Question

Huntington Medical Center purchased a used low-field MRI scanner 2 years ago for $445,000. Its operating cost is $375,000 per year and it can be sold for $155,000 anytime in the next 3 years. The Center’s director is considering replacing the presently owned MRI scanner with a state-of-the-art 3 Tesla machine that will cost $2.5 million.The operating cost of the new machine will be $300,000 per year, but it will generate extra revenue that is expected to amount to $575,000 per year. The new unit can probably be sold for $800,000 3 years from now. You have been asked to determine how much the presently owned scanner would have to be worth on the open market for the AW values of the two machines to be the same over a 3-year planning period. The Center’s MARR is 12% per year. The presently owned scanner should be worth $ on the open market.

Answer 1

i = 12%, t =3yrs

Original price of the old machine is sunk cost. therefore it will not be used for calculation

Investment in new machine = 2500000 ,

Operating cost per year = 300000, Income each year = 575000

Net cash flow = 575000-300000 = 275000

Salvage value = 800000 at the end of 3 yrs from now

Annual worth of new machine = -2500000 (A/P, 12%, 3) + 275000 + 800000 (A/F, 12%, 3 yrs)

= -2500000 * 0.416348 +275000 +800000 * 0.296348

= -528791.6

Let S be the worth of old scanner in the open market then AW of old scanner

Operating cost of old scanner = 375000, Salvage value 155000 in next 3 yrs

= - S * (A/P, 12%, 3) -375000 +155000 *(A/F, 12%, 3)

= - 0.416348 * S - 375000 + 155000 * 0.296348

= - 0.416348 *S - 375000 + 45933.94

= - 0.416348 *S - 329066.06

To calculate minimum worth on machine in open market

annual worth of old machine = annual worth of new machine

- 0.416348 * S - 329066.06 = -528791.6

S= 199725.54/0.416348

S = 479708.17