Question

marshall-miller & company is considering the purchase of a new machine for $50,000, installed. the machine has a tax life of 5 years. under the new tax law, the machine is eligible for 100% bonus depreciation, so it will be fully depreciated at t = 0. the firm expects to operate the machine for 4 years and then to sell it for $21,500. if the marginal tax rate is 25%, what will the after - tax salvage value be when the machine is sold at the end of year 4?
$12,551
$12,877
$12,225
$16,125
$14,833

Explanation:

Step1: Determine Book Value

Since the machine is fully depreciated at \( t = 0 \), the book value at the end of Year 4 is \( \$0 \).

Step2: Calculate Tax on Gain

The sale price is \( \$21,500 \). The gain on sale is \( \text{Sale Price} - \text{Book Value} = 21500 - 0 = 21500 \). The tax on the gain is \( \text{Gain} \times \text{Tax Rate} = 21500 \times 0.25 = 5375 \).

Step3: Calculate After - Tax Salvage Value

The after - tax salvage value is \( \text{Sale Price} - \text{Tax on Gain} = 21500 - 5375 = 16125 \). Wait, no, wait. Wait, the machine is fully depreciated, so the book value is 0. But maybe I made a mistake. Wait, no, the formula for after - tax salvage value is: If \( \text{Sale Price} > \text{Book Value} \), then \( \text{After - tax Salvage} = \text{Sale Price}-(\text{Sale Price}-\text{Book Value})\times\text{Tax Rate} \). So substituting the values: \( \text{Book Value} = 0 \), \( \text{Sale Price} = 21500 \), \( \text{Tax Rate}=0.25 \). So \( 21500-(21500 - 0)\times0.25=21500 - 5375 = 16125 \). Wait, but let's check the options. One of the options is $16,125.

Answer:

$16,125