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

Answer 1

Step-1: Calculate Initial Investment in Project:

Purchase Price of New Harvester (Assumed)	X
Less:
Proceed from Sale of Old Harvester	22,600
Tax Savings on Loss of Sale of Old Harvester	7994
Initial Investment	X - 30,594

Note: Calculation of Loss on Sale of Old Harvester:

Annual Depreciation of Old Harvester = Purchase Price / Economic Life = 91,000 / 15 = 6,066.67

Book Value of Old Harvester Today = 91,000 – Depreciation for 5 year = 91,000 – (6,066.67 *5) = 60,666.65

Loss = Sale Value – Book Value = 22,600 – 60,666.65 = 38,066.65

Tax Gain = Loss on Sale of Old Harvester * Tax Rate = 38066.65 * 21% = 7,993.99

Step-2: Calculate the Annual Savings from New Harvester:

Savings from Reduction in Operating Expenses = 14,600

*Tax Savings on Annual Depreciation = 0.10X * 21% = 0.021X

Total Annual Savings = 14,600 + 0.021X

(*Note: Annual Depreciation of New Harvester = Purchase Price/ 10 = X/10 = 0.10X)

Step-3: NPV of Project

PV of Annual Savings = Annual Savings * PV Annuity Factor (10 years, 14%)

                                       = (14,600 * 0.021X) * 5.2161 = 76,155.06 + 0.1095X

If the PV of Annual Savings are equal to Initial Investment i.e. NPV zero, then we will get the break-even purchase price;

Initial Investment = PV Annual Savings

X - 30,594 = 76,155.06 + 0.1095X

0.8905X = 106,749.06

X = 119,875.41

(Calculation may vary due to not rounding of amount to two decimal)