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	​$	3,000		​$	3,000	​$	6,000
2		4,000			3,000		6,000
3		5,000			3,000		(6,000)
4		(6,000)			3,000		(6,000)
5		6,000			5,000		16,000

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?

Answer 1

A
Discount rate	0.08
Year	0	1	2	3	4	5
Cash flow stream	0	3000	4000	5000	-6000	6000
Discounting factor	1	1.08	1.1664	1.259712	1.360489	1.469328
Discounted cash flows project	0	2777.778	3429.355	3969.161	-4410.179	4083.499
NPV = Sum of discounted cash flows
NPV A =	9849.61
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
B
Discount rate	0.08
Year	0	1	2	3	4	5
Cash flow stream	0	3000	3000	3000	3000	5000
Discounting factor	1	1.08	1.1664	1.259712	1.360489	1.469328
Discounted cash flows project	0	2777.778	2572.016	2381.497	2205.0896	3402.916
NPV = Sum of discounted cash flows
NPV B =	13339.3
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
C
Discount rate	0.08
Year	0.00%	1	2	3	4	5
Cash flow stream	0	6000	6000	-6000	-6000	16000
Discounting factor	1	1.08	1.1664	1.259712	1.360489	1.469328
Discounted cash flows project	0	5555.556	5144.033	-4762.99	-4410.179	10889.33
NPV = Sum of discounted cash flows
NPV C =	12415.75
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor