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.) |
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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 |
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 |
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