Question

Blue Angel, Inc., a private firm in the holiday gift industry, is considering a new project. The company currently has a target debt-equity ratio of .40, but the industry target debt-equity ratio is .35. The industry average beta is 1.20. The market risk premium is 6.4 percent and the risk-free rate is 4 percent. Assume all companies in this industry can issue debt at the risk-free rate. The corporate tax rate is 23 percent. The project requires an initial outlay of $800,000 and is expected to result in a $96,000 cash inflow at the end of the first year. The project will be financed at the company’s target debt-equity ratio. Annual cash flows from the project will grow at a constant rate of 6 percent until the end of the fifth year and remain constant forever thereafter.

      

Calculate the NPV of the project. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

NPV = present value of cash inflows of first 5 years + present value of horizon value at end of 5th year - initial investment.

cost of capital = (weight of debt * cost of debt) + (weight of equity * cost of equity).

The weights of debt and equity are the target company weights of 0.40 and 0.60.

cost of debt = risk free rate * (1 - tax rate)  = 4% * (1 - 23%) = 3.08%

cost of equity = risk free rate + (beta * market risk premium)

cost of equity = 4% + (1.2 * 6.4%) = 11.68%.

cost of capital = (0.40 * 3.08%) + (0.6 * 11.68%) = 8.24%.

Horizon value at end of year 5 = constant cash cash flow after 5 years / cost of capital.

present value = future value / (1 + cost of capital)^{number of years}

Present value of present value of cash inflows of first 5 years = $425,480.36

Horizon value = $81,574.75 / 8.24% = $989,984.89.

Present value of horizon value =  $989,984.89 / (1 + 8.24%)⁵ = $666,330.43.

NPV =  $425,480.36 + $666,330.43 - $800,000 = $291,810.79