Finance: Problem Set II
Chapter 9 # 17: Present values
Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year; $2.20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $33. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.)
Answer:
The following formula calculates the present values: PV = FV/ (1+r) ^t, where
FV is the cash flow, discount rate r = 11%, t = year.
From there: 1st year = $2.00 x 0.901= PV= $1.80
2nd year = $2.20 x 0.802 = PV= $1.79
3rd year = $35.40 x 0.731 = PV=$25.88
Total PV= $29.47
Thus, the PV of total benefit is $29.47
Chapter 9 # 22: Alternative present values
Your rich godfather has offered you a choice of one of the three following alternatives: $10,000 now; $2,000 a year for eight years; or $24,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?
Answer: I found two answers for the same problems. One is bringing the present value to the future and the other is bringing the future value to the present. In each one of them, different solutions were proposed.
A. Present Value to the future
Option 1: $10,000 now with 11% interest.
$10,000 x 11% = $11,100(10,000 + 1,100)
1,100 x 8 yrs = $8,800 + $10,000 = $18,800
$10,000 now with 12% interest.
$10,000 x 12% = $11,200 (10,000 + 1,200)
1,200 x 8 yrs = $ 9,600 + 10,000 = $19,600
Option 2: $2,000 a year for eight years.
$2,000 x 11% = $2,220
$2,220 x 8 Years = $17,760
$2,000 x 12% = $2,240
$2,240 x 8 Years = $17,920
Option 3
$24,000 at the end of eight years.
Choice: Option 3. The rate of return in Options 1 and 2 is less than what is offered in option 3 at the end of eight years.
Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year; $2.20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $33. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.)
Answer:
The following formula calculates the present values: PV = FV/ (1+r) ^t, where
FV is the cash flow, discount rate r = 11%, t = year.
From there: 1st year = $2.00 x 0.901= PV= $1.80
2nd year = $2.20 x 0.802 = PV= $1.79
3rd year = $35.40 x 0.731 = PV=$25.88
Total PV= $29.47
Thus, the PV of total benefit is $29.47
Chapter 9 # 22: Alternative present values
Your rich godfather has offered you a choice of one of the three following alternatives: $10,000 now; $2,000 a year for eight years; or $24,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?
Answer: I found two answers for the same problems. One is bringing the present value to the future and the other is bringing the future value to the present. In each one of them, different solutions were proposed.
A. Present Value to the future
Option 1: $10,000 now with 11% interest.
$10,000 x 11% = $11,100(10,000 + 1,100)
1,100 x 8 yrs = $8,800 + $10,000 = $18,800
$10,000 now with 12% interest.
$10,000 x 12% = $11,200 (10,000 + 1,200)
1,200 x 8 yrs = $ 9,600 + 10,000 = $19,600
Option 2: $2,000 a year for eight years.
$2,000 x 11% = $2,220
$2,220 x 8 Years = $17,760
$2,000 x 12% = $2,240
$2,240 x 8 Years = $17,920
Option 3
$24,000 at the end of eight years.
Choice: Option 3. The rate of return in Options 1 and 2 is less than what is offered in option 3 at the end of eight years.