Question

1. What is the maximum amount a company would be willing to pay today to purchase a

machine if it is expected to provide annual savings of $10,000 for 10 years and to have a

resale value of $25,000 at the end of that period? Assume the business wants to earn 5% on its investment and that the annual savings are realized at year end.

Please show all of the factors used in the calculation – PV, I/Y, N, etc. – NOT just the answer.

If the calculation involves an annuity, please indicate if it is an ordinary annuity or an annuity due.

Answer 1

Solution:

Expected annual savings from the Machine = $10,000 for 10 years (realized at each year end i.e. an ordinary annuity)

Resale value at the end of 10 year period = $25,000

Required rate of return = 5%

The maximum amount the Company would be willing to pay today to purchase the machine is the present value of the future cash flows discounted @ 5%

Therefore, present value of the future cash flows = present value of an ordinary annuity of $10,000 for a period of 10 years + present value of $25,000 for the cash flow occuring at Year 10

=PVIFA ($10,000,5%, 10 years) + PVIF($25,000, 5%, 10th year) = ($10,000 * 7.7217) + ($25,000 * 0.6139) [Using Present value interest factor table]

= $77,217 + $15,347.50 = $92,564.50

Therefore, the maximum amount the Company would be willing to pay today to purchase the machine is $92,564.50