Investment X offers to pay you $5,700 per year for 9 years, whereas Investment Y offers to pay you $7,500 per year for 5 years. a. 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.) b. If the discount rate is 23 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.)

(a) Present value of investment X is $40,514.58, and present value of investment Y is $32,471.08.

(a) Present value of investment X is $20,936.68, and present value of investment Y is $21,026.05.

Explanation:

To calculate these, we use the formula for calculating the present value of an ordinary annuity is stated as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value of the cash flow

P = yearly payment

r = discount rate

n = number of years

We therefore apply equation (1) as follows:

a. 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.)

For investment X

PV = Present value of the cash flow = ?

P = yearly payment = $5,700

r = discount rate = 5%. or 0.05

n = number of years = 9

Substitute the values into equation (1) to have:

PV = $5,700 * ((1 - (1 / (1 + 0.05))^9) / 0.05)

PV = $5,700 * 7.10782167564406

PV = $40,514.58

Therefore, present value of investment X is $40,514.58.

For investment Y

PV = Present value of the cash flow = ?

P = yearly payment = $7,500

r = discount rate = 5%. or 0.05

n = number of years = 5

Substitute the values into equation (1) to have:

PV = $7,500 * ((1 - (1 / (1 + 0.05))^5) / 0.05)

PV = $7,500 * 4.32947667063082

PV = $32,471.08

Therefore, present value of investment Y is $32,471.08.

b. If the discount rate is 23 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.)

For investment X

PV = Present value of the cash flow = ?

P = yearly payment = $5,700

r = discount rate = 23%. or 0.23

n = number of years = 9

Substitute the values into equation (1) to have:

PV = $5,700 * ((1 - (1 / (1 + 0.23))^9) / 0.23)

PV = $5,700 * 3.6731020827622

PV = $20,936.68

Therefore, present value of investment X is $20,936.68.

For investment Y

PV = Present value of the cash flow = ?

P = yearly payment = $7,500

r = discount rate = 23%. or 0.23

n = number of years = 5

Substitute the values into equation (1) to have:

PV = $7,500 * ((1 - (1 / (1 + 0.23))^5) / 0.23)

PV = $7,500 * 2.80347297773543

PV = $21,026.05

Therefore, present value of investment Y is $21,026.05.

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