Question

(Present value​) The state​ lottery's million-dollar payout provides for ​$3 ​million(s) to be paid over 19 years in 20 payments of $ 150 comma 000. The first $ 150 comma 000 payment is made​ immediately, and the 19 remaining $ 150 comma 000 payments occur at the end of each of the next 19 years. If 12 percent is the appropriate discount​ rate, what is the present value of this stream of cash​ flows? If 24 percent is the appropriate discount​ rate, what is the present value of the cash​ flows?

Answer 1

Answer:

Pv if i is 12%= $1,254,866.53

PV if i=24% = $764,507.77

Explanation:

The stream of cash flows described here is an annuity due, 20 equal payments in equal intervals, with the 1st payment being received today and the last one at the end on the 19th year.

$PV=\frac{Pmt[1-(1+i)^{-n}]}{i} *(1+i)$

Where Pmt is equal payments made each period

             i is the required rate of return per period

             n is the number of periods

given that i = 0.12

$PV = \frac{150,000[1-(1+0.12)^{-20} ]}{0.12} *(1.12) = 1,254,866.53$

if i is 0.24;

$PV= \frac{150,000[1-(1+0.24)^{-20} ]}{0.24} *(1.24) = 764,507.77$