Question

One year​ ago, your company purchased a machine used in manufacturing for

$105,000.

You have learned that a new machine is available that offers many​ advantages; you can purchase it for

$140,000

today. It will be depreciated on a​ straight-line basis over ten​ years, after which it has no salvage value. You expect that the new machine will contribute EBITDA​ (earnings before​ interest, taxes,​ depreciation, and​ amortization) of

$45,000

per year for the next ten years. The current machine is expected to produce EBITDA of

$25,000

per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, after which it will have no salvage​ value, so depreciation expense for the current machine is

$9,545

per year. All other expenses of the two machines are identical. The market value today of the current machine is

$50,000.

Your​ company's tax rate is

20 %,

and the opportunity cost of capital for this type of equipment is

11 %

Is it profitable to replace the​ year-old machine?

The NPV of the replacement is

Answer 1

Particular	Cost	Depreciation	EBITDA	Tax benefit on Depreciation @ 20%	Total cash flow (a)	Cumulative PV for 10 Years @ 11% (b)	NPV of Cash benefit (a) * (b)	Profit on buying
Old machine	$        1,05,000	$             9,545	$        25,000	$               1,909	$ 26,909	5.8892	$ 1,58,473.02	$                  53,473.02
New machine	$        1,40,000	$           14,000	$        45,000	$               2,800	$ 47,800	5.8892	$ 2,81,503.76	$              1,41,503.76

As profit from buying the new machine is greater than old machine, it is profitable to replace the old machine with newer one.

Cumulative PV is calculated using the formula

The table of PV @ 11% is attached below

Year	PV @ 11%
1	0.9009
2	0.8116
3	0.7312
4	0.6587
5	0.5935
6	0.5346
7	0.4817
8	0.4339
9	0.3909
10	0.3522
Cumul.	5.8892