In: Finance
The state lottery's million-dollar payout provides for $11 million to be paid in 20 installments of 50,000 per payment. The first 50,000 payment is made immediately, and the
19 remaining 50,000 payments occur at the end of each of the next 19 years. If 7 percent is the discount rate, what is the present value of this stream of cash flows? If
14 percent is the discount rate, what is the present value of the cash flows?
a. If 7 percent is the discount rate, the present value of the annuity due is
$____?
Present value of annuity due = 50000 + present value of ordinary 19 year annuity. | |||||
a) | Present value of an ordinary annuity = C*[(1-(1/(1+r)^t))/r] | ||||
where C is the annuity payment 50000. | |||||
r is the interest rate that is .07. | |||||
t is the time period in years that is 19. | |||||
Present value of ordinary 19 year annuity | 50000*[(1-(1/(1.07)^19))/.07] | ||||
Present value of ordinary 19 year annuity | 50000*[(1-(1/3.616528))/.07] | ||||
Present value of ordinary 19 year annuity | 50000*[(1-(.276508))/.07] | ||||
Present value of ordinary 19 year annuity | 50000*[.723492/.07] | ||||
Present value of ordinary 19 year annuity | 50000*[10.3356] | ||||
Present value of ordinary 19 year annuity | 516779.8 | ||||
Present value of annuity due = 50000 +516779.8 | |||||
Present value of annuity due = 566779.8 | |||||
If 7 percent is the discount rate, the present value of the annuity due is | |||||
$566779.8. | |||||
b) | Present value of an ordinary annuity = C*[(1-(1/(1+r)^t))/r] | ||||
where C is the annuity payment 50000. | |||||
r is the interest rate that is .14. | |||||
t is the time period in years that is 19. | |||||
Present value of ordinary 19 year annuity | 50000*[(1-(1/(1.14)^19))/.14] | ||||
Present value of ordinary 19 year annuity | 50000*[(1-(1/12.05569))/.14] | ||||
Present value of ordinary 19 year annuity | 50000*[(1-(.082948))/.14] | ||||
Present value of ordinary 19 year annuity | 50000*[.917052/.14] | ||||
Present value of ordinary 19 year annuity | 50000*[6.550369] | ||||
Present value of ordinary 19 year annuity | 327518.4 | ||||
Present value of annuity due = 50000 + 327518.4 | |||||
Present value of annuity due = 377518.4 | |||||
If 14 percent is the discount rate, the present value of the annuity due is | |||||
$377518.4. |