Question

Leisure Vacations is considering a 5-year project which will require the purchase of $1.4 million in new 5-Year MACRS equipment The MACRS rates are 20 percent, 32 percent, 19.2 percent, 11.52 percent, 11.52 percent, and 5.76 percent for Years 1 to 6, respectively. The firm desires a minimal 14 percent rate of return and the tax rate is 34 percent. The equipment can be sold at the end of the project for an estimated $225,000. What is the amount of the aftertax salvage value? Select one: a. $95,322.15 b. $162,418.54 c. $147,600.00 d. $175,917.60 e. $144,238.97

Answer 1

The aftertax salvage value can be calculated by determining the book value of the equipment and subtracting the tax liability on that value. The book value is calculated as the initial cost minus the accumulated depreciation, which is found using the MACRS rates. The tax liability is then computed by multiplying the gain or loss with the tax rate. Finally, the after-tax salvage value is obtained by subtracting the tax liability from the market value of the equipment.

Step-by-step explanation:

The after-tax salvage value can be calculated as the difference between the market value of the equipment and the tax liability on that value. To calculate the tax liability, we need to first calculate the book value of the equipment, which is the initial cost minus the accumulated depreciation. The accumulated depreciation is calculated using the MACRS rates. The book value at the end of Year 5 is equal to the initial cost minus the sum of the depreciation deductions for Year 1 to Year 5.

Let's calculate the aftertax salvage value:

1. Depreciation deductions for Year 1 to Year 5

• Year 1: 20% of $1.4 million = $280,000
• Year 2: 32% of $1.4 million = $448,000
• Year 3: 19.2% of $1.4 million = $268,800
• Year 4: 11.52% of $1.4 million = $161,280
• Year 5: 11.52% of $1.4 million = $161,280

Accumulated depreciation at the end of Year 5:

$280,000 + $448,000 + $268,800 + $161,280 + $161,280 = $1,319,360

Book value at the end of Year 5:

$1.4 million - $1,319,360 = $80,640

Gain or loss:

Market value of equipment - Book value at the end of Year 5:

$225,000 - $80,640 = $144,360

Tax liability:

Tax rate x Gain or loss:

0.34 x $144,360 = $49,102.40

Aftertax salvage value:

Market value of equipment - Tax liability:

$225,000 - $49,102.40 = $175,897.60

Therefore, the amount of the aftertax salvage value is $175,897.60 (option d).

Answer 2

The aftertax salvage value will be $175,917.60

Step-by-step explanation:

The Modified Accelerated Cost Recovery System (MACRS) is the tax depreciation system in the United States.

aftertax salvage value:

When a company perform a sale of a long term asset, if the sales value is higher than the book value, it must pay taxes for the diference.

So this definition sets the formula:

( salvage - book value ) x tax rate = tax expense in the sale

so the salvage value after tax will be:

salvage value - tax expense

Resuming

salvage value - (salavage value - book value) x tax rate = after tax salvage value

Now moving to this particular question:

The assets is being sold at the end of the project, which menas at year 5. Using the MACRS you can determinate each year depreciation, you need to know the book value at the end of year 5

Year Rate Depreciation Expense Book Value

adquisition $1.400.000

1 20% $280.000 $1.120.000

2 32% $448.000 $672.000

3 19.2% $268.800 $403.200

4 11.52% $161.280 $241.920

5 11.52% $161.280 $80.640

6 5.76% $80.640 $-

We got that the book value at year 5 is $80.640 and we also know that the salvage value estimated is for $225,000 and the tax rate will be of 34%

Now we calculate with the previous formula:

225,000 - (225,000 - 80640) x 34% = $175,917.60

The desired rate of return is not used in this calculation because that is use to determinate if an investment can yield that rate. Here we work with the facts of how much will the asset will worth after the fifth year being the taxes paid. The 14% will be use to determinate wether it is convinient or not to do the project.