Question

I have tried answering this several times and get the wrong answer Please assist: Huntington Medical Center purchased a used low-field MRI scanner 2 years ago for $445,000. Its operating cost is $325,000 per year and it can be sold for $145,000 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 $1.5 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 $525,000 per year. The new unit can probably be sold for $825,000 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 $ 613937.60 613937.60 Incorrect on the open market.

Answer 1

For old machine

Let m be the market value of old machine

Operating cost = 325000

Cost of investment 2 yrs ago will not factor into analysis as it is a sunk cost

Salvage value = 145000,

i =9% =0.09

t =3yrs

AW of old machine = m * (A/P, 9%, 3 yrs) - 325000 + 145000 (A/F, 9%, 3 yrs)

= 0.3950547 * m - 325000 + 145000 * 0.3050547

= 0.3950547 m - 280768.185

Now for new machine

Investment = 1500000

Salvage value = 825000 at the end of three years

Revenue = 525000

O&M Cost = 300000

i =0.09

AW of new machine = -1500000 * (A/P, 9%, 3 yrs) + 525000 - 300000 + 825000 *(A/F, 9%, 3 yrs)

= -1500000 * 0.3950547 +225000 +825000*0.3050547

= -115910.87

now find m to have both the options equal AW, then

0.3950547 m - 280768.18 = -115910.87

m = 164857.31/0.3950547

m = 417302.4963 ~ 417302.5