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			3,000		15,000

What is the present value of each of these three investments if the appropriate discount rate is 13 ​percent?

a.  What is the present value of investment A at an annual discount rate of 13 ​percent?

b. What is the present value of investment B at an annual discount rate of 13 ​percent?

c. What is the present value of investment C at an annual discount rate of 13 ​percent?

Answer 1

(a)
Project A
Year	Cash Flow	P.V.F. @ 13% for respective years	Present Value (cash flow * P.V.F.)
n		(1/(1+0.13)^n
1	$1,000.00	0.8850	$884.96
2	$2,000.00	0.7831	$1,566.29
3	$3,000.00	0.6931	$2,079.15
4	-$4,000.00	0.6133	-$2,453.27
5	$4,000.00	0.5428	$2,171.04
			________
			$4,248.16
			________
So, Present value of Project A is $4,248.16 at 13% discount rate.
(b)
Project B
Year	Cash Flow	P.V.F. @ 13% for respective years	Present Value (cash flow * P.V.F.)
n		(1/(1+0.13)^n
1	$1,000.00	0.8850	$884.96
2	$1,000.00	0.7831	$783.15
3	$1,000.00	0.6931	$693.05
4	$1,000.00	0.6133	$613.32
5	$3,000.00	0.5428	$1,628.28
			________
			$4,602.75
			________
So, Present value of Project B is $4,602.75 at 13% discount rate.
(c)
Project C
Year	Cash Flow	P.V.F. @ 13% for respective years	Present Value (cash flow * P.V.F.)
n		(1/(1+0.13)^n
1	$5,000.00	0.8850	$4,424.78
2	$5,000.00	0.7831	$3,915.73
3	-$5,000.00	0.6931	-$3,465.25
4	-$5,000.00	0.6133	-$3,066.59
5	$15,000.00	0.5428	$8,141.40
			________
			$9,950.07
			________
So, Present value of Project C is $9,950.07 at 13% discount rate.