Question

Gemini, Inc., an all-equity firm, is considering a $1.7 million investment 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 $595,000 per year for four years. The investment will not change the risk level of the firm. The company can obtain a four-year, 9.5 percent loan to finance the project from a local bank. They will receive the total amount needed for investment ($1.7 million at time 0 and all principal will be repaid in one balloon payment at the end of the fourth year (similar to a bond). Every year the company would need to pay interest (@9.5%). If the company finances the project entirely with equity, the firm’s cost of capital would be 13 percent. The corporate tax rate is 30 percent. Calculate the cash flows and NPV for the two cases: a) If the company finances the project entirely with equity, and b) if the company finances the project entirely with the bank loan. Are the answers different? If so, why? Should the project be undertaken? (Hint: In the first case you need to discount your cash flows at 13% and in the second case with 9.5% when you calculate NPV).

Answer 1

Solution:

Calculation of the Cash Flows and NPV for the Two Cases:

a) If the company finances the project entirely with equity,

NPV of financing side effects equals the after-tax present value of the cash flows will resulting from the firm’s debt, Thus,

APV = NPV(All-Equity) + NPV(Financing Side Effects)

So, the NPV of each part of the APV equation is as follows:

NPV (All-Equity)

NPV = -Purchase Price + PV[(1 - tC)(EBTD)] + PV(Depreciation Tax Shield)

The initial investment of $1.7 million will be fully depreciated over four years using the straight-line method. The Annual depreciation expense is as follows,

Depreciation = $1,700,000/4

Depreciation = $425,000

NPV = -$1,700,000 + (1 - 0.30) ($595,000) PVIFA_13%,4 + (0.30) ($425,000) PVIFA_9.5%,4

NPV (All-equity) = -$52,561.35.

b) if the company finances the project entirely with the bank loan,

NPV (Financing Side Effects):

The net present value of financing side effects equals the after tax present value of cash flows which is resulting from the firm’s debt. So, the NPV of the financing side effects are as follows,

NPV = Proceeds (Net of flotation) - Aftertax PV (Interest Payments) - PV (Principal Payments) + PV (Flotation Cost Tax Shield)

The annual flotation costs that will be expensed each year are as follows,

Annual flotation expense = $45,000/4

Annual flotation expense = $11,250.

Then the NPV is as follows,

NPV = ($1,700,000 - 45,000) - (1 - 0.30) (0.095) ($1,700,000) PVIFA_9.5%,4 - $1,700,000/1.0954 + 0.30 ($11,250) PVIFA_9.5%,4

NPV = $121,072.23.

So, the APV of the project is:

APV = NPV(All-Equity) + NPV(Financing Side Effects)

APV = -$52,561.35 + $121,072.23

APV = $68,510.88

By the Above Calculation, the Company has to Accept the Second Case, because it has the Positive NPV (Net Present Value).