Problem 57 Present and future values of a cash flow stream A

Problem 5-7 Present and future values of a cash flow stream An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $600 at the end of Year 6 a. If other investments of equal risk earn 11% annually, what is its present value? Round your answer to the nearest cent b. If other investments of equal risk earn 11% annually, what is its future value? Round your answer to the nearest cent.

Solution

a.

Present Value = Sum of (Present value of all future cash flows)

Present Value = 100/(1+11%)^1 + 100/(1+11%)^2 + 100/(1+11%)^3 + 200/(1+11%)^4 + 300/(1+11%)^5 + 600/(1+11%)^6

Present Value = 874.94

b.

Future Value = Sum of (Future value of all cash flows)

Future Value = 100*(1+11%)^5 + 100*(1+11%)^4 + 100*(1+11%)^3 + 200*(1+11%)^2 + 300*(1+11%)^1 + 600*(1+11%)^0

Future Value = 1,636.50

Presenting in table form:

Present Value

Future Value

Year

Cash flows = CF

Df = 1/(1+11%)^Year

Present Value = CF x Df

CF x (1+11%)^(6-Year)

0

0.00

1.000000

0.00

Exclude investment

1

100.00

0.900901

90.09

168.51

2

100.00

0.811622

81.16

151.81

3

100.00

0.731191

73.12

136.76

4

200.00

0.658731

131.75

246.42

5

300.00

0.593451

178.04

333.00

6

600.00

0.534641

320.78

600.00

7

8

Total

874.94

1,636.50

			Present Value	Future Value
Year	Cash flows = CF	Df = 1/(1+11%)^Year	Present Value = CF x Df	CF x (1+11%)^(6-Year)
0	0.00	1.000000	0.00	Exclude investment
1	100.00	0.900901	90.09	168.51
2	100.00	0.811622	81.16	151.81
3	100.00	0.731191	73.12	136.76
4	200.00	0.658731	131.75	246.42
5	300.00	0.593451	178.04	333.00
6	600.00	0.534641	320.78	600.00
7
8
		Total	874.94	1,636.50