Question

​(Present value of an uneven stream of payments​) You are given three investment alternatives to analyze. The cash flows from these three investments are as​ follows:

Investment
End of Year	A			B		C
1	​$	1,000		​$	1,000	​$	5,000
2		2,000			1,000		5,000
3		3,000			1,000		(5,000)
4		(4,000)			1,000		(5,000)
5		4,000			5,000		15,000

What is the present value of each of these three investments if the appropriate discount rate is 8 ​percent?

a.  What is the present value of investment A at an annual discount rate of 8 ​percent?

b.  What is the present value of investment B at an annual discount rate of 8 ​percent?

c.  What is the present value of investment C at an annual discount rate of 8 ​percent?

Answer 1

Ans a) 4804.31

b) 6715.04

c) 11480.76

a)	Year	Project Cash Flows (i)	DF@ 8%	DF@ 8% (ii)	PV of Project A ( (i) * (ii) )
	1	1000	1/((1+8%)^1)	0.926	925.93
	2	2000	1/((1+8%)^2)	0.857	1,714.68
	3	3000	1/((1+8%)^3)	0.794	2,381.50
	4	-4000	1/((1+8%)^2)	0.735	(2,940.12)
	5	4000	1/((1+8%)^3)	0.681	2,722.33
			PRESENT VALUE		4,804.31

b)	Year	Project Cash Flows (i)	DF@ 8%	DF@ 8% (ii)	PV of Project A ( (i) * (ii) )
	1	1000	1/((1+8%)^1)	0.926	925.93
	2	1000	1/((1+8%)^2)	0.857	857.34
	3	1000	1/((1+8%)^3)	0.794	793.83
	4	1000	1/((1+8%)^2)	0.735	735.03
	5	5000	1/((1+8%)^3)	0.681	3,402.92
			PRESENT VALUE		6,715.04

c)	Year	Project Cash Flows (i)	DF@ 8%	DF@ 8% (ii)	PV of Project A ( (i) * (ii) )
	1	5000	1/((1+8%)^1)	0.926	4,629.63
	2	5000	1/((1+8%)^2)	0.857	4,286.69
	3	-5000	1/((1+8%)^3)	0.794	(3,969.16)
	4	-5000	1/((1+8%)^2)	0.735	(3,675.15)
	5	15000	1/((1+8%)^3)	0.681	10,208.75
			PRESENT VALUE		11,480.76