Final answer:
The net present value (NPV) of the project is $21,986.38.
Step-by-step explanation:
To calculate the net present value (NPV) of the project, we first need to calculate the cost of equity capital using the CAPM model. The CAPM model states that the cost of equity is equal to the risk-free rate plus the beta of the project multiplied by the market risk premium. In this case, the risk-free rate is 3.8 percent, the market risk premium is 7 percent, and the average beta of the comparable companies is 1.27 ((1.23 + 1.16 + 1.38 + 1.33) / 4). So the cost of equity capital is 3.8% + 1.27 * 7% = 12.89%.
Next, we calculate the levered beta of the project using the debt-value ratio. The levered beta is the weighted average of the unlevered betas of the comparable companies, with weights proportional to the debt-value ratio. In this case, the debt-value ratio is 0.4, so the levered beta is 1.27 * 0.4 + (1 - 0.4) = 0.508 + 0.6 = 1.108.
Now, we can calculate the cost of capital (WACC) using the levered beta and the cost of equity capital. The WACC is the weighted average of the cost of equity and the cost of debt, with weights proportional to the equity-value ratio and the debt-value ratio. In this case, the equity-value ratio is 1 - 0.4 = 0.6, the cost of equity capital is 12.89%, and the yield to maturity of the bonds is 6.4%. So the WACC is 0.6 * 12.89% + 0.4 * 6.4% = 7.734%.
Finally, we can calculate the NPV of the project using the WACC and the cash flows. The NPV is the sum of the present values of the cash flows, where the present value of each cash flow is calculated by dividing the cash flow by (1 + WACC)^(number of years from now). In this case, the cash flows are $843,000 per year for 20 years, and the WACC is 7.734%. So the NPV is:
(843,000 / (1 + 7.734%)^1) + (843,000 / (1 + 7.734%)^2) + ... + (843,000 / (1 + 7.734%)^20) - 5.1 million = $21,986.38