QuestionJuly 20, 2025

Your company is considering a new project that will require 100,000 of new equipment at the start of the project. The equipment will have a depreciable life of 10 years and will be depreciated to a book value of 25,000 using straight-line depreciation. The cost of capital is 11 percent, and the firm's tax rate is 21 percent. Estimate the present value of the tax benefits from depreciation. Multiple Choice 34,894 44,169 9,276 16,997

Your company is considering a new project that will require 100,000 of new equipment at the start of the project. The equipment will have a depreciable life of 10 years and will be depreciated to a book value of 25,000 using straight-line depreciation. The cost of capital is 11 percent, and the firm's tax rate is 21 percent. Estimate the present value of the tax benefits from depreciation. Multiple Choice 34,894 44,169 9,276 16,997
Your company is considering a new project that will require 100,000 of new equipment at the start of the project. The equipment will have a
depreciable life of 10 years and will be depreciated to a book value of 25,000 using straight-line depreciation. The cost of capital is 11 percent, and
the firm's tax rate is 21 percent. Estimate the present value of the tax benefits from depreciation.
Multiple Choice
 34,894
 44,169
 9,276
 16,997

Solution
4.4(323 votes)

Answer

\ 9,276 Explanation 1. Calculate Annual Depreciation **Straight-line depreciation**: \text{Annual Depreciation} = \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Life}} = \frac{100,000 - 25,000}{10} = 7,500. 2. Calculate Tax Shield per Year **Tax Shield**: \text{Tax Shield} = \text{Depreciation} \times \text{Tax Rate} = 7,500 \times 0.21 = 1,575. 3. Calculate Present Value of Tax Shields **Present Value of Annuity Formula**: PV = C \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) where C = 1,575, r = 0.11, n = 10. PV = 1,575 \times \left(\frac{1 - (1 + 0.11)^{-10}}{0.11}\right) = 1,575 \times 5.8892 = 9,276.

Explanation

1. Calculate Annual Depreciation<br /> **Straight-line depreciation**: $\text{Annual Depreciation} = \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Life}} = \frac{100,000 - 25,000}{10} = 7,500$.<br /><br />2. Calculate Tax Shield per Year<br /> **Tax Shield**: $\text{Tax Shield} = \text{Depreciation} \times \text{Tax Rate} = 7,500 \times 0.21 = 1,575$.<br /><br />3. Calculate Present Value of Tax Shields<br /> **Present Value of Annuity Formula**: $PV = C \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$ where $C = 1,575$, $r = 0.11$, $n = 10$.<br /> $PV = 1,575 \times \left(\frac{1 - (1 + 0.11)^{-10}}{0.11}\right) = 1,575 \times 5.8892 = 9,276$.
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