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 $12,100 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 $52,500 and has been depreciated by the straight-line method. The old harvester can be sold for $20,100 today. The new harvester will be depreciated by the straight-line method over its 10-year life. The corporate tax rate is 24 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.

Answer 1

Input Data
Cost of New Machine ( Let be X)	X
Reduction in Operating Cost	$                     12,100
Old Machine's Current Market Value	$                     20,100
Old Machine's Current Book Value	$                     35,000
Tax Rate	24%
Required Rate	14%
PV of Outflows	Amount	Remarks
Cost of Machine	X
Market Value of Old Machine	$                     20,100
Tax Saving on sale of old Machine	$                        3,576	($35000-$20100)*24%
Total Outflows	X-$ 23,676
PV of Inflows	Amount	Remarks
After tax reduction in operating cost ( a )	$                        9,196
Tax benefit on Depreciation on old machine (b)	$                           840	($52,500/15 years ) *24%
Tax benefit on Depreciation on new machine ( c )	0.024X	(X/10 Years) * 24%
Net operating cash Flows (d) = (a-b+c)	$ 8,356 + 0.024X
Using the required rate of return of 14 % the cumulative PV Factor is	5.2161
Total PV Inflow in 10 years	$43585.86+ 0.1252X
Since NPV is zero
PV of Inflows - PV of outflows = Zero
$ 43585.86+0.1252X - (X-$ 23676 ) = 0
Solving above, value of the machine is	$               76,887.11