Question

The state​ lottery's million-dollar payout provides for ​$1 ​million(s) to be paid over 24 years in 25 payments of $40,000. The first $40,000 payment is made​ immediately, and the 24 remaining $40,000 payments occur at the end of each of the next 24 years. If 9 percent is the appropriate discount​ rate, what is the present value of this stream of cash​ flows? If 18 percent is the appropriate discount​ rate, what is the present value of the cash​ flows?

Answer 1

The present value of stream of cash flows of $40,000 at the end of each year over 24 years is calculated in excel through the PV function as follows:

PV(Rate, Nper, -pmt) = PV(9%, 24, -40000) = $388,264.47.

The first payment of $40,000 is made immediately which implies that it has a present value of $40,000. Therefore, the present value of 25 payments of $40,000 over 24 years with the first payment occurring immediately = $388,264.47 + $40,000 = $428,264.47.

The computation of present value of the same stream of cash flows when the discount rate is 18% is as follows:

PV(18%, 24, -40000) = $218,037.96.

Hence, the present value of 25 payments of $40,000 over 24 years with the first payment occurring immediately = $218,037.96 + $40,000 = $258,037.96.