Question

1. Consider an uneven cash flow stream: Show formulas and work without using excel

Year	Cash Flow
0	$2,000
1	$2,000
2	$0
3	$1,500
4	$2,500
5	$4,000

1. • What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an account that pays 10 percent annually?
   • What cash flow today (Year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000 at the end of Year 5? (Assume that the cash flows for Years 1 through 5 remain the same.)

Answer 1

Ans : Future cash flows = present value * (1+r)ⁿ

r = 10%

Future value = $ 2000 * (1+10%)⁵ + 0 *(1.1)⁴ + $ 1,500 *(1.1)³ + $ 2,500*(1.1)² + $ 4,000*(1.1)

= 2,000 * 1.6105 + 0 + 1500*1.331 + 2500*1.21 + 4000*1.1

= 3221.02 + 0 + 1996.5 + 3025 + 4400

= $ 12,642.52

(2) Let x be the amount to be in the year 1

Future value - 1996.5 - 3025 - 4400 = X*1.6105

20,000-1996.5-3025-4400 = X*1.6105

$10,578.5 / 1.6105 = X

X = $ 6,568.416

Amount to be in year 1 = $ 6588.416