk-Free Rate) = 76,190.48
The levered equity value of the firm is the difference between the present value of the expected cash flows and the present value of the debt, which is:
Levered Equity Value = PV - PV of Debt = 76,190.48 = $13,809.52
The cost of capital for the firm's levered equity is then the expected cash flow divided by the levered equity value, minus 1, expressed as a percentage:
Cost of Capital for Levered Equity = (Expected Cash Flow / Levered Equity Value - 1) * 100%
Substituting the given values, we get:
Cost of Capital for Levered Equity = (13,809.52 - 1) * 100% = 650%
Therefore, the cost of capital for the firm's levered equity is closest to 650%, which is not among the provided answer choices. Please check the question again as there might be a mistake in the provided answer choices.
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