Terrell Industries is considering two alternative ways to depreciate a proposed investment.The investment has an initial cost of $100,000 and an expected five-year life.The two alternative depreciation schedules follow: Assuming that the company faces a marginal tax rate of 40 percent and has a cost of capital of 10 percent,what is the difference between the two methods in the present value of the depreciation tax benefit? Present value tables or a financial calculator are required.

Question

Terrell Industries is considering two alternative ways to depreciate a proposed investment.The investment has an initial cost of $100,000 and an expected five-year life.The two alternative depreciation schedules follow:  Assuming that the company faces a marginal tax rate of 40 percent and has a cost of capital of 10 percent,what is the difference between the two methods in the present value of the depreciation tax benefit? Present value tables or a financial calculator are required.

Quizplus · Accepted Answer

Using the straight-line method, the annual depreciation is ($100,000/5) = $20,000.

Using the MACRS method, the annual depreciation for year 1 is ($100,000 * 0.20) = $20,000. For year 2, it is ($100,000 * 0.32) = $32,000. For year 3, it is ($100,000 * 0.192) = $19,200. For year 4, it is ($100,000 * 0.1152) = $11,520. For year 5, it is ($100,000 * 0.1152) = $11,520.

To calculate the present value of the tax benefit, we first need to calculate the tax savings from each depreciation method.

With the straight-line method, the tax savings each year will be ($20,000 * 0.4) = $8,000. To find the present value of these tax savings, we can use the present value of an annuity formula:

PV = PMT * [(1 - (1 / (1 + r)n)) / r] where PMT is the annual tax savings, r is the discount rate (which is the cost of capital in this case), and n is the number of years.

Using this formula, we get:

PV (straight-line) = $8,000 * [(1 - (1 / (1 + 0.1)5)) / 0.1] = $29,698.

With the MACRS method, the tax savings each year will be as follows:

Year 1: ($20,000 * 0.4) = $8,000
Year 2: ($32,000 * 0.4) = $12,800
Year 3: ($19,200 * 0.4) = $7,680
Year 4: ($11,520 * 0.4) = $4,608
Year 5: ($11,520 * 0.4) = $4,608

To find the present value of these tax savings, we can use the present value of a mixed stream formula:

PV = (PMT1 / r) * [(1 - (1 / (1 + r)n1)) / (1 + r)] + (PMT2 / r) * [(1 - (1 / (1 + r)n2)) / (1 + r)^n1]

where PMT1 and PMT2 are the annual tax savings, n1 and n2 are the number of years for each PMT, and n is the total number of years.

Using this formula, we get:

PV (MACRS) = ($8,000 / 0.1) * [(1 - (1 / (1 + 0.1)1)) / (1 + 0.1)] + ($12,800 / 0.1) * [(1 - (1 / (1 + 0.1)2)) / (1 + 0.1)^1] + ($7,680 / 0.1) * [(1 - (1 / (1 + 0.1)3)) / (1 + 0.1)^2] + ($4,608 / 0.1) * [(1 - (1 / (1 + 0.1)4)) / (1 + 0.1)^3] + ($4,608 / 0.1) * [(1 - (1 / (1 + 0.1)5)) / (1 + 0.1)^4] 
= $26,820.

Therefore, the difference between the two methods in the present value of the tax benefit is:

$26,820 - $29,698 = -$2,878

Since the MACRS method has a lower present value of the tax benefit, the straight-line method is the better choice.

Terrell Industries Is Considering Two Alternative Ways to Depreciate a Proposed