Question

Ms. T. Potts, the treasurer of Ideal China, has a problem. The company has just ordered a new kiln for $640,000. Of this sum, $80,000 is described by the supplier as an installation cost. Ms. Potts does not know whether the Internal Revenue Service (IRS) will permit the company to treat this cost as a tax-deductible current expense or as a capital investment. In the latter case, the company could depreciate the $80,000 straight-line over 5 years. The tax rate is 30% and the opportunity cost of capital is 5%.

a. What is the present value of the cost of the kiln if the installation cost is treated as a separate current expense?
b. What is the present value of the cost of the kiln if the installation cost is treated as a part of the capital investment? (Round your answer to the nearest whole dollar amount.)

Answer 1

a]

As the entire installation cost is treated as a current expense, it is expensed immediately for tax purposes, and no discounting is required.

base cost = total cost - installation cost = $640,000 - $80,000 = $560,000

Cost of kiln = base cost + (installation cost * (1 - tax rate))

Cost of kiln = $560,000 + ($80,000 * (1 - 30%))

Cost of kiln = $616,000

present value of the cost of the kiln =  $616,000

b]

present value of the cost of the kiln = total cost - present value of tax shields

present value = future value / (1 + cost of capital)^{number of years}

tax shield in each year = (installation cost / depreiciable life in years) * tax rate

tax shield in each year = ($80,000 / 5) * 30% = $4,800

present value of tax shields = ($4,800 / (1 + 5%)¹) + ($4,800 / (1 + 5%)²) + ($4,800 / (1 + 5%)³) + ($4,800 / (1 + 5%)⁴) + ($4,800 / (1 + 5%)⁵)

present value of tax shields = $20,781.49

present value of the cost of the kiln = $640,000 - $20,781.49

present value of the cost of the kiln = $619,219