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18 April, 07:42

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 $

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  1. 18 April, 11:10
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    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

    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
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