Question

The Cornchopper Company is considering the purchase of a new harvester.

The new harvester is not expected to affect revenue, but operating expenses will be reduced by $13,400 per year for 10 years.

The old harvester is now 5 years old, with 10 years of its scheduled life remaining. It was originally purchased for $71,000 and has been depreciated by the straight-line method.

The old harvester can be sold for $21,400 today.

The new harvester will be depreciated by the straight-line method over its 10-year life.

The corporate tax rate is 25 percent.

The firm’s required rate of return is 14 percent.

The initial investment, the proceeds from selling the old harvester, and any resulting tax effects occur immediately.

All other cash flows occur at year-end.

The market value of each harvester at the end of its economic life is zero.

  

Determine the break-even purchase price in terms of present value of the harvester. This break-even purchase price is the price at which the project’s NPV is zero. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

?

Answer 1

Post tax salvage value of the old machine = Sale Value - Tax on gain on sale

Book value of old machine at the time of sale = Purchase cost - accumulated depreciation over 5 years

= 71,000 - 71,000 x 5 / 15 = 47,333.33

Loss on sale = Book value - sale value = 47,333.33 - 21,400 = 25,933.33

hence, tax advantage on loss = Loss x tax rate = 25,933.33 x 25% = 6,483.33

Post tax salvage value of the old machine = Sale Value + Tax advantage on sale in loss = 21,400 + 6,483.33 = $ 27,883.33

If C is the purchase cost of the new machine then initial investment = C0 = Purchase cost - post tax salvage value of the old machine = C - 27,883.33

Annual cash flows, A = [Cost saved - incremental depreciation] x (1 - tax rate) + incremental depreciation = [13,400 - (C/10 - 71,000 / 15)] x (1 - 25%) + (C/10 - 71,000 / 15) = 8,866.67 + 0.025C

This annual cash flows A occur as annuity over n = 10 years; discount rate = r = 14%

Hence, NPV = - C0 + PV of A as annuity = - C0 + A/r x [1 - (1 + r)-n] = - (C - 27,883.33) + (8,866.67 + 0.025C) / 14% x [1 - (1 + 14%)-10] = 27,883.33 - C + (8,866.67 + 0.025C) x 5.2161 = 74,132.89 - 0.8696C

This break-even purchase price is the price at which the project’s NPV is zero.

Hence, 74,132.89 - 0.8696C = 0

Hence, the break-even purchase price in terms of present value of the harvester, C = 74,132.89 / 0.8696 = $ 85,249.70