Mba 503 Problem Set 2

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Chapter 9, Problem 17
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.)

Present value of a single amount
PV = FV x PVIF or Appendix B
Year 1: FV = 2.00; i = 0.11; n = 1; PV = 2.00 [0.901] = 1.80 Year 2: FV = 2.20; i = 0.11; n = 2; PV = 2.20 [0.813] = 1.79 Year 3: FV = 2.40; i = 0.11; n = 3; PV = 2.40 [0.731] = 1.75 When FV = 33, i = 0.11; n =3; PV = 33[0.731] = 24.12

Total PV = 1.80+1.79+1.75+24.12 = 29.46

Chapter 9, Problem 22
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? Present value of annuity (Appendix D)

PVA = A x PVIFA
Alternative 1: $10,000 now; PVA = $10,000
Alternative 2 at 11%: $2,000 a year for eight years; PVA = 2000[5.146] = $10,292 Alternative 2 at 12%: $2,000 a year for eight years; PVA = 2000[4.968] = $ 9,936

Present value of a single amount (Appendix B)
PV = FV x PVIF
Alternative 3 at 11%: $24,000 at the end of eight years; PV = 24000[0.434] = $10.416 Alternative 3 at 12%: $24,000 at the end of eight years; PV = 24000[0.404] = $ 9,696

Alternative 3 would be the best choice at 11%.
Alternative 1 would be the best choice at 12%.

Chapter 9, Problem 23
You need $28,974 at the end of nine 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.

a.What single payment could be made at the beginning of the first year to achieve this objective? b.What amount could you pay at the end of each year annually for 10 years to achieve this same objective? a.Present value of a single amount (Appendix B)

PV = FV x PVIF (i = 8%, n = 10)
PV = 28974 [0.463]
PV = 13,415

b.Annuity equaling a present value (Appendix C)
A = PVA/PVIFA (i = 8%, n = 10)
PVA = A/ PVIFA
PVA = 28974/ [14.487]
PVA = 2,000

Chapter 10, Problem 2
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:

a.7 percent.
b.10 percent.
c.13 percent.

a.Price of bond = interest payment + principal payment at maturity Price of bond = 932.32 + 184.00
Price of bond = 1,116.32

Present value of interest payment (Appendix D)
PVA = A x PVIFA
PVA = (1000x0.08) x PV (i = 7%, n=25)
PVA = 80 x (11.654)
PVA = 932.32

Present value of principal payment at maturity (Appendix B)
PV = FV x PVIF
PV = 1000 x PV (i= 7%, n=25)
PV = 1000 x 0.184
PV = 184.00

b.b. Price of bond = interest payment + principal payment at maturity Price of bond = 726.16 + 92.00
Price of bond = 818.16

Present value of interest payment (Appendix D)
PVA = A x PVIFA
PVA = (1000x0.08) x PV (i = 10%, n=25)
PVA = 80 x (9.077)
PVA = 726.16

Present value of principal payment at maturity (Appendix B)
PV = FV x PVIF
PV = 1000 x PV (i= 10%, n=25)
PV = 1000 x 0.092
PV = 92.00

c.Price of bond = interest payment + principal payment at maturity Price of bond = 586.40 + 47.00
Price of bond = 633.40

Present value of interest payment (Appendix D)
PVA = A x PVIFA
PVA = (1000x0.08) x PV (i = 13%, n=25)
PVA = 80 x (7.330)
PVA = 586.40

Present value of principal payment at maturity (Appendix B)
PV = FV x PVIF
PV = 1000 x PV (i= 13%, n=25)
PV = 1000 x 0.047
PV = 47.00...
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