Question

Huntington Medical Center purchased a used low-field MRI scanner 2 years ago for $445,000. Its operating cost is $450,000 per year and it can be sold for $165,000 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 million.The operating cost of the new machine will be $400,000 per year, but it will generate extra revenue that is expected to amount to $475,000 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 10% per year.

The presently owned scanner should be worth $___________ on the open market.

Answer 1

Let X = presently owned scanner's worth, then

Set AW of old machine = AW of the new machine

-X(A/P,10%,3) - 450,000+165,000(A/F,10%,3) = -2,000,000(A/P,10%,3)+(475,000 - 400,000)+800,000(A/F,10%,3)

-X(0.4021) - 450,000 +165,000 * (0.3021) = -2,000,000 * (0.4021) + 75,000 + 800,000 * (0.3021)

-0.4021X - 450,000 + 49846.5 = -804,200 + 75,000+241,680

-0.4021X - 400,153.50 = -487,520

-0.4021X = -487,520 + 400,153.50

-0.4021X = -87,366.50

X = -87,366.50 / -0.4021

X = 217,275.55

The presently owned scanner should be worth $217,275.55 on the open market.