Gemini, Inc., an all-equity firm, is considering an investment of $1.73 million
ID: 2783223 • Letter: G
Question
Gemini, Inc., an all-equity firm, is considering an investment of $1.73 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 $607,000 per year for four years. The investment will not change the risk level of the firm. The company can obtain a four-year, 8.8 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 $57,000 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 12 percent. The corporate tax rate is 35 percent. Using the adjusted present value method, calculate the APV of the project. (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) APV $
Explanation / Answer
Adjusted present value of a project is equal to the net present value of the project under all-equity financing plus the net present value of any financing side effects (debt financing).
In simpler words, APV = PV of cashflows + PV of tax savings
APV = NPV of (All-Equity) + NPV of (Financing Side Effects)
NPV of financing side effects = After-tax present value of the cash flows resulting from debt
NPV of (All-Equity):
NPV = -Initial Investment + PV * [(1-TC) * (Earnings Before Taxes and Depreciation)] + PV of (Depreciation Tax Shield)
Since the initial investment of $1.73 million will be fully depreciated over four years using the straight-line method, annual depreciation expense = $1730000 / 4 = $432500
NPV = -$1730000 + (1-0.35) * [$607,000 /(1+12%)4] + (0.35)* [$432500 /(1+12%)4]
= -$1730000 + $250743.658 + $96201.549 = -$1383054.793
NPV of (Financing Side Effects):
The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt.
NPV(Financing Side Effects) = (Proceeds - flotation costs) – After-Tax PV(Interest Payments) – PV(Principal Payments) + PV(Flotation Cost Tax Shield)
debt cash flows should be discounted at the pre-tax cost of debt 8.5%. Since $57000 in flotation costs will be amortized over the four-year life of the loan, $14250 = ($57000 / 4) of flotation costs will be expensed per year.
NPV(Financing Side Effects) = ($1730000 - $57000) – (1 – 0.35) * 0.085 * [$1730,000/(1+8.5%)4]– [$1730,000/(1.085)4] + (0.30) * ($14250) * /(1+8.5%)4
= $1673000 - $68969.87 - $1248323.512 + $3084.73 = $358791.348
APV
APV = NPV(All-Equity) + NPV(Financing Side Effects)
= -$1383054.793 + $358791.348 = -$1024263.445
APV is negative suggesting Gemini should not go ahead with the project.
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