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 .35, but the industry target debt–equity ratio is .30. The industry average beta is 1.90. The market risk premium is 6 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 34 percent. The project requires an initial outlay of $682,000 and is expected to result in a $102,000 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

Given Information

Industry Average Beta = 1.90

Market Risk premium (r_m – r_f) = 6%

Risk free rate (r_f) = 4%

Required return on equity (r_e) = r_f + Beta * (r_m – r_f) = 4% + 1.90 * 6% = 15.40%

Interest rate on debt (r_d) = r_f = 4%

Tax Rate (T) = 34%

Formula for WACC

WACC = W_d * (r_d * (1-Tax)) + W_e * r_e

W_d &W_e – Weights of debt & equity shares, respectively

r_d & r_e   - Required returns debt & equity shares, respectively

Project to be financed at company’s target debt-equity (D/E) ratio of 0.35

Now, D/E = 0.35

=> W_d = D/(D+E) = 0.35/(0.35+1) = 25.93%

=> W_e = E/(D+E) = 1/(0.35+1) = 74.07%

So, WACC = W_d * (r_d * (1-Tax)) + W_e * r_e = 0.2593* (0.04* (1-0.34)) + 0.7407 * 0.1540

WACC = 12.09%

Now, initial outlay (Inv) = $682,000

Cash Flow at the end of first year (CF1) = $102,000

Cash Flow growth rate = 4% till the end of 5^th year after which it is constant

Cash Flow at the end of second year (CF2) = $102,000 * (1+0.04) = $ 106,080

Cash Flow at the end of third year (CF3) = $ 106,080 * (1+0.04) = $110,323

Cash Flow at the end of fourth year (CF4) = $110,323 * (1+0.04) = $ 114,736

Cash Flow at the end of fifth year (CF5) = $ 114,736 * (1+0.04) = $ 119,326 (which continues forever)

4^th year end onwards there is perpetual annuity of $ 119,326.

Sum of perpetual annuity is given by = Constant Cash Flow/ Required rate

= $ 119,326/(0.1209) = $ 986,826 (TV, Terminal value at end of year 4)

Now, NPV of the project = -Inv + CF1/(1+WACC) + CF2/(1+WACC)² + CF3/(1+WACC)³ + CF4/(1+WACC)⁴ + TV/(1+WACC)⁴

NPV = -682,000 + 102,000/(1+0.1209) + 106,080/(1+0.1209)² + 110.323/(1+0.1209)³ + 114,736/(1+0.1209)⁴ + 986,826/(1+0.1209)⁴

So, Project NPV = $ 269,529