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 $12,300 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 $55,500 and has been depreciated by the straight-line method. The old harvester can be sold for $20,300 today. The new harvester will be depreciated by the straight-line method over its 10-year life. The corporate tax rate is 40 percent. The firm’s required rate of return is 13 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

	The PV fof the known cash flows are:
1]	After tax sale proceeds of old harvester:
	Sale proceeds	$            20,300
	Book value of the old harvester = 55500-(55500/15)*5 =	$            37,000
	Loss on sale = 37000-20300 =	$            16,700
	Tax shield on loss = 16700*40% =	$              6,680
	After tax sale proceeds of old harvester = 20300+6680 =	$            26,980
2]	PV of after tax savings in operating expenses = 12300*(1-40%)*(1.13^10-1)/(0.13*1.13^10) =	$            40,046
3]	Depreciation tax shield lost on old harvester = -3700*40%*(1.13^10-1)/(0.13*1.13^10) =	$            -8,031
4]	NPV of know cash flows	$            58,995
5]	For 0 NPV, the cost of the new harvester - the PV of the depreciation tax shield of new harvester should equal $58,995.
	If the cost of the new harvester is x, the PV of the
	depreciation tax shield = x*(1/10)*40%*(1.13^10-1)/(0.13*1.13^10) = x*0.217050
	So, 58995 = x-x*0.217050
	Therefore, x [the brekeven purchase price] = 58995/(1-0.217050) =	$            75,350
	Break-even purchase price in terms of present value of the harvester = $75,350.