Chapter 09: Time Value of Money
Chapter 9
Time Value of Money
Discussion Questions
9-1.
How is the future value (Appendix A) related to the present value of a single
sum (Appendix B)?
The future value represents the expected worth of a single amount, whereas the
present value represents the current worth.
FV = PV (1 + I)n future value
( )
luePresent va
1
1
FVPV
+
=n
i
9-2.
How is the present value of a single sum (Appendix B) related to the present
value of an annuity (Appendix D)?
The present value of a single amount is the discounted value for one future
payment, whereas the present value of an annuity represents the discounted
value of a series of consecutive future payments of equal amount.
9-3.
Why does money have a time value?
Money has a time value because funds received today can be invested to reach a
greater value in the future. A person would rather receive $1 today than $1 in
ten years, because a dollar received today, invested at 6 percent, is worth
$1.791 after ten years.
9-4.
Does inflation have anything to do with making a dollar today worth more than
a dollar tomorrow?
Inflation makes a dollar today worth more than a dollar in the future. Because
inflation tends to erode the purchasing power of money, funds received today
will be worth more than the same amount received in the future.
Chapter 09: Time Value of Money
9-5.
Adjust the annual formula for a future value of a single amount at 12 percent
for 10 years to a semiannual compounding formula. What are the interest
factors (FVIF) before and after? Why are they different?
( )
Semiannual 3.20720n 6%,i
Annual 106.310n %,12i
AAppendix FVPVFV IF
==
==
=
The more frequent compounding under the semiannual compounding
assumption increases the future value so that semiannual compounding is worth
.101 more per dollar.
9-6.
If, as an investor, you had a choice of daily, monthly, or quarterly
compounding, which would you choose? Why?
The greater the number of compounding periods, the larger the future value.
The investor should choose daily compounding over monthly or quarterly.
9-7.
What is a deferred annuity?
A deferred annuity is an annuity in which the equal payments will begin at
some future point in time.
9-8.
List five different financial applications of the time value of money.
Different financial applications of the time value of money:
Equipment purchase or new product decision,
Present value of a contract providing future payments,
Future value of an investment,
Regular payment necessary to provide a future sum,
Regular payment necessary to amortize a loan,
Determination of return on an investment,
Determination of the value of a bond.
Chapter 9
Problems
1. Future value (LO2) You invest $2,500 a year for three years at 8 percent.
a. What is the value of your investment after one year? Multiply $2,500 × 1.08.
b. What is the value of your investment after two years? Multiply your answer to part a
by 1.08.
Chapter 09: Time Value of Money
9-3
c. What is the value of your investment after three years? Multiply your answer to part b
by 1.08. This gives your final answer.
d. Confirm that your final answer is correct by going to Appendix A (future value of
$1), and looking up the future value for n = 3, and i = 8 percent. Multiply this tabular
value by $2,500 and compare your answer to the answer in part c. There may be a
slight difference due to rounding.
9-1. Solution:
a. $2,500 × 1.08 = $2,700
2. Present value (LO3) What is the present value of:
a. $8,000 in 10 years at 6 percent?
b. $16,000 in 5 years at 12 percent?
c. $25,000 in 15 years at 8 percent?
9-2. Solution:
Appendix B
PV = FV × PVIF
3. Present Value (LO3)
a. What is the present value of $100,000 to be received after 40 years with an
18 percent discount rate?
b. Would the present value of the funds in part a be enough to buy a $125 concert
ticket?
9-3. Solution:
Chapter 09: Time Value of Money
9-4
Appendix B
4. Present Value (LO4) You will receive $4,000 three years from now. The discount rate is
10 percent.
a. What is the value of your investment two years from now? Multiply $4,000 × .909
(one year’s discount rate at 10 percent).
b. What is the value of your investment one year from now? Multiply your answer to
part a by .909 (one year’s discount rate at 10 percent).
c. What is the value of your investment today? Multiply your answer to part b by .909
(one year’s discount rate at 10 percent).
d. Confirm that your answer to part c is correct by going to Appendix B (present value
of $1) for n = 3 and i = 10%. Multiply this tabular value by $4,000 and compare your
answer to part c. There may be a slight difference due to rounding.
9-4. Solution:
a. $4,000 × .909 = $3,636
5. Future value (LO2) If you invest $12,000 today, how much will you have:
a. In 6 years at 7 percent?
b. In 15 years at 12 percent?
c. In 25 years at 10 percent?
d. In 25 years at 10 percent (compounded semiannually)?
9-5. Solution:
Appendix A
FV = PV × FVIF
Chapter 09: Time Value of Money
9-5
a. $12,000 × 1.501 = $ 18,012
6. Present value (LO3) Your aunt offers you a choice of $20,000 in 50 years or $45 today.
If money is discounted at 13 percent, which should you choose?
9-6. Solution:
Appendix B
7. Present Value (LO3) Your uncle offers you a choice of $100,000 in 10 years or $45,000
today. If money is discounted at 8 percent, which should you choose?
9-7. Solution:
Appendix B
8. Present Value (LO3) In Problem 7, if you had to wait until 12 years to get the $100,000,
would your answer change? All other factors remain the same.
9-8. Solution:
Appendix B
Chapter 09: Time Value of Money
9-6
9. Present Value (LO3) You are going to receive $200,000 in 50 years. What is the
difference in present value between using a discount rate of 15 percent versus 5 percent?
9-9. Solution:
Appendix B
$200,000 $200,000
.001 (15%,50) .187 (5%,50)
$200 $17,400
The difference is $17,200
$17,400
200
$17,200
−
10. Present Value (LO3) How much would you have to invest today to receive:
a. $12,000 in 6 years at 12 percent?
b. $15,000 in 15 years at 8 percent?
c. $5,000 each year for 10 years at 8 percent?
d. $40,000 each year for 40 years at 5 percent?
9-10. Solution:
Appendix B (a and b)
PV = FV × PVIF
11. Future value (LO2) If you invest $8,000 per period for the following number of periods,
how much would you have?
Chapter 09: Time Value of Money
9-7
a. 7 years at 9 percent.
b. 40 years at 11 percent.
9-11. Solution:
Appendix C
FVA = A × FV IFA
12. Future value (LO2) You invest a single amount of $12,000 for 5 years at 10 percent. At
the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How
much will you have after 17 years?
9-12. Solution:
Appendix A
FV = PV × FVIF (5years, 10%)
13. Present value (LO3) Mrs. Crawford will receive $6,500 a year for the next 14 years from
her trust. If a 8 percent interest rate is applied, what is the current value of the future
payments?
9-13. Solution:
Appendix D
14. Present value (LO3) John Longwaite will receive $100,000 in 50 years. His friends are
very jealous of him. If the funds are discounted back at a rate of 14 percent, what is the
present value of his future “pot of gold”?
Chapter 09: Time Value of Money
9-8
9-14. Solution:
Appendix B
15. Present Value (LO3) Sherwin Williams will receive $18,000 a year for the next 25 years
as a result of a picture he has painted. If a discount rate of 10 percent is applied, should he
be willing to sell out his future rights now for $160,000?
9-15. Solution:
Appendix D
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
17. Present value (LO3) The Western Sweepstakes has just informed you that you have won
$1 million. The amount is to be paid out at the rate of $50,000 a year for the next 20 years.
With a discount rate of 12 percent, what is the present value of your winnings?
9-17. Solution:
Appendix D
Chapter 09: Time Value of Money
9-9
18. Present value (LO3) Rita Gonzales won the $60 million lottery. She is to receive
$1 million a year for the next 50 years plus an additional lump sum payment of $10 million
after 50 years. The discount rate is 10 percent. What is the current value of her winnings?
9-18. Solution:
Appendix D
PVA = A × PVIFA (10%, 50 periods)
19. Future value (LO2) Bruce Sutter invests $2,000 in a mint condition Nolan Ryan baseball
card. He expects the card to increase in value 20 percent a year for the next five years.
After that, he anticipates a 15 percent annual increase for the next three years. What is the
projected value of the card after eight years?
9-19. Solution:
Appendix A
FV = PV × FVIF (20%, 5 periods)
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.)
Chapter 09: Time Value of Money
9-10
9-20. Solution:
Appendix C
21. Future value (LO2) At a growth (interest) rate of 8 percent annually, how long will it take
for a sum to double? To triple? Select the year that is closest to the correct answer.
9-21. Solution:
Appendix A
22. Present value (LO3) If you owe $30,000 payable at the end of five years, what amount
should your creditor accept in payment immediately if she could earn 11 percent on her
money?
9-22. Solution:
Appendix B
23. Present value (LO3) Barney Smith invests in a stock that will pay dividends of $3.00 at
the end of the first year; $3.30 at the end of the second year; and $3.60 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 $50. 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.)
9-23. Solution: