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A device can be purchased now for $20,000 and depreciated by 5-year SL depreciation and zero...

A device can be purchased now for $20,000 and depreciated by 5-year SL depreciation and zero salvage value. The net benefit from the device, before deducting depreciation, is $9,000 per year. After 2 years, the device will not be needed and can be sold. During the 2-year period, inflation rate is 6%/yr.  The company has a 50% combined federal and state tax rate. If it requires a real 10% after-tax rate of return, what should be the selling price of the device after 2-year usage?

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Answer:

Purchase price=$20,000.

SL(Straight line) Depreciation with zero salvage and 5 year life=$20,000/5=$4,000/year.

Net benefit from device before depreciation=$9,000/year.

Net benefit after depreciation=$9,000-$4,000=$5,000/year.

Book value of machinery after 2 years=$20,000-2*4,000=$12,000.

Tax on benefit @50%=$5,000*50%=$2500

After tax net benefit=$2500.

Required return rate is 10%.

Present value of returns=$2500/(1+0.1)+$2,500/(1+0.1)2=$2273+$2066=$4339.

To get return of 10%, After tax present value of selling price should be equal to Purchase price-Present value of returns.

After tax P.v of sale proceeds after 2 years=$20,000-$4,339=$15,661.

After tax future value=$15,661(1+0.1)2=$18950.

Let us suppose selling price=x.

Tax=50%*(x-Book value,12000)

After tax future value=Before tax future value/selling price-Tax.

$18,950=x-[(50%*x)-(50%*$12000)]

$18950=x-[(0.5x)-$6000]

$18950=x-0.5x+$6000.

$18950-$6000=0.5x.

$12950/0.5=x

$25900=Selling price of the machinery after 2 years.

Rahul Sunny answered 2 years ago
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