Question

​(Related to Checkpoint​ 6.6)  

​(Present value of annuities and complex cash flows​)

You are given three investment alternatives to analyze. The cash flows from these three investments are as​ follows:

Investment Alternatives
End of Year	A		B		C
1	​$	16,000			​$	16,000
2		16,000
3		16,000
4		16,000
5		16,000	​$	16,000
6				16,000		80,000
7				16,000
8				16,000
9				16,000
10				16,000		16,000

Assuming an annual discount rate of 22 ​percent, find the present value of each investment.

a.  What is the present value of investment A at an annual discount rate of 22 percent?

​ ​(Round to the nearest​ cent.)

b.  What is the present value of investment B at an annual discount rate of

22 ​percent?  ​(Round to the nearest​ cent.)

c.  What is the present value of investment C at an annual discount rate of 22 ​percent? 

​(Round to the nearest​ cent.)

Answer 1

(a)-The Present value of investment A at an annual discount rate of 22 percent

Year	Annual Cash Inflow ($)	Present Value factor at 22%	Present Value of Annual Cash Flow ($)
1	16,000	0.819672	13,114.75
2	16,000	0.671862	10,749.80
3	16,000	0.550707	8,811.31
4	16,000	0.451399	7,222.39
5	16,000	0.369999	5,919.99
6	0	0.303278	0
7	0	0.248589	0
8	0	0.203761	0
9	0	0.167017	0
10	0	0.136899	0
TOTAL			45,818.24

The Present value of investment A = $45,818.24

(a)-The Present value of investment B at an annual discount rate of 22 percent

Year	Annual Cash Inflow ($)	Present Value factor at 22%	Present Value of Annual Cash Flow ($)
1	0	0.819672	0
2	0	0.671862	0
3	0	0.550707	0
4	0	0.451399	0
5	16,000	0.369999	5,919.99
6	16,000	0.303278	4,852.45
7	16,000	0.248589	3,977.42
8	16,000	0.203761	3,260.18
9	16,000	0.167017	2,672.28
10	16,000	0.136899	2,190.39
TOTAL			22,872.70

The Present value of investment B = $22,872.70

(a)-The Present value of investment C at an annual discount rate of 22 percent

Year	Annual Cash Inflow ($)	Present Value factor at 22%	Present Value of Annual Cash Flow ($)
1	16,000	0.819672	13,114.75
2	0	0.671862	0
3	0	0.550707	0
4	0	0.451399	0
5	0	0.369999	0
6	80,000	0.303278	24,262.25
7	0	0.248589	0
8	0	0.203761	0
9	0	0.167017	0
10	16,000	0.136899	2,190.39
TOTAL			39,567.39

The Present value of investment C = $39,567.39

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.