Huntington Medical Center purchased a used lowfield MRI scan

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 $160,000 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 $360,000 per year, but it will generate extra revenue that is expected to amount to $500,000 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 9% per year. The presently owned scanner should be worth $ on the open market.

Solution

For the new machine, Annual net benefit = Extra revenue - Operating cost = $(500,000 - 360,000) = $140,000

AE, New mchine ($) = - 2,500,000 x A/P(9%, 3) + 140,000 + 800,000 x P/F(9%, 3) x A/P(9%, 3)

= - 2,500,000 x 0.3951** + 140,000 + 800,000 x 0.7722** x 0.3951**

= - 987,750 + 140,000 + 244,072

= - 603,678

For existing machine, purchase cost paid 2 years ago is a sunk cost and excluded from cash flow analysis.

For equivalence, AW of existing machine = AW of new machine. If current market worth of existing machine be V,

V x A/P(9%, 3) + 375,000 + 160,000 x P/F(9%, 3) x A/P(9%, 3) = - 603,678

V x 0.3951** + 375,000 + 160,000 x 0.7722** x 0.3951** = - 603,678

V x 0.3951 + 375,000 + 48,815 = - 603,678

V x 0.3951 = - 1,027,493

V = - $2,600,589

The present machine is worth $2,600,589 in open market.

**From A/P and P/F factor tables