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 .45, but the industry target debt-equity ratio is .40. The industry average beta is 1.10. The market risk premium is 6.1 percent and the risk-free rate is 4.7 percent. Assume all companies in this industry can issue debt at the risk-free rate. The corporate tax rate is 25 percent. The project requires an initial outlay of $885,000 and is expected to result in a $113,000 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 4 percent until the end of the fifth year and remain constant forever thereafter.

Calculate the NPV of the project.

Answer 1

Cost of debt = Risk free rate = 4.7%

Industry Beta = 1.10

Unlevered Beta = Industry Beta/ {1 + (1- tax rate)*Industry target debt equity ratio}

Unlevered Beta = 1.10/ {1 + (1 - 0.25) * 0.40) = 1.10/1.3 = 0.846

Levered Beta = Unlevered Beta * { 1 + (1 - tax rate)* company's debt equity ratio}

Levered Beta = 0.846 * { 1 + (1 -0.25)*0.45} = 1.131

Cost of equity = Risk free rate + Levered Beta * Market Risk Premium

Cost of equity = 4.7% + 1.131*6.1% = 4.7% + 6.903 = 11.603%

Company's D/E ratio = 0.45

Debt proportion = 0.45 / (1 + 0.45) = 31.03%

WACC = Cost of debt * Debt proportion * (1- Tax rate) + Cost of equity * Equity proportion

WACC = 4.7*31.03* (1-0.25) + 11.603*(1 - Debt proportion)

WACC = 4.7 * 0.3103 * (1-0.25) + 11.603*(1 - 0.3103)

WACC = 9.096%

Annual cash flows from the project will grow at a constant rate of 4 percent until the end of the fifth year and remain constant forever thereafter

Initial inflow = $113,000

Inflow at year 5 = 113,000 * (1 + growth rate)^4 = 113,000 * (1 + 0.04)^4 =$132,194

Present value of cash flows = Initial inflow/ (WAAC - growth rate)*[1- {(1+growth rate)/(1 +WACC)}^5]

Present value of cash flows (year 1 to 5) at t=0 = 113,000/ (9.096-4) * [1 -{(1+0.04)/(1+0.09096)}^5] = $471,717.5

PV of cash flow from year 6 onward at t=0 = (132,194/wacc)*(1/(1+WACC)^5)

PV of cash flow from year 6 onward at t=0 = 1453320.141 * (1/1.5454) = $940,409.81

NPV = P.V. of inflows - initial investment = $471,717.5 + $940,409.81 - $885,000 = $527,127.326