Question

One year​ ago, your company purchased a machine used in manufacturing for 115000 . You have learned that a new machine is available that offers many​ advantages; you can purchase it for 170000 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 45000 per year for the next ten years. The current machine is expected to produce EBITDA of 25000 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 10455 per year. All other expenses of the two machines are identical. The market value today of the current machine is 50000. 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?find NPV

Answer 1

In these type of questions, first make a summary of data so that we do not have to look at the question again and again while solving.

Current Machine	Value	115000
Depriciation	Given	10455
Market Value of Current Machine	50000
EBITDA	Current	25000

New Machine		170000
Depriciation	=170000/10	17000
EBITDA	New Machine	45000

Tax	20%
Cost of Capital	11%

Now

Let's calculate some basic things which we require in final calculation

Increase in EBITDA = EBITDA (New) - EBITDA (old)

Increase in EBITDA = 45000 - 25000 = 20000

Incremental Depriciation = 17000-10455 = 6545

Year	Present Value @ 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
Present Value Annuity Factor (PVAF)	5.8892

On the basis of above calculations, we can find the present value of cash inflow

Incremental EBITDA	20000
Incremental Depriciation	(6545)
Profit before tax	13455
Tax @ 20%	(2691)
Profit After Tax	10764
Add: Depriciation	6545
Cash Inflow	17309
PVAF (11%, 10 years)	5.8892
Present Value of Cash Inflow (17309 x 5.8892)	101936.717

Now

Let's Calculate the cash outflow

But before that, We have to find the tax savings in selling the current machinery

Current Machinery
Purchased		115000
Depriciation		(10455)
Book Value		104545
Market Value		50000
Loss on sale		54545
Tax Saving on loss on sale	=54545*20%	10909

Present Value of Cash Ourflow
Purchase of New Machinery	170000
Less:
Tax Saving in Old Machinery	-10909
Sale of Old Machinery	-50000
Present Value of Cash Outflow	109091

Net Present Value

Present Value of Cash Inflow	101936.72
Present Value of Cash Outflow	109091.00
Net Present Value	-7154.28

As the Net Present Value is negative, it is not profitable to replace old machinery.

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