Final answer:
The NPV of the project is calculated to be $60,429.20. The initial market value of the unlevered equity is equal to the present value of its expected cash flows, $135,429.20. When the project is financed through debt, the cash flows of the levered equity become $88,286.50, which is the expected cash flows minus the debt repayment.
Step-by-step explanation:
To compute the Net Present Value (NPV) of this uncertain project, we must first calculate the expected cash flow. Since there are two equally likely outcomes, the expected cash flow is ($149,012 + $189,561) / 2, which equals $169,286.50. To discount this back to its present value, we use the formula PV = Cash Flow / (1 + r), where r is the project's cost of capital. Therefore, the present value of the expected cash flow is $169,286.50 / (1 + 0.25), which gives $135,429.20. Subtracting the initial investment of $75,000 from the present value gives us the NPV: $135,429.20 - $75,000 = $60,429.20.
Next, the initial market value of the unlevered equity can be determined by discounting the expected cash flow at the cost of capital, which we already computed as the present value of $135,429.20, as no new financing is assumed.
For the levered equity, when the $75,000 is raised by borrowing at the risk-free interest rate. The debt will be paid back with interest, which means the levered equity holders will receive the expected cash flows of the project minus the repayment amount.
Borrowing at 8% risk-free interest rate, the repayment amount will be $75,000 (1+0.08) = $81,000.
Hence, the expected cash flow for the levered equity is $169,286.50 - $81,000 = $88,286.50. Discounting this at the project's cost of capital provides the initial value of the levered equity, which will be less than the unlevered equity due to the return demanded for the additional risk incurred by leveraging.