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

Depreciation of old machine = $71,000 / 15 = $4,733.33

Book value of old harvester = Cost - Accumulated Depreciation

= $71,000 - ($4,733.33 * 5)

= $47,333.35

After tax salvage value = Market value + Tax rate (Book value – Market Value)

= $21,400 + 0.25 ($47,333.35 - $21,400)

= $27,883.34

Let the cost of new harvester be x.

Depreciation of new machine = x / 10 = 0.1x

Tax shield on new depreciation = (0.1x) * 0.25 = 0.025x

Tax shield on old depreciation = $4,733.33 * 0.25 = $1,183.33

Incremental tax shield on depreciation = 0.025x - $1,183.33

PV of Incremental tax shield on depreciation = (0.025x - $1,183.33) * PVAF (14%, 10 years)

= 0.13x – $6,172.37

Reduction in costs = $13,400

After tax savings = $13,400 * (1 – 0.25) = $10,050

PV of after tax savings = $10,050 * PVAF (14%, 10 years)

= $52,421.81

NPV = PV of salvage of old machine + PV of depreciation tax shield + PV of savings – Initial cost

0 = $27,883.34 + (0.13x – $6,172.37) + $52,421.81 – x

0 = $74,132.78 – 0.87x

0.87x = $74,132.78

x = $85,210.09