Finance: Problem Set II

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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. B.Future Value to the Present
Option 1: $10,000 now; PV=$10,000
Option 2: $2,000 at 11% in 8 years
2,000 x 5.146 = $10,292
$2,000 at 12% in 8 years
2,000 x 4.968 = $9,936
Option 3: $24,000 in 8 years, to present value, at 11%
24,000 x 0.434 = $10,416
$24,000 in 8 years, to the present value, at 12%
24,000 x 0.404 = $9,696
Choice: The first option would be $24,000 in 8 years at 11%
In both options, the choice would be the same answer: $24,000 in 8 years.

Chapter 9 # 23: Payments required
You need $28,974 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year. 1.What single payment could be made at the beginning of the first year to achieve this objective? Answer: Present Value

PV = FV x PVIF ( i=8%, n=10)
PV = 28,974 x 0.463
PV = 13,415
2.What amount could you pay at the end of each year annually for 10 years to achieve this same objective? Answer: Annuity
A = PVA / PVIFA (i=8%, n=10)
PVA = A / PVIFA
PVA = 28,974 x 14.487
PVA = 2,000
Chapter 10 # 2: Bond value
Midland Oil has $1,000 par value bonds outstanding at 8 percent interest. The bonds will mature in 25 years. Compute the current price of the bonds if the present yield to maturity is: 1.7 percent.

Answer: PVa = A x PV(i=7%, n=25)
PVa = 80 x 11.654 = 932.32 = Present Value of interest payment PVm = FV x PV (i=7%, n=25)
PVm = 1000 x 0.184 = 184 = Present Value of principal payment at maturity Price of the bond = PVa + PVm = 932.32 + 184 = $1,116.32
2. 10 percent.
Answer: PVa = 80 x 9.077 = 726.16 = Present Value of interest payment PVm = 1000 x 0.092 = 92 = Present Value of principal payment at maturity Price of the bond = 726.16 + 92 = $818.16
3.13 percent.
Answer: PVa = 80 x 7.330 = 586.40 = Present Value of interest payment PVm = 1000 x 0.047 = 47 = Present Value of principal payment at...
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