Question

Huntington Medical Center purchased a used low-field MRI scanner 2 years ago for $445,000. Its operating cost is $425,000 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 $2.5 million.The operating cost of the new machine will be $380,000 per year, but it will generate extra revenue that is expected to amount to $625,000 per year. The new unit can probably be sold for $775,000 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

We will use the AW method for comparison.

AW = - Initial investment (A/P, i, t) + salvage value (A/F, i, t) - annual operating costs (note the minus sign before the initial investment)

(A/P, i , t) = [ i * (1+i)^t]/[(1+i)^t - 1] = [ 10% * (1+10%)³]/[(1+10%)³ - 1] = 0.4021

(A/F, i, t) = i / [(1+i)^t - 1] = 10% / [(1+10%)³ - 1] = 0.3021

Now AW New Machine:

Initial cost = $2.5 million ; operating cost = $380,000 ; incremental revenue = $625000 hence annual cash flows for AW = (-380,000 + 625000) = $245,000 ; Salvage Value = $775,000

AW = - 2,500,000*0.4021 + 775,000 * 0.3021 + 245,000 = - 526,148.04

Let the salvage value of presently owned machine be X for the AW of both machines to be same.

(A/P, i , t) = [ i * (1+i)^t]/[(1+i)^t - 1] = [ 10% * (1+10%)⁵]/[(1+10%)⁵ - 1] = 0.2638

(A/F, i, t) = i / [(1+i)^t - 1] = 10% / [(1+10%)⁵ - 1] = 0.1638

Then we have :

-526148.04 = -445000 * 0.2638 - 425000 + X * 0.1638

solving for X, we get X = $ 99158.05