Question

Investment X offers to pay you $5,000 per year for nine years, whereas Investment Y offers to pay you $7,500 per year for five years.

a. Calculate the present value for Investments X and Y if the discount rate is 5 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

b. Calculate the present value for Investments X and Y if the discount rate is 15 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

(a)-Present value for Investments X and Y if the discount rate is 5 percent.

Present value for Investments X

Year	Annual cash flows ($)	Present Value Factor (PVF) at 5.00%	Present Value of the annual cash flows ($) [Annual cash flow x PVF]
1	5,000	0.952381	4,761.90
2	5,000	0.907029	4,535.15
3	5,000	0.863838	4,319.19
4	5,000	0.822702	4,113.51
5	5,000	0.783526	3,917.63
6	5,000	0.746215	3,731.08
7	5,000	0.710681	3,553.41
8	5,000	0.676839	3,384.20
9	5,000	0.644609	3,223.04
TOTAL			35,539.11

Present value for Investments X is $35,539.11

Present value for Investments Y

Year	Annual cash flows ($)	Present Value Factor (PVF) at 5.00%	Present Value of the annual cash flows ($) [Annual cash flow x PVF]
1	7,500	0.952381	7,142.86
2	7,500	0.907029	6,802.72
3	7,500	0.863838	6,478.78
4	7,500	0.822702	6,170.27
5	7,500	0.783526	5,876.45
TOTAL			32,471.08

Present value for Investments Y is $32,471.08

(b)-Present value for Investments X and Y if the discount rate is 15 percent.

Present value for Investments X

Year	Annual cash flows ($)	Present Value Factor (PVF) at 15.00%	Present Value of the annual cash flows ($) [Annual cash flow x PVF]
1	5,000	0.869565	4,347.83
2	5,000	0.756144	3,780.72
3	5,000	0.657516	3,287.58
4	5,000	0.571753	2,858.77
5	5,000	0.497177	2,485.88
6	5,000	0.432328	2,161.64
7	5,000	0.375937	1,879.69
8	5,000	0.326902	1,634.51
9	5,000	0.284262	1,421.31
TOTAL			23,857.92

Present value for Investments X is $23,857.92

Present value for Investments Y

Year	Annual cash flows ($)	Present Value Factor (PVF) at 15.00%	Present Value of the annual cash flows ($) [Annual cash flow x PVF]
1	7,500	0.869565	6,521.74
2	7,500	0.756144	5,671.08
3	7,500	0.657516	4,931.37
4	7,500	0.571753	4,288.15
5	7,500	0.497177	3,728.83
TOTAL			25,141.16

Present value for Investments Y is $25,141.16

NOTE    

The formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], where “r” is the discount / interest rate and “n” is the number of years.