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 $1,000,000
savings per year in operating costs. Given that the tax rate is 46%,
After-tax Savings in operating costs = (1 - 0.46)*1000000 = $540,000
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 $1,200,000 per year for the next 5 years
(since its cost is $6,000,000 and it will be depreciated straight line
during its 5-year life). The depreciation for the old machine would be
$600,000 per year (its current book value is $3,000,000 and it will be
depreciated straight line for the next 5 years until full
depreciation). Clearly, thus,
Incremental Depreciation = 1200000 - 600000 = $600,000
The tax shield generated by this depreciation will be:
Tax Shield = 0.46 * 600000 = $276,000
Therefore, we find that:
Incremental Cash Flows = 540000 + 276000 = $816,000 per year, for 5 years.
Let's now find the initial capital outlay. We know that the old
machine is being sold $2,400,000, while its book value is $3,000,000.
Therefore, the after-tax salvage value is:
After-Tax Salvage Value = 2400000 - 0.46*(2400000 - 3000000) = $2,676,000
Now, since the new machine costs $6,000,000, we get that the initial
capital outlay is: 6000000 - 2676000 = $3,324,000.
So now we have all the incremental cash flows generated by the
replacement of the machine. We know that a net $3,324,000 will have to
be paid today for the replacement, and a net $816,000 will be
"received" each year for the next 5 years. Therefore, at a 12%
required rate of return, the present value of the replacement is:
NPV = -3,324,000 + 816,000/1.12 + 816,000/1.12^2 + ... + 816,000/1.12^5
NPV = -382,503
Since the NPV is negative, the machine should not be replaced.
I've also written this analysis in an Excel file. You can download it from
For another "Replacement Problem" example, look at this pdf document:
I hope this helps! If you have any doubt regarding my answer, please
don't hesitate to request clarification before rating it. Otherwise, I
await your rating and final comments.