Question

Your company is considering a payment plan to pay for a large piece of equipment. There are two payment options available:

Make a lump sum payment of $400000, or

Make 25 annual payments of $40000 each, with the first payment to be made today.

The key to make the right choice is to compute the present value of the 25 installment payment, and then compare the PV to the lump sum payment. You would then choose the lower amount because you'll be paying less.

What's the present value of the installment payment plan, assuming that the proper annual discount rate is 7.00%?

Answer 1

Present Value of installment can be calculated using formula for PV of annuity due as:

PV = P + P x [{1-(1+r)^-(n-1)}/r]

PV = Future value of annuity due

P = Periodic Payment = $ 40,000

r = Rate per period = 7 % = 0.07 p.a.

n = Numbers of periods = 25

PV = $ 40,000 + $ 40,000 x [{1-(1+0.07)^-(25-1)}/0.07]

PV = $ 40,000 + $ 40,000 x [{1-(1.07)^-(25-1)}/0.07]

PV = $ 40,000 + $ 40,000 x [{1-(1.07)^-24}/0.07]

PV = $ 40,000 + $ 40,000 x [(1-0.197147)/0.07]

PV = $ 40,000 + $ 40,000 x (0.802853/0.07)

PV = $ 40,000 + $ 40,000 x 11.46933

PV = $ 40,000 + 458,773.36 = $ 498,773.36

Single payment of $ 400,000 option should be opted as the PV of installments $ 498,773.36 is more than it.