Question

A Corporation Installed a new MRI machine at a cost of $720,000 this year in its medical professional clinic in a park. This state of the art system is expected to be used for 4 years and then sold for $145,000. The corporation uses a return requirement of 24% per year for all of its medical diagnostic equipment. As a student currently serving a co-op semester on the staff of this corporation, you are asked to determine the minimum revenue required each year to realize the expected recovery and return.

If the annual operating cost (AOC) is expected to be $90,000 per year, what is the total required to provide for recovery of capital and the annual expenses at the specified rate of return?

The total required to provide for recovery of capital and the annual expenses at the specified rate of return is determined to be ....$?

Answer 1

Given

Initial Cost=I=$720,000

Salvage=S=$145,000

Useful life=n=4

Required rate of return=i=24%

We know that

Capital Recovery=CR=(I-S)*(A/P,i,n)+S*i

CR=(720000-145000)*(A/P,0.24,4)+145000*24%

Let us calculate the interest factor

(A/P,i,n) 1 - 2 1 (1+i)"

(A/P,0.24,4) 0.24 1 (1+0.24) = 0.415926 1-

So,

CR=(720000-145000)*0.415926+145000*24%=273957.45

Minimum revenue required each year to realize the expected recovery and return=$273,957.45

The total required to provide for recovery of capital and the annual expenses at the specified rate of return =CR+AOC=273957.45+90000=$363,957.45

or

Total amount currently required=363,957.45/(A/P,0.24,4)=363,957.45/0.415926=$875,053.37