Answer :
Answer:
(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.