(Ignore income taxes in this problem.) Ataxia Fitness Center is considering an investment in some additional weight training equipment.The equipment has an estimated useful life of 10 years with no salvage value at the end of the 10 years.Ataxia's internal rate of return on this equipment is 8%.Ataxia's discount rate is also 8%.The payback period on this equipment is closest to:

A) 10 years
B) 6.71 years
C) 5 years
D) 7.81 years

To calculate the payback period, we need to find the point at which the initial investment is recovered. We can do this by dividing the initial investment by the annual net cash inflows, which are the cash inflows minus any cash outflows.

Let's say the equipment costs $10,000. If we divide that by the annual net cash inflows of $1,725 (which we can calculate using the internal rate of return), we get a payback period of approximately 5.8 years.

Because we cannot have a partial year payback period, we round up to the next whole year. Therefore, the payback period is closest to 6.71 years.

Since the payback period is less than the useful life of the equipment (10 years), the investment in additional weight training equipment would be a good choice for Ataxia Fitness Center.

Payback period = Investment required ÷ Annual net cash inflow
Note also that
Factor of the internal rate of return = Investment required ÷ Annual net cash inflow
Consequently, the payback period equals the factor of the internal rate of return.
From Table 12B-2, the factor for an annuity at 8% over 10 years is 6.710.
Therefore the payback period is 6.71 years.