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 $14,600 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 $91,000 and has been depreciated by the straight-line method.

The old harvester can be sold for $22,600 today.

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

The corporate tax rate is 21 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.)

  

NOTE*** answer is not 91309.2 or 109154.41 or 110898.7 or 119875.42 or 117742.56

Answer 1

	c)	Present Value(PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=discount rate=Required Rate of return =14%=0.14
		N=Year   of Cash Flow
		Annual depreciation of old harvestor	$6,067	(91000/15)
		Book value of old harvestor today	$60,667	(91000-5*6067)
		Market value of old harvestor today	$22,600
		Loss on sales =60667-22600=	$38,067
		Tax Savings on loss =38067*21%	$7,994
		Total Cash Flow on sales today	$30,594	(22600+7994)
		After tax annual savings=14600*(1-0.21)	$11,534
		Depreciation on new harvestor		(
	N	Year	0	1	2	3	4	5	6	7	8	9	10
	a	Cash Flow From Selling Old Harvestor	$30,594
	b	After tax Annual Savings		$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	SUM
		Present Value =(cashflow)/(1.14^N)	$30,594	$10,118	$8,875	$7,785	$6,829	$5,990	$5,255	$4,609	$4,043	$3,547	$3,111	$90,757
		Depreciation tax shield (Assume $1)		$1	$1	$1	$1	$1	$1	$1	$1	$1	$1	SUM
		Present Value		$0.877	$0.769	$0.675	$0.592	$0.519	$0.456	$0.400	$0.351	$0.308	$0.270	$5.21612
		Assume Breakeven cost of new investor =X
		Annual depreciation of New harvestor	X/10=0.1X
0.8905		Annual depreciation of old harvestor	$6,067
$84,110.98		Increase in Depreciation=0.1X-6067				$0.1095	$6,645.70
		Annual Depreciation tax Shield=(0.1X-6067)*0.21
		Present Value of annual depreciation tax shield =(0.1X-6067)*0.21*5.21612
		For Break Even:
		Present Value of Cash Inflow=Present Value of Cash Outflow=X
		90757+(0.1X-6067)*0.21*5.21612=X
		90757+0.1095X-6645.70=X
		0.8905X=84110.98
		X=84110.98/0.8905=	$94,453.65
		Breakeven cost of new harvestor=	$94,453.65
		BREAK EVEN PURCHASE PRICE FOR NPV=0	$94,454
		Annual Depreciation=94454/10=	$9,445
		Increase in depreciation =9445-6067=	$3,379
		Annual Depreciation tax shield=3379*0.21	$710
		CHECKING WITH NEW HARVESTOR PRICE =	$94,454
	N	Year	0	1	2	3	4	5	6	7	8	9	10
	a	Cash outflow for new investor	-$94,454
	b	Annual depreciation tax shied		$710	$710	$710	$710	$710	$710	$710	$710	$710	$710
	c	Cash Flow From Selling Old Harvestor	$30,594
	d	After tax Annual Savings		$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534	$11,534
	CF=a+b+c+d	Net Cash Flow	-$63,860	$12,244	$12,244	$12,244	$12,244	$12,244	$12,244	$12,244	$12,244	$12,244	$12,244
	PV=CF/(1.14^N)	Present Value of net cash flow	-$63,860	$10,740	$9,421	$8,264	$7,249	$6,359	$5,578	$4,893	$4,292	$3,765	$3,303
		NPV =0
		There may be minor differences due to approximation
		ANSWER:$94,454