Buying an Ultrasound Machine for Your Hospital

Your hospital needed to upgrade several ultrasound (US) machines in the operating room last year. You looked at two different machines which surgeons were equally happy to use.

Ultrasound company 1 offered their machine for an initial $8,000 investment and then, 5 equal payments of $1500/year for maintenance. At the end of the 5 years you would own the machine in full and there are no other costs. Life expectancy of the machine is well beyond 5y.

Ultrasound company 2 offered their machine for an initial investment of $10,000 and then, 4 equal payments of $1000/year for maintenace. At the end of the 4 years you would own the machine in full, again with no other costs and a life expectancy >5 years.

The opportunity cost of capital is 6%.

Your manager says you should buy US machine #2 because it costs $14,000, while US machine #1 costs $8000 plus $7500 in maintenace and the $15,500 is unfavorable by $1500 when compared to the other machine.

Which US machine should you buy? Show your calculations to your management team to support your decision. Calculate the PV of total cost for each machine and then the equivalent annual annuity for each.

To get you started, here's a way to set up the problem:

Year	US 1	US 2
0	$8,000	$10,000
1	$1,500	$1,000
2	$1,500	$1,000
3	$1,500	$1,000
4	$1,500	$1,000
5	$1,500