Question

A hospital wants to buy a new MRI machine for $400,000. The annual revenue from the machine is estimated at $110,000 per year while maintenance costs per year are calculated to be $20,000. The salvage value at the end of the machine's five-year operational life is $100,000. You have been asked to determine the IRR of this project and to make a recommendation regarding the proposed purchase. The hospital's MARR is 20% per year.

Answer 1

Woking in 1000s and assuming that the annual costs and benefits are incurred at the end of each year.

Annual maintenance = 110

Annual cost = 20

So annual net benefit = 110-20 = 90

IRR is the rate of return for which the net present value of the project is greater than or equal to zero. That is, the project is profitable .

So,

When

i = 0.10 NPV = 3.26294

i = x NPV = 0

i = 0.20 NPV = - 90.65715

By linear interpolation,

Or, x = 0.1035 = 10.35%

The MARR is 20%.

We know that there is a negative relationship between the rate of return and the net present value. Since the IRR is 10.35% any rate of return above 10.35% will make the project non profitable. So the project should not be accepted by the hospital at an MARR of 20%. The hospital should accept the project only if MARR is less than or equal to 10.35%.