Question

Investment X offers to pay you $4,800 per year for 9 years, whereas Investment Y offers to pay you $7,100 per year for 5 years. If the discount rate is 6 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.) If the discount rate is 16 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

Answer:

At Discount rate=6%=0.06:

For investment X:

$PV_X=\ 4,800*\frac{1-\frac{1}{(1+0.06)^9}}{0.06} \\PV_X=\ 32,648.12$

For investment Y:

$PV_Y=\ 7,100*\frac{1-\frac{1}{(1+0.06)^5}}{0.06} \\PV_Y=\ 29,907.78$

At Discount rate=16%=0.16:

For investment X:

$PV_X=\ 4,800*\frac{1-\frac{1}{(1+0.16)^9}}{0.16} \\PV_X=\ 22,111.41$

For investment Y:

$PV_Y=\ 7,100*\frac{1-\frac{1}{(1+0.16)^5}}{0.16} \\PV_Y=\ 23,247.48$

Explanation:

Amount paid annually Due to investment X=A=$4,800

Amount paid annually Due to investment Y=A=$7,100

Number of years for investment X =n=9

Number of years for investment Y=n=5

Formula:

$PV=A(\frac{1-\frac{1}{(1+r)^n}}{r})$

At Discount rate=6%=0.06:

For investment X:

$PV_X=\ 4,800*\frac{1-\frac{1}{(1+0.06)^9}}{0.06} \\PV_X=\ 32,648.12$

For investment Y:

$PV_Y=\ 7,100*\frac{1-\frac{1}{(1+0.06)^5}}{0.06} \\PV_Y=\ 29,907.78$

At Discount rate=16%=0.16:

For investment X:

$PV_X=\ 4,800*\frac{1-\frac{1}{(1+0.16)^9}}{0.16} \\PV_X=\ 22,111.41$

For investment Y:

$PV_Y=\ 7,100*\frac{1-\frac{1}{(1+0.16)^5}}{0.16} \\PV_Y=\ 23,247.48$