Question

4 P5-35 Relationship between future value and present value: Mixed stream The table below shows a mixed cash flow stream except that the cash flow for year 3 is missing. $10,000 5,000 Year 1 Year 2 Year 3 Year 4 Year 5 20,000 3,000 PART 2 Financial Tools Suppose that somehow you know that the present value of the entire stream is $32,911.03 and that the discount rate is 4%. What is the amount of the missing cash flow in year 3?

Answer 1

Let X be the CF at Year 3

Year	CF	PVF @4%	Disc CF
1	$ 10,000.00	0.961538	$           9,615.38
2	$   5,000.00	0.924556	$           4,622.78
3	X	0.888996	0.8890X
4	$ 20,000.00	0.854804	$         17,096.08
5	$   3,000.00	0.821927	$           2,465.78
PV of CFs			33800 + 0.8890X

Given PV of CFs = 32911.03

Thus 33800 + 0.8890X = 32911.03

0.8890X = 32911.03 - 33800

= -888.97

X = -888.97 / 0.8890

= -1000

Year 3 CF is $ -1000