Propel Corporation plans to make a $51.3 million investment, initially funded completely with debt. The free cash flows of the investment and Propel's incremental debt from the project are shown here: Propel's incremental debt for the project will be paid off according to the predetermined schedule shown. Propel's debt cost of capital is 8.8%, and its tax rate is 34%. Propel also estimates an unlevered cost of capital for the project of 11.1%. a. Use the APV method to determine the levered value of the project at each date and its initial NPV. b. Calculate the WACC for this project at each date. How does the WACC change over time? Why? c. Compute the project's NPV using the WACC method. d. Compute the equity cost of capital for this project at each date. How does the equity cost of capital change over time? Why? e. Compute the project's equity value using the FTE method. How does the initial equity value compare with the NPV calculated in parts (a) and (c)? Hint: Make sure to round all intermediate calculations to at least four decimal places. ... a. Use the APV method to determine the levered value of the project at each date and its initial NPV. The levered value of the project at each date will be: (Round all answers to two decimal places.) Year APV ($ million) 0 1 2 3 Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Year 0 1 2 3 Free cash flows ($ million) Debt ($ million) - 51.3 41.4 18.9 23.2 51.3 31.9 13.9 0.0 Print Done Propel Corporation plans to make a $55.0 million investment, initially funded completely with debt. The free cash flows of the investment and Propel's incremental debt from the project are shown here: Propel's incremental debt for the project will be paid off according to the predetermined schedule shown. Propel's debt cost of capital is 10.0%, and its tax rate is 42%. Propel also estimates an unlevered cost of capital for the project of 15.0%. a. Use the APV method to determine the levered value of the project at each date and its initial NPV. b. Calculate the WACC for this project at each date. How does the WACC change over time? Why? c. Compute the project's NPV using the WACC method. d. Compute the equity cost of capital for this project at each date. How does the equity cost of capital change over time? Why? e. Compute the project's equity value using the FTE method. How does the initial equity value compare with the NPV calculated in parts (a) and (c)? Hint: Make sure to round all intermediate calculations to at least four decimal places. Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Year 0 1 2 3 Free cash flows ($ million) Debt ($ million) - 55.0 45.0 25.0 30.0 55.0 35.0 20.0 0.0 Print Done a. Use the APV method to determine the levered value of the project at each date and its initial NPV. We first compute unlevered value of the project at each date by discounting the project's future FCF at rate ru = 15.0%: ($ million) Free cash flows V(Unlevered) Year 0 Year 1 Year 2 Year 3 - 55.0 77.76 45.0 25.0 30.0 44.42 26.09 Then we compute the value of the future interest tax shields at each date by discounting at rate D = 10.0%: ($ million) Debt Interest at 10.0% Tax shield at 42% PV(ITS) Year 0 Year 1 Year 2 Year 3 55.0 35.0 20.0 0.0 5.50 3.50 2.00 2.31 1.47 0.84 3.95 2.03 0.76 Finally, we compute V = APV = V + PV (ITS): Finally, we compute V = APV = V + + PV (ITS): ($ million) V(Unlevered) PV(ITS) APV Year 0 Year 1 Year 2 Year 3 77.76 44.42 26.09 3.95 2.03 0.76 81.71 46.45 26.85 To calculate the project's NPV, use the following equation: NPV=APV - Initial investment Therefore, NPV $81.71 million - $55.0 million = $26.71 million The project's NPV will be $26.71 million. b. Calculate the WACC for this project at each date. How does the WACC change over time? Why? To compute the WACC at each date, use the following expression: D ('D+ ('u 'D)) wacc -UD+EC D D where the debt-to-value ratio, is given by D+ E' and the debt persistence, , is given by PV(ITS) TC XD (since all tax shields are predetermined). Therefore, ($ million) Year 0 Year 1 Year 2 Year 3 Debt 55.0 35.0 20.0 0.0 APV 81.71 46.45 26.85 DIV- 67.31% 75.35 74.49% PV(ITS) 3.95 2.03 0.76 =PV(ITS)/TcxD 17.1% 13.8% 9.0% "wacc 11.931% 11.617% 11.731% The WACC decreases from date 0 to 1 and increases from date 1 to 2. The WACC fluctuates because the leverage ratio of the project changes over time. c. Compute the project's NPV using the WACC method. We can compute the levered value of the project by discounting the FCF using the WACC at each date as in the following formulas: V = v= = FCF3 1+rwacc (2) FCF+ V 1+rwacc (1) FCF + 1 1+rwacc (0) Therefore, $30.0 million = = $26.8502 million 1 +0.11731 $25.0 million + $26.8502 million = $46.4537 million 1 +0.11617 $45.0 million+ $46.4537 million = $81.7054 million 1 +0.11931 To calculate the NPV, use the following equation: NPV= = - Initial investment Therefore, NPV = $81.7054 million - $55.0 million = $26.71 million The project's NPV using the WACC method will be $26.71 million. d. Compute the equity cost of capital for this project at each date. How does the equity cost of capital change over time? Why? To compute the project's equity cost of capital, use the following formula: re=ru+ D-PV (ITS) E -x (ru-ro) Therefore, Therefore, ($ million) Year 0 Year 1 Year 2 Year 3 D-PV (ITS) 51.05 32.97 19.24 E=V-D 26.71 11.45 6.85 (D-PV (ITS))/E 1.91 2.88 2.81 "E 24.6% 29.4% 29.1% The equity cost of capital rises and then falls with the project's effective debt-equity ratio. e. Compute the project's equity value using the FTE method. How does the initial equity value compare with the NPV calculated in parts (a) and (c)? We first compute FCFE at each date by deducting the after-tax interest expenses (equivalently, deducting interest and adding back the tax shield) and adding net increases in debt as in the following equation: FCFE = FCF - Interest + Tax shield + Debt. Therefore, ($ million) Year 0 Year 1 Year 2 Year 3 Free cash flows - 55.0 45.0 25.0 30.0 -Interest at 10.0% + Tax shield at 42% + Increment in debt FCFE 55.0 0.00 -5.50 2.31 - 20.0 21.81 -3.50 -2.00 1.47 - 15.0 7.97 0.84 - 20.0 8.84 Then we compute the equity value of the project by discounting FCFE using r at each date using the following formulas: E2 FCFE3 E = 1+E (2) E = = = FCFE2 + E2 Eo Therefore, 1+re (1) FCFE + E 1+re (0) $8.84 million E2= $6.85 million 1 + 0.291 $7.97 million + $6.85 million E 1 +0.294 Eo = = $11.45 million $21.81 million + $11.45 million 1 +0.246 = $26.69 million The project's equity value using the FTE method is $26.69 million. The value of the equity is comparable to the one computed in parts (a) and (c).