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

Someone please get this question right only if you know you can, try to use excel or somthing

Answer 1

Let us first start by calculating the present value of annual savings resulting from new harvester.

This will be $14,600 annually discounted at 14%.

The Present value annuity factor (PVAF) for 14% for 10 years is 5.2161.

The present value of annual savings is $14,600 * 5.2161 = $76,155.06

We will add the selling price of the harvester to this. Since it is being sold today, the selling price is the present value itself.

Selling price is $22,600.

Thus, total present value till now = $76,155.06 + $22,600 = 98,755.06

Moreover, the pending depreciation on book value will be allowed immediately to the company. This means 91000*(10/15)*21% = 12,740 is allowed today as tax deduction as stated in the question.

Thus, total present value till now = $76,155.06 + $22,600 + $12,740 = 1,11,495.06

Now, we must note that if the harvester is sold today, we will not get to depreciate the old harvester for the next 10 years.

Although depreciation by itself does not constitute any cash flows, it leads to tax savings, and that is a cash flow.

This means that if the old harvester is sold today, we will lose out on annual tax savings on depreciation on this harvester.

Annual depreciation is $91,000/15 = $6,066.67.

Applying 21% corporate tax rate on this depreciation, we find out that the company is losing out on $1,274 of tax savings each year for the next 10 years.

Applying PVAF of 5.2161, the present value of tax savings lost is $1,274*5.2161 = $6,645.31

Thus, current NPV = $111,495.06 - $6,645.31 = 104,849.75

Now, we are left with two types of cash flows:

1) Amount to be paid for new harvester. (Assume this to be x)

2) Annual tax savings on the depreciation of this new harvester.

Annual depreciation (assuming straight line method) would be 0.1x. Tax savings on this would be 0.1x * 21% = 0.021x.

To calculate the present value of all the tax savings during the 10 year period, we would multiply the annual tax savings with the PVAF 5.2161

This means the total present value of all tax savings on depreciation would be 0.021x * 5.2161 = 0.1095x.

If we want to find breakeven point (NPV=0), we can make the following equation

$104,849.75 - x + 0.1095x = 0

Solving for x, we get x = (92,109.75/0.8905) = $1,17,742.56

Thus, break-even purchase price in terms of present value of the harvester is $1,17,742.56.

For further help, I am attaching an excel calculation of NPV with all these values.