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 .50. The industry average beta is 1.10. The market risk premium is 6.9 percent and the risk-free rate is 4.5 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 $825,000 and is expected to result in a $101,000 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 5 percent until the end of the fifth year and remain constant forever thereafter.
Calculate the NPV of the project.
Project Debt to Equity Ratio = Firm's Target Debt to Equity Ratio = 0.45, Industry Debt to Equity Ratio = 0.5, Industry Average Beta = 1.1, Tax Rate = 23 %
Calculation of Project (firm's) Equity Beta:
Industry Equity Beta = Industry Average Beta = 1.1, Industry Debt to Equity Ratio (DE1) = 0.5
Therefore, Industry Asset Beta = B(IA) = 1.1 / [1+(1-Tax Rate) x DE1] = 1.1 / [1+(1-0.23) x (0.5)] = 0.72202
Firm's Equity Beta = B(PE) = B(IA) x [1+(1-Tax Rate) x Project Debt to Equity Ratio] = 0.72202 x [1+(1-0.23) x (0.45)] = 0.9722
Risk - Free Rate = Rf = 4.5 % and Market Risk Premium = 6.9 % = MRP
As per CAPM, project's cost of equity = ke = Rf + B(PE) x MRP = 4.5 + 0.9722 x 6.9 = 11.2082 % ~ 11.21 %
Cost of Debt = Risk_Free Rate = kd = 4.5 %
Project DE Ratio = 0.45
Therefore, Debt Proportion = D = (0.45/1.45) and Equity Proportion = (1/1.45) = E
Weighted Average Cost of Capital of the Project = WACC = (0.45/1.145) x 4.5 x (1-0.23) + (1/1.145) x 11.21 = 9.09158 % ~ 9.092 %
Initial Project Outlay = $ 825000, Expected Year 1 Cash Inflow = CF1 = $ 101000
Initial 5-Year Growth Rate of Cash Flow = 5 %
CF1 = $ 101000, CF2 = 101000 x 1.05 = $ 106050. CF3 = 106050 x 1.05 = $ 111352.5, CF4 = 111352.5 x 1.05 = $ 116920.125, CF5 = 116920.125 x 1.05 = $ 122766.13125
Post Year 5, the Project Cash Flows remain constant at this level forever
Total Present Value of Initial Growth Phase Cash Flows = P1 = 101000 / (1.09092) + 106050 / (1.09092)^(2) + 111352.5 / (1.09092)^(3) + 116920.125 / (1.09092)^(4) + 122766.13125 / (1.09092)^(5) = $ 429467.9192
Total Present Value of Perpetually Constant Cash Flows = P2 = [122766.13125/(0.09092)] x [1/(1.09092)^(5)] = $ 873942.87
Therefore, Total Present Value of Project = P = P1 + P2 = 429467.9192 + 873942.87 = $ 1303410.794
Project NPV = P - Initial Outlay = 1303410.794 - 825000 = $ 478410.794 ~ $ 478410.79
Blue Angel, Inc., a private firm in the holiday gift industry, is considering a new project....
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