In: Finance
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
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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