Question

Knotts, Incorporated, an all-equity firm, is considering an investment of $1.32 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 $470,000 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. All principal will be repaid in one balloon payment at the end of the fourth year. The bank will charge the firm $45,000 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 14 percent. The corporate tax rate is 25 percent. Calculate the adjusted present value of the project.

Answer 1

To compute the adjusted present value of Knotts, Incorporated's project, one must calculate the unlevered NPV of the project's cash flows and then add the net present value of the financing benefits (e.g., tax shield on the interest payments). This involves using the straight-line method to calculate depreciation, determining taxable income, and applying the tax rate to find taxes saved and after-tax income. Financing effects like the floating fees, interest tax shields, and the balloon payment's present value also need to be accounted for.

Step-by-step explanation:

To calculate the adjusted present value (APV) of Knotts, Incorporated's potential project, we must consider both the unleveraged project value and the financing effects separately. First, we calculate the project's unleveraged NPV by discounting the cash flows at the company's cost of equity, and then we add the present value of the financing effects.

The annual depreciation is $1.32 million / 4 years = $330,000. Each year's after-tax operating cash flow is calculated as follows: $470,000 - $330,000 (depreciation) = $140,000 taxable income. The taxes saved due to depreciation $330,000 x 25% tax rate = $82,500, so the total after-tax income is $140,000 - $140,000 x 25% + $82,500 = $187,500 each year.

To calculate the NPV of the project, we discount the after-tax cash flows at the cost of equity:

1. NPV = $187,500 / (1 + 0.14)^1 + $187,500 / (1 + 0.14)^2 + $187,500 / (1 + 0.14)^3 + $187,500 / (1 + 0.14)^4

The present value of the financing effects includes the tax shield on the loan's interest payments and the amortized flotation fees. Since the interest rate is 9.5% on the $1.32 million loan, the annual interest expense is $125,400. The tax shield is $125,400 x 25% = $31,350 per year. As the loan is repaid in a balloon payment, we calculate the present value of all tax shields and the flotation costs over the life of the loan.

Finally, we add the initial outlay of the project and the present value of the loan repayment at the end of year 4:

APV = Unlevered NPV + PV of Tax Shields - Initial Investment - PV of Loan Repayment - PV of Flotation Fees

Note that to calculate the exact figure, you would need to perform the individual present value calculations at the respective discount rates (cost of capital for the project and the interest rate for the debt) for each cash flow.

Answer 2

To calculate the adjusted present value (APV) of the project, calculate the present value (PV) of the tax shield and the PV of the project's cash flows. The PV of the tax shield is calculated using the depreciation expense and tax rate. The PV of the cash flows is calculated using the cash flow and discount rate.

Step-by-step explanation:

To calculate the adjusted present value (APV) of the project, we need to calculate the present value (PV) of the tax shield and the PV of the project's cash flows. The PV of the tax shield is the tax savings resulting from the depreciation expense. In this case, the annual depreciation expense is $330,000 ($1.32 million divided by 4 years), and the tax rate is 25 percent.

The tax savings can be calculated as: Tax savings = Depreciation expense * Tax rate. So, the tax savings per year will be $82,500 ($330,000 * 25%).

The PV of the tax shield can be calculated using the formula: PV = Tax savings / Discount rate. In this case, the discount rate is the firm's cost of equity capital, which is 14 percent.

Using the formula, the PV of the tax shield will be: PV = $82,500 / 0.14 = $589,285.71 (rounded to the nearest dollar).

The PV of the project's cash flows can be calculated using the formula: PV = Cash flow / Discount rate. In this case, the cash flow per year is $470,000, and the discount rate is the cost of the loan, which is 9.5 percent.

The PV of the project's cash flows will be: PV = $470,000 / 0.095 = $4,947,368.42 (rounded to the nearest dollar).

The adjusted present value (APV) of the project is the sum of the PV of the tax shield and the PV of the project's cash flows:

APV = PV of tax shield + PV of cash flows = $589,285.71 + $4,947,368.42 = $5,536,654.13 (rounded to the nearest dollar).