(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 14%. Ataxia's discount rate is also 14%. The payback period on this equipment is closest to: Multiple Choice 1.92 years 2.70 years 3.70 years 5.22 years

Question

contestada

Respuesta :

tahneetakhan tahneetakhan · Answer 1 · 2019-12-20T11:51:17+01:00

Answer:

D: 5.22 years

Explanation:

Let the initial outlay be 100,000.

At IRR, Present Value of inflows = Present Value of outflows.

Present value of annuity= Annuity1 - (1+interest rate)^-time period/rate

100,000 = Annuity1-(1.14)^-10/0.14

100,000 = Annuity * 5.2161156

Annuity = 100,000 / 5.2161156

= 19,171.35

Payback Period = Initial outlay / Annual cash flows

=(100,000 /19,171.35)

= 5.2161 years

Answer Link

okpalawalter8 okpalawalter8 · Answer 2 · 2022-06-01T16:36:43+02:00

Ataxia Fitness Center is considering an investment in some additional weight, The payback period on this equipment is closest to

P= 5.2161 years

Generally, the equation for the Present value of the annuity is mathematically given as

[tex]PA= A1 - (1+I)^ {-T/R[/tex]

Therefore

[tex]100,000 = A1-(1.14)^{-10/0.14 }\\\\100,000 = A * 5.2161156\\\\A = 100,000 / 5.2161156[/tex]

A= 19,171.35

In conclusion, the Payback Period

[tex]P= IO / Annual cash flow[/tex]

Hence

[tex]P=(100,000 /19,171.35)[/tex]

P= 5.2161 years