Question

One year ago, your company purchased a machine used in manufacturing for $90,000.You have learned that a new machine is available that offers many advantages and you can purchase it for $150,000 today. It will be depreciated on a straight-line basis over 10 years and has no salvage value.

You expect that the new machine will produce a gross margin (revenues minus operating expenses other than depreciation) of $60,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $25,000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, and has no salvage value, so depreciation expense for the current machine is $8,182 per year. The market value today of the current machine is $5,000. Your company's tax rate is 42 %,and the opportunity cost of capital for this type of equipment is 10 %. Should your company replace its machine?

a. Yes. With an NPV of $32,577, there is a profit from replacing the machine.

b. Yes. With an NPV of $42,688, there is a profit from replacing the machine.

c. Yes. With an NPV of $52,797, there is a profit from replacing the machine.

d. No. With an NPV of -$2,797, there is a loss from replacing the machine.

e. No. With an NPV of -$22,973, there is a loss from replacing the machine.

Answer 1

In order to find the present value of replacing the machine, we must

calculate the incremental cash flows that result from doing it.

First of all, notice that the new machine will represent a $35000

savings per year in gross margin. Given that the tax rate is 42%,

then,

After-tax Savings in operating costs = (1-0.42)*35000 = $20300

There will also be some savings due to the fact that the depreciation

tax shield will be greater for the new machine. The depreciation for

the new machine will be $15000 per year for the next 10 years

(since its cost is $150000 and it will be depreciated straight line

during its 10-year life). The depreciation for the old machine would be

$8182 per year (its current book value is $81818 and it will be

depreciated straight line for the next 10 years until full

depreciation). Clearly, thus,

Incremental Depreciation = 15000-8182 = $6818

The tax shield generated by this depreciation will be:

Tax Shield = 0.42 * 6818 = $2863.56

Therefore, we find that:

Incremental Cash Flows = 20300+2864 = $23164 per year, for 10 years.

Let's now find the initial capital outlay. We know that the old

machine is being sold 5000 while its book value is 90,000.

Now, since the new machine costs $150000, we get that the initial

capital outlay is: 150,000-5000 = $145000

So now we have all the incremental cash flows generated by the

replacement of the machine. We know that a net $145000 will have to

be paid today for the replacement, and a net $23164 will be

"received" each year for the next 10 years. Therefore, at a 10%

required rate of return, the present value of the replacement is:

NPV = -145000 + 23164/1.10 + 23164/1.10^2 + ... + 23164/1.10^10

NPV = -2,797

As npv is negative , we should not accept the replacement decision.

Since the NPV is negative, the machine should not be replaced.