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 $13,100 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 $67,000 and has been depreciated by the straight-line method.

The old harvester can be sold for $21,100 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.)

Answer 1

Let the Cost of New Harvestor machine be $   x

Cost of New Harvestor machine                                            = x

- Sale proceeds of old harvestor machine                    = $ 21100

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Cash Outflow                                               =          x- 21100

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Purchase cost of Old Harvester machine                                                      = $ 67,000

Less: Depreciation for 5 years { ( 67,000/15 years ) x 5 years}                   = 23,333

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Book Value of Old Harvestor machine                                                          = $ 44,667

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Base for Incremental Depreciation:-

Depreciation to be calculated on incremental value.

Purchase cost of New Machine =                                  x

Less – Book value of Old Harvestor Machine           =                      44,667

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                        Base for Incremental depreciation                                         = x -44667

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Therefore, Incremental Depreciation (10% SLM method)   = 0.10 x - 4467

Calculation of Incremental Cash flows and CFAT associated with replacement of Old Harvester machine

Reduction in Operating expenses due to new Harvester                               = $ 13,100

Less : Incremental Depreciation                                                                 = 0.10 x - 4467

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Incremental Net Profit before Tax                                                  = 13100 – (0.10 x – 4467)

Incremental Net Profit before Tax =              - 0.10 x + 17567

Less Tax @ 21 %

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Incremental Net Profit after Tax          =        0.79 (- 0.10 x + 17567)

Add : Incremental depreciation                       =0.10 x - 4467

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Incremental CFAT           =                 0.79 (- 0.10 x + 17567)   + 0.10 x – 4467

            Incremental CFAT                          = 0.021 x + 9411

X PVIFA (14 %, 10 years)                          = 5.216

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Present Value of Incremental CFAT = 5.216 (0.021 x + 9411)

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To determine Breakeven Purchase price of New Harvestor

At Breakeven price,

The cash outflow = Present value of CFAT

Cash Outflow                                      =          x- 21100

Present Value of Incremental CFAT = 5.216 (0.021 x + 9411)

x- 21100 = 5.216 (0.021 x + 9411)

Solving we get, x = 78,774

Breakeven price of New Harvestor machine = $ 78,774

PVIFA (14%, 10 years) is calculated using formula

PVIFA = [1 – {1/ (1+ r)^ n}/ r ]