Suppose that you are able to generate an annual depreciation deduction of $34,000 that would otherwise have been taxed at a 30% rate each year for 5 years. Determine the present value of the annual tax savings using a 7.5% discount rate.

Question

Quizplus · Accepted Answer

Step 1: Calculate the annual tax savings as follows:
Annual depreciation deduction = $34,000
Tax rate = 30%
Tax savings = Annual depreciation × tax rate = $34,000 × 30% = $10,200

Step 2: Calculate the present value factor for 5 years at a discount rate of 7.5% using the present value of an annuity formula:
Present value factor = (1 - (1 + discount rate)-n) / discount rate
where n is the number of periods
Present value factor = (1 - (1 + 0.075)-5) / 0.075 = 3.627

Step 3: Calculate the present value of the tax savings using the present value factor as follows:
Present value = Tax savings × present value factor = $10,200 × 3.627 = $37,002

Therefore, the present value of the annual tax savings is $41,268 ($37,002 ÷ (1 + 0.075)). Option B is the correct answer.

Suppose That You Are Able to Generate an Annual Depreciation