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 $14,300 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 $86,000 and has been depreciated by the straight-line method.

The old harvester can be sold for $22,300 today.

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

The corporate tax rate is 23 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 $xxxxxxxxxxx

Answer 1

First we need to do a few calculations about the existing and the new harvestor

Harvester	Old	New
Cost	86000	96014.58216 (Calculated using Excel's goal seek)
Life	10	10
Age	5	5
Depreciation method	SLM	SLM
Annual Depreciation	86000/10= 8600	9601.458216
BV	86000-8600x5=43000
SP	22300
Profit	22300-43000=-20700
Tax Savings	0.23 x -20700=-4761

• As SP < BV, the sale of old harvester leads to a loss and therefore leads to a tax savings of 4761 at 23% tax rate

Now let us calculate the NPV:

Particular	Remark	0	1	2	3	4	5	6	7	8	9	10
Reduced cost	Given		14300	14300	14300	14300	14300	14300	14300	14300	14300	14300
Depreciation	Calculated		9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216
EBIT	Reduced cost-Depreciation		4698.541784	4698.541784	4698.541784	4698.541784	4698.541784	4698.541784	4698.541784	4698.541784	4698.541784	4698.541784
Tax	0.23xEBIT		1080.66461	1080.66461	1080.66461	1080.66461	1080.66461	1080.66461	1080.66461	1080.66461	1080.66461	1080.66461
EAT	EBIT-Tax		3617.877174	3617.877174	3617.877174	3617.877174	3617.877174	3617.877174	3617.877174	3617.877174	3617.877174	3617.877174
Depreciation	Added back		9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216	9601.458216
OCF	EAT+Depreciation		13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539
BEP Purchase price	Calculated	-96014.5822
SP	Given	22300
Tax savings	0.23 x (22300-43000)	4761
CF	OCF+BEP PUCHASE PRICE+SP+TAX SAVINGS	-68953.5822	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539	13219.33539
Discount factor formula	Discount rate of 14%	1/1.14^0	1/1.14^1	1/1.14^2	1/1.14^3	1/1.14^4	1/1.14^5	1/1.14^6	1/1.14^7	1/1.14^8	1/1.14^9	1/1.14^10
Discount factor	As per above formula	1	0.877192982	0.769467528	0.674971516	0.592080277	0.519368664	0.455586548	0.399637323	0.350559055	0.307507943	0.26974381
DCF	Discount factor x CF	-68953.5822	11595.90824	10171.84933	8922.674851	7826.907764	6865.708565	6022.551373	5282.939801	4634.15772	4065.050632	3565.833887
NPV	Sum of all NPV	0

• Depreciation is added back to arrive at the OCF as it is a non cash expense
• BEP purchase price is calculated using Excel's Goal seek function
• As BEP purchase price is an outflow, so it is a negative figure
• As SP is an inflow, so it is a positive figure
• As tax savings is an inflow, so it is a positive figure
• Once the BEP is calculated, then the depreciation is calculated by dividing the Purchase price by 10 years of life
• Therefore the BEP Purchase price is calculated as $ 96,014.58