Question

The Cornchopper Company is considering the purchase of a new harvester. The new harvester is not expected to affect revenues, but pretax 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 $70,500 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 35 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.)

Purchase price $

Answer 1

Let us first find Book value of old Harvestor, for that we need to find Depreciation
Depreciation = Purchase price - salvage value / No of years
= 70500-0/15
=70500/15
=4700 $ p.a
Hence Book value of old harvestor = Purchase price - (5 x Depreciation p.a)
= 70500 - (5 x 4700)
= 70500 - 23500
= 47000 $

Now let us calculate cash flow from sale of old harvestor

Particulars	Amount
Sales price of old harvestor	21400
Book Value of old harvestor	47000
Loss	25600.0000
Tax shield @ 35%	8960
Cash flow from sale of old harvestor (21400+8960)	30360

Let Purchase price of new harvestor be X
Thus initial Investment = X - 30360

Now let us calculate Annual cash flow

Particulars	Amount
Savings in pre tax operating expense	13400
Tax on above @ 35%	4690
After tax savings in operating cost	8710
Add: Tax shield on depreciaton (0.1X * 35%)	0.035X
Annual Cash flow from operation	8710 + 0.035X

Thus for break-even purchase price
Initial Investment = Annual cash flow x PVIFA(14%,10)
X - 30360 = (8710 + 0.035X)5.2161
X - 30360 = 45432.23 + 0.1826X
0.8174X = 75792.23
X = 92719.41 $

Thus price of new harvester = $ 92719.41