Question

Problem 6-2 Present Value and Multiple Cash Flows (LO 1] Investment X offers to pay you $5,500 per year for 9 years, whereas Investment Y offers to pay you $7,900 per year for 5 years. If the discount rate is 5 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Present value of from projects

Answer:

Project X = $39,092.90

Project Y = $34,203.05

Since cash flows are uniform we can use annuity method for calculating the present value, formula for calculating present value is as follows

Present value = Cash flow * Present value annuity factor (at interest rate for N years)

Calculation for project X

Cash flow = $5,500

Present value annuity factor is calculated at the Discount rate of 5% for 9 years i.e. for the period of cash inflows.

Present Value              = $5,500 * 7.1078

                                    = $ 39,092.90

Calculation for project X

Cash flow = $7,900

Present value annuity factor is calculated at the Discount rate of 5% for 5years i.e. for the period of cash inflows.

Present Value             = $7,900 * 4.3295

                                    = $ 34,203.05

How to compute annuity factor (@13.60%)

Annuity factor is sum total of present value factor for N years

For Project X (5% for 9 years)

periods	Present value factor @ 5%
1	0.9524
2	0.9070
3	0.8638
4	0.8227
5	0.7835
6	0.7462
7	0.7107
8	0.6768
9	0.6446
Present value Annuity factor   (sum of present value factor)	7.1078

For Project Y (5% for 5 years)

periods	Present value factor @ 5%
1	0.9524
2	0.9070
3	0.8638
4	0.8227
5	0.7835
Present value Annuity factor   (sum of present value factor)	4.3298

Calculation of Discounting Factor (Present Value Factor)

Discount Factor = 1/ (1+R) N

R = Discount Rate (i.e. = 5%)

N = No of years

E.g. for year 2 Discount Factor = 1/ (1.05)2

                                                                = 1/ (1.05) (1.05)

                                                =   0.9070