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1. A hospital is planning to purchase a new MRI machine
that costs $2 million. The expected useful life of the
machine is 10 years and the annual maintenance cost is
$100,000. The hospital uses a discount rate of 8% for
capital budgeting decisions. What is the net present value
(NPV) of the investment?
a) $1,080,000
b) $1,200,000
c) $1,320,000
d) $1,440,000*
Rationale: The NPV is the difference between the present
value of the cash inflows and the cash outflows of the
investment. The cash inflows are the annual savings from
using the new machine, which are assumed to be $300,000
per year for 10 years. The cash outflows are the initial cost
of the machine and the annual maintenance cost. The
present value of the cash inflows is calculated by using the
annuity formula: PV = C * (1 - 1/(1 + r)^n) / r, where C is
the annual cash flow, r is the discount rate, and n is the
number of periods. The present value of the cash outflows
is calculated by adding the initial cost and the present value
of the maintenance cost, which is also an annuity.
Therefore, NPV = 300,000 * (1 - 1/(1 + 0.08)^10) / 0.08 -
2,000,000 - 100,000 * (1 - 1/(1 + 0.08)^10) / 0.08 =
$1,440,000.
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