Question

Investment X offers to pay you $5,500 per year for 9 years, whereas Investment Y offers to pay you $8,000 per year for 5 years. If the discount rate is 8 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.) Present Value Investment X $ Investment Y $ If the discount rate is 20 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.) Present Value Investment X $ Investment Y $

Answer 1

a). Present value for investment X=$24,762.32, at 8% discount

Present value for investment Y=$27,223.33

b). Present value for investment X=$9,593.43, at 20% discount

Present value for investment Y=$16,075.10

Step-by-step explanation:

A).

Step 1

Determine the future value of investment X using the expression;

Future value for X=payments per year×number of years

where;

payments per year=$5,500

number of years=9 years

replacing;

Future value of X=(5,500×9)=$49,500

Step 2

Determine the present value of investment X as shown;

F.V=P.V(1+r)^n

where;

F.V=future value of investment=$49,500

P.V=unknown

r=discount rate=8%=8/100=0.08

n=number of years=9 years

replacing;

49,500=P.V(1+0.08)^9

49,500=P.V(1.08)^9

P.V=24,762.32

Present value for investment X=$24,762.32

Determine the future value of investment Y using the expression;

Future value for Y=payments per year×number of years

where;

payments per year=$8,000

number of years=5 years

replacing;

Future value of Y=(8,000×5)=$40,000

Step 2

Determine the present value of investment Y as shown;

F.V=P.V(1+r)^n

where;

F.V=future value of investment=$40,000

P.V=unknown

r=discount rate=8%=8/100=0.08

n=number of years=5 years

replacing;

40,000=P.V(1+0.08)^5

40,000=P.V(1.08)^5

P.V=27,223.33

Present value for investment Y=$27,223.33

B).

Step 1

Determine the future value of investment X using the expression;

Future value for X=payments per year×number of years

where;

payments per year=$5,500

number of years=9 years

replacing;

Future value of X=(5,500×9)=$49,500

Step 2

Determine the present value of investment X as shown;

F.V=P.V(1+r)^n

where;

F.V=future value of investment=$49,500

P.V=unknown

r=discount rate=20%=20/100=0.2

n=number of years=9 years

replacing;

49,500=P.V(1+0.2)^9

49,500=P.V(1.2)^9

P.V=9,593.43

Present value for investment X=$9,593.43

Determine the present value of investment Y as shown;

F.V=P.V(1+r)^n

where;

F.V=future value of investment=$40,000

P.V=unknown

r=discount rate=20%=20/100=0.2

n=number of years=5 years

replacing;

40,000=P.V(1+0.2)^5

40,000=P.V(1.2)^5

P.V=16,075.10

Present value for investment Y=$16,075.10