1.A medical lab wants to upgrade its MRI machine. Their financial department ass

Question

1.A medical lab wants to upgrade its MRI machine. Their financial department assessed that the lab will add about $250,000 to their annual revenues. The cost of operating and maintaining the new machine is $15,000 per year, and additional labor & material expenses will be $40,000 yearly. The lab expects to use the new MRI for five years, after which its salvage value will be zero. The MRI machine falls into a three-year class MACRS depreciation. The lab’s tax rate is 40% and its after-tax MARR is 16%.

A) How much can the lab afford to pay for the MRI machine?

B) Vendor A, who offers the MRI machine at the price determined in question a) states that the lab's annual revenues will be $290,000, while vendor B offers to sell them the MRI machine for $420,000. In both cases all the other givens remain unchanged. Which vendor should the company choose?

Explanation / Answer

a) The lab can afford to pay $548371 (maximum for the machine). Workings and checking are done below: 1 2 3 4 5 Increase in EBITDA 195000 195000 195000 195000 195000 tax @ 40% 78000 78000 78000 78000 78000 117000 117000 117000 117000 117000 pvif @ 16% 0.8621 0.7432 0.6407 0.5523 0.4761 pv 100862 86950 74957 64618 55705 cumulative pv 383092 macrs depreciation rate % 33.33 44.44 14.82 7.41 0 tax savings*depreciation rate-% 13.332 17.776 5.928 2.964 0 pv @ 16% 11.493103 13.21046 3.79782 1.63699 0 pv of tax savings from depreciation ( as a % of the cost of the machine) 30.14 % Maximum price that the lab can afford to pay is that price for which npv is 0. NPV is 0, where PV of benefits = Cost of the machine = 383092 + 30.14% of cost of machine. or 383092 = 69.86% of cost of the machine; so cost of machine = $548371 check: 1 2 3 4 5 Increase in EBITDA 195000 195000 195000 195000 195000 depreciation (cost 548371) 182772 243696 81269 40634 0 EBIT 12228 -48696 113731 154366 195000 Tax @ 40% 4891 -19478 45493 61746 78000 EBIT(1-t) 7337 -29218 68239 92619 117000 Add depreciation 182772 243696 81269 40634 0 Yearly cash flows after tax 190109 214478 149507 133254 117000 pvif @ 16% 0.8621 0.7432 0.6407 0.5523 0.4761 pv 163887 159392 95783 73595 55705 cumulative pv 548362 macrs depreciation rate % 33.33 44.44 14.82 7.41 0 b) Vendor A-supplies the machine at $548371, but revenues will be 290000 instead of 250000. 1 2 3 4 5 Increase in EBITDA 235000 235000 235000 235000 235000 depreciation (cost 548371) 182772 243696 81269 40634 0 EBIT 52228 -8696 153731 194366 235000 Tax @ 40% 20891 -3478 61493 77746 94000 EBIT(1-t) 31337 -5218 92239 116619 141000 Add depreciation 182772 243696 81269 40634 0 Yearly cash flows after tax 214109 238478 173507 157254 141000 pvif @ 16% 0.8621 0.7432 0.6407 0.5523 0.4761 pv 184577 177228 111159 86850 67132 cumulative pv 626946 initial investment 548371 NPV 78575 macrs depreciation rate % 33.33 44.44 14.82 7.41 0 Vendor B supplies at $420000, with no change in revenues: 1 2 3 4 5 Increase in EBITDA 195000 195000 195000 195000 195000 depreciation (cost 420000) 139986 186648 62244 31122 0 EBIT 55014 8352 132756 163878 195000 Tax @ 40% 22006 3341 53102 65551 78000 EBIT(1-t) 33008 5011 79654 98327 117000 Add depreciation 139986 186648 62244 31122 0 Yearly cash flows after tax 172994 191659 141898 129449 117000 pvif @ 16% 0.8621 0.7432 0.6407 0.5523 0.4761 pv 149133 142434 90908 71493 55705 cumulative pv 509674 Initial cost of the machine 420000 NPV 89674 macrs depreciation rate % 33.33 44.44 14.82 7.41 0 Company will chose Vendor B, as the NPV is higher at $89674

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