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 10 years. Ataxia's internal rate of return is 14%. It's discount rate is also 14%. The payback period on this equipment is closest to:. a. 2.70 years
b. 1.90 years
c. 5.22 years
d. 3.70 years

6.71 years

Explanation:

Solution

Recall that,

Ataxia Fitness center has an equipment with a useful life estimated to be = 10 years

No Savage value at the end  of = 10 years

Internal rate of return of equipment = 8%

rate of discount = 8%

Now,

From the  Exhibit 13B-1 and Exhibit 13B-2,

Let the initial outlay be $50000

The present value of inflows at irr be =present value of outflows.

let value of  present annuity=Annuity[1-(1+interest rate)^-time period]/rate

Thus,

Be entering the values we get

Annuity[1-(1.08)^-10]/0.08 =50000

5000 =Annuity[1-(1.08)^-10]/0.08

50000=Annuity*6.710081399

Annuity=50000/6.710081399 = =$7451.474435

So, the period of payback =initial outlay/annual cash flows

=(50000/7451.474435)

=6.71 years

Therefore the pay back period on this equipment is = 6.71 years

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