Question

You are evaluating a potential investment in equipment. The equipment's basic price is $138,000, and shipping costs will be $4,100. It will cost another $20,700 to modify it for special use by your firm, and an additional $6,900 to install it. The equipment falls in the MACRS 3-year class that allows depreciation of 33% the first year, 45% the second year, 15% the third year, and 7% the fourth year. You expect to sell the equipment for 22,100 at the end of three years. The equipment is expected to generate revenues of $131,000 per year with annual operating costs of $67,000. The firm's marginal tax rate is 25.0%. What is the value of the after-tax cash flow associated with the sale of the equipment?

a. $16,575
b. $19,545
c. $10,221
d. $7,666
e. $9,324

Answer 1

The after-tax cash flow from the sale of the equipment is calculated by determining the book value at the end of three years, figuring out the gain from the sale, and then subtracting the tax on the gain. In this case, the after-tax cash flow from the sale is $19,545.

Step-by-step explanation:

To calculate the after-tax cash flow from the sale of the equipment, we need to consider the salvage value, the book value at the time of the sale, and the taxes on the gain or loss of the sale of the equipment.

Firstly, we need to calculate the accumulated depreciation over the 3 years using the MACRS rates provided: 33% for the first year, 45% for the second year, and 15% for the third year. The initial cost basis for depreciation includes the purchase price plus costs for shipping, modifications, and installation, which is $138,000 + $4,100 + $20,700 + $6,900 = $169,700.

Accumulated depreciation is calculated as follows:
Year 1: $169,700 * 33% = $56,001
Year 2: $169,700 * 45% = $76,365
Year 3: $169,700 * 15% = $25,455

Total depreciation over the 3 years is: $56,001 + $76,365 + $25,455 = $157,821.

The book value of the equipment at the end of the third year is the initial cost basis minus the accumulated depreciation: $169,700 - $157,821 = $11,879.

Since the equipment is sold for $22,100, there is a gain on sale: $22,100 - $11,879 = $10,221.

The tax on this gain at the firm's marginal tax rate of 25% is: $10,221 * 25% = $2,555.25.

Therefore, the after-tax cash flow from the sale is the sale price minus the tax on the gain: $22,100 - $2,555.25 = $19,544.75, which rounds to $19,545 when considering answer choices.