Chapter 9



Chapter 9

Time Value of Money

16. Present value (LO3) General Mills will receive $27,500 per year for the next 10 years as a payment for a weapon he invented. If a 12 percent rate is applied, should he be willing to sell out his future rights now for $160,000?

9-16. Solution:

Appendix D

PVA = A × PVIFA (12%, 10 periods)

PVA = $27,500 × 5.650 = $155,375

Yes, the present value of the annuity is worth less than $160,000.

20. Future value (LO2) Christy Reed has been depositing $1,500 in her savings account every December since 2001. Her account earns 6 percent compounded annually. How much will she have in December 2010? (Assume that a deposit is made in December of 2010. Make sure to count the years carefully.)

9-20. Solution:

Appendix C

FVA = A × FVIFA (6%, n = 10)

FVA = $1,500 × 13.181 = $19,771.50

31. Quarterly compounding (LO5) Beverly Hills started a paper route on January 1, 2004. Every three months, she deposits $300 in her bank account, which earns 8 percent annually but is compounded quarterly. On December 31, 2007, she used the entire balance in her bank account to invest in an investment at 12 percent annually. How much will she have on December 31, 2010?

9-31. Solution:

Appendix C

FVA = A × FVIFA (2%, 16 periods)

FVA = $300 × 18.639 = $5,591.70 after four years

Appendix A

FV = PV × FVIF (12%, 3 periods)

FV = $5,591.70 × 1.405

FV = $7,856.34 after three more years

32. Yield (LO4) Franklin Templeton has just invested $8,760 for her son (age one). This money will be used for his son’s education 17 years from now. He calculates that he will need $60,000 by the time the boy goes to school. What rate of return will Mr. Templeton need in order to achieve this goal?

9-32. Solution:

Appendix B

[pic]

Or

Alternative solution

Appendix A

[pic]

33. Yield with interpolation (LO4) On January 1, 2008, Mr. Dow bought 100 shares of stock at $12 per share. On December 31, 2010, he sold the stock for $18 per share. What is his annual rate of return? Interpolate to find the answer.

9-33. Solution:

Appendix B

[pic]

[pic] Return is between 14%-15% for 3 years

[pic]

[pic]

14% + (.008/.017) (1%)

14% + .471 (1%)

14.47%

38. Deferred annuity (LO3) Rusty Steele will receive the following payments at the end of the next three years: $4,000, $7,000, and $9,000. Then from the end of the fourth year through the end of the tenth year, he will receive an annuity of $10,000. At a discount rate of 10 percent, what is the present value of all future benefits?

9-38. Solution:

First find the present value of the first three payments.

PV = FV × PVIF (Appendix B) i = 10%

1) $4,000 × .909 = $3,636

2) 7,000 × .826 = 5,782

3) 9,000 × .751 = 6,759

$16,177

Then find the present value of the deferred annuity.

Appendix D will give a factor for a seven period annuity (fourth year through the tenth year) at a discount rate of 10 percent. The value of the annuity at the beginning of the fourth year is:

[pic]

This value at the beginning of year four (end of year three) must now be discounted back for three years to get the present value of the deferred annuity. Use Appendix B.

[pic]

Finally, find the total present value of all future payments.

Present value of first three payments $16,177

Present value of the deferred annuity 36,559

$52,736

9-38. (Continued)

OR

Take the PVIFA for 10 years at 10% and subtract the PVIFA for 3 years at 10% to end up with the 7 year deferred annuity.

PVIFA = 6.145 (10 years at 10%)

PVIFA = 2.487 ( 3 years at 10%)

PVIFA = 3.658 (years 4 through 10 years at 10%)

$10,000 × 3.658 = $36,580

Present value of first three payments $16,177

Present value of the deferred annuity 36,580

$52,757

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