Question

A hospital is considering purchasing a new medical dispensing cabinet that will cost $200,000. It believes that this cabinet will reduce the amount of labor required to track and administer medications and will also result in fewer expired medicines. It estimates the medical dispensing cabinet will result in savings of $30,000 at the end of year one and that the savings will increase by $5,000 per year for each of the 7 years that the machine will be used. What is the IRR of this investment?

If the hospital's MARR is 12%, should they invest in this cabinet?

Answer 1

Let IRR be i%, then as per given condition

30000*(P/A,i%,7) + 5000*(P/G,i%,7) = 200000

Dividing by 5000

6*(P/A,i%,7) + (P/G,i%,7) = 40

using trail and error method

When i = 11%, value of 6*(P/A,i%,7) + (P/G,i%,7) = 6*4.712196 + 12.187158 = 40.460336

When i = 12%, value of 6*(P/A,i%,7) + (P/G,i%,7) = 6*4.563757 + 11.644267 = 39.026806

using interpolation

i = 11% + (40.460336-40)/(40.460336-39.026806)*(12%-11%)

i = 11 %+ 0.32% = 11.32%

As IRR < MARR, this investment should not be selected