Question

Q: Gemini,Inc,an all-equity firm,is considering a $2. I million investment that will be depreciated according to the straight-line method over its three-year life. The project is expected to generate earnings before taxes and depreciation of $900,000 per year for three years. The investment will not change the risk level of the firm. Gemini can obtain a three-year,12. 5% loan to finance the project from a local bank. All principal will be repaid in one balloon payment at the end of the third year. The bank will charge the firm S21,000 in flotation fees,which will be amortized over the three-year life of the loan. If Gemini financed the project entirely with equity,the firms cost of capital would be 18%. The corporate tax rate is 30%. Using the Adjusted Present Value(APV)method,determine whether or not Gemini should undertake the project.

Answer 1

Project APV = NPV of all-equity financed project + NPV of debt financing

1). NPV of all-equity financed project = -Initial investment + PV of [EBITDA*(1-Tax rate) + depreciation*tax rate]

EBITDA = 900,000; Tax rate = 30%; depreciation = initial investment/life = 2,100,000/3 = 700,000

[EBITDA*(1-Tax rate) + depreciation*tax rate] = 900,000*(1-30%) + (700,000*30%) = 840,000

Cost of equity ke = 18%;

PV(840,000) = 840,000*[1 -(1+18%)^-3]/18% = 840,000*2.17 = 1,826,389.26

NPV = - 2,100,000 + 1,826,389.26 = -273,610.74

2). NPV of debt financing = Net proceeds + PV(flotation cost tax shield) - PV(after-tax interest payment) - PV(principal payment)

Net proceeds = loan amount - flotation cost = 2,100,000 - 21,000 = 2,079,000

Pre-tax cost of debt kd = 12.5%

Flotation cost is amortized over the life so amortization per year = 21,000/3 = 7,000

Flotation tax shield = amortization*tax = 7,000*30% = 2,100

PV(flotation tax shield) = 2,100*[1 - (1+12.5%)^-3]/12.5% = 5,000.82

After-tax interest payment = (1- tax rate)*interest rate*principal = (1-30%)*12.5%*2,100,000 = 183,750

PV(after-tax interest payment) = 183,750*[1-(1+12.5%)^-3]/12.5% = 437,572.02

Principal payment = 2,100,000 at the end of 3 years.

PV of principal payment = 2,100,000/(1+12.5%)^3 = 1,474,897.12

NPV of debt financing = 2,079,000 + 5,000.82 - 437,572.02 - 1,474,897.12 = 171,531.69

APV of the project = -273,610.74 + 171,531.69 = -102,079.05

The project should not be undertaken as it has a negative APV.