Question

Knotts, Inc., an all-equity firm, is considering an investment of $1.77 million that will be depreciated according to the straight-line method over its four-year life. The project is expected to generate earnings before taxes and depreciation of $606,000 per year for four years. The investment will not change the risk level of the firm. The company can obtain a four-year, 8.6 percent loan to finance the project from a local bank. All principal will be repaid in one balloon payment at the end of the fourth year. The bank will charge the firm $56,000 in flotation fees, which will be amortized over the four-year life of the loan. If the company financed the project entirely with equity, the firm’s cost of capital would be 13 percent. The corporate tax rate is 25 percent.

   

Using the adjusted present value method, calculate the APV of the project.

Answer 1

APV = NPV of all-equity cash flows + NPV of financing side effects

Step 1: NPV of all-equity cash flows = - initial investment + PV of all Free Cash Flows (FCF)

= - initial investment + PV of[ (1-Tax rate)*EBTD] + PV of Depreciation*Tax rate

PV of [(1-Tax rate)*EBTD]: [(1-Tax rate)*EBTD] = (1-25%)*606,000 = 454,500

PMT = 454,000; N = 4; rate = 13%, solve for PV. PV = 1,351,897.22

PV of Depreciation*Tax rate: Depreciation*Tax rate = (1,770,000/4)*25% = 110,625

PMT = 110,625; rate = 13%; N = 4, solve for PV. PV = 329,050.89

NPV = -1770,000 + 1,351,897.22 + 329,050.89 = -89,051.89

Step 2: NPV of financing side effects = Net proceeds - Aftertax PV of interest payments - PV of principal payment + PV of flotation cost shield

Net proceeds = debt amount - flotation costs = 1,770,000 - 56,000 = 1,714,000

Interest payment = (1-Tax rate)*interest rate*debt amount = (1-25%)*8.6%*1,770,000 = 114,165

PMT = 114,165; N = 4; rate = 8.6%, solve for PV. PV of interest payment = 373,133.41

Principal payment = 1,770,000; PV = 1,770,000/(1+8.6%)^4 = 1,272,488.79

Flotation cost over 4 years = 56,000/4 = 14,000; Flotation tax shield = 25%*14,000 = 3,500

PV of floation tax shield: PMT = 3,500; N = 4; rate = 8.6%, solve for PV. PV = 11,439.29

NPV of financing side effects = 1,714,000 - 373,133.41 - 1,272,488.79 + 11,439.29 = 79,817.10

Step 3: APV = -89,051.89 + 79,817.10 = -9,234.80