Question

4. Please watch this video on TVM using BAIlPlus Part 2 (7:45): Given the following cash flows and a compound growth rate of 9 percent Year Cash Flow (S): 50 60 60 75 75 75 90 a. What is the present value of this stream of uneven cash flows? b. What is the future value of this stream of uneven cash flows? c. W hat amount per year could you substitute as an annuity that would be equal to this stream of uneven cash flows using the same 9 percent? Words:414 et 490 名 F3 909 F -il er 4 5 9

Answer 1

Answer a
Calculaton of present value of uneven cash flows
Year	Cash flow	Present value factor @ 9%	Present Values
0	$50.00	1.00000	$50.00
1	$60.00	0.91743	$55.05
2	$60.00	0.84168	$50.50
3	$75.00	0.77218	$57.91
4	$75.00	0.70843	$53.13
5	$75.00	0.64993	$48.74
6	$90.00	0.59627	$53.66
Present Value of uneven cash flows			$369.00
Answer b
Calculaton of future value of uneven cash flows
Year	Cash flow	Future value factor @ 9%	Present Values
0	$50.00	1.67710	$83.86
1	$60.00	1.53862	$92.32
2	$60.00	1.41158	$84.69
3	$75.00	1.29503	$97.13
4	$75.00	1.18810	$89.11
5	$75.00	1.09000	$81.75
6	$90.00	1.00000	$90.00
Future Value of uneven cash flows			$618.85
Answer c
Using present value of annuity formula , we can calculate the annuity.
Present value of annuity = P*{[1 - (1+r)^-n]/r}
Present value of annuity = present value of uneven cash flows = $369
P = annuity = ?
r = discount rate = 9%
n = number of years = 6
369 = P*{[1 - (1+0.09)^-6]/0.09}
369 = P*4.485919
P = 82.26
Annuity = $82.26