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.
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)?
9-3. Why does money have a time value?
Money has a time value because funds received today can be invested to reach a
9-4. Does inflation have anything to do with making a dollar today worth more than
a dollar tomorrow?
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?
( )
IF
FV PV FV Appendix A
12%, 10 3.106 Annual
6%, 20 3.207 Semiannual
i n
i n
= ´
= =
= =
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?
9-7. What is a deferred annuity?
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
Chapter 9
Problems
1. You invest $3,000 for three years at 12 percent.
a. What is the value of your investment after one year? Multiply $3,000 × 1.12.
b. What is the value of your investment after two years? Multiply your answer to part a
by 1.12.
c. What is the value of your investment after three years? Multiply your answer to part b
by 1.12. This gives your final answer.
d. Combine these three steps by using the formula
( )
1
n
FV PV i= ´ +
to find the future
value of $3,000 in 3 years at 12 percent interest.
9-1. Solution:
a.
1
(1 )
$3,000 (1.12)
$3,360
n
FV PV i
FV
FV
= ´ +
= ´
=
b.
1
(1 )
$3,360 (1.12)
$3,763.20
n
FV PV i
FV
FV
= ´ +
= ´
=
c.
1
(1 )
$3,763.20 (1.12)
$4,214.78
n
FV PV i
FV
FV
= ´ +
= ´
=
d.
3
(1 )
$3,000 (1.12)
$4, 214.78
n
FV PV i
FV
FV
= +
= ´
=
Calculator Solution:
(d)
N I/Y PV PMT FV
Solution using TVM Tables:
a. $3,000 × 1.12 = $3,360.00
2. Present value (LO9-3) What is the present value of
a. $7,900 in 10 years at 11 percent?
b. $16,600 in 5 years at 9 percent?
c. $26,000 in 14 years at 6 percent?
9.2. Solution:
a.
b.
5
1
(1 )
1
$16,600 (1.09)
$10,788.86
n
PV FV
i
PV
PV
= ´ +
= ´
=
c.
14
1
(1 )
1
$26,000 (1.06)
$11,499.82
n
PV FV
i
PV
PV
= ´ +
= ´
=
Calculator Solution:
(a)
N I/Y PV PMT FV
(b)
N I/Y PV PMT FV
(c)
N I/Y PV PMT FV
Appendix B
PV = FV × PVIF
a. $ 7,900 × .352 = $2,781
3. Present Value (LO9-3)
a. What is the present value of $140,000 to be received after 30 years with a
14 percent discount rate?
b. Would the present value of the funds in part a be enough to buy a $2,900 concert
ticket?
9.3. Solution:
(a)
1
(1 )
n
PV FV
i
= ´ +
30
1
$140, 000 1.14
PV = ´
Calculator Solution:
(a)
N I/Y PV PMT FV
Appendix B
PV = FV × PVIF (14%, 30 periods)
4. Present Value (LO9-4) you will receive $6,800 three years from now. The discount rate is
10 percent.
a. What is the value of your investment two years from now? Multiply $6,800 by
1
1.10
æ ö
ç ÷
è ø
or divide by 1.10 (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
1
1.10
æ ö
ç ÷
è ø
.
c. What is the value of your investment today? Multiply the part b answer by
1
1.10
æ ö
ç ÷
è ø
.
d. Use the formula
1
(1 )
n
PV FV
i
= ´ +
to find the present value of $6,800 received
three years from now at 10 percent interest.
9-4. Solution:
a.
1
1
(1 )
1
$6,800 (1.10)
$6,181.82
n
PV FV
i
PV
PV
= ´ +
= ´
=
b.
1
1
(1 )
1
$6,181.82 (1.1)
$5,619.83
n
PV FV
i
PV
PV
= ´ +
= ´
=
c.
1
1
(1 )
1
$5,619.83 (1.1)
$5,108.94
n
PV FV
i
PV
PV
= ´ +
= ´
=
d.
3
1
(1 )
1
$6,800 (1.1)
$5,108.94
n
PV FV
i
PV
PV
= ´ +
= ´
=
Calculator Solution:
(d)
N I/Y PV PMT FV
Solution using TVM Tables:
a. $6,800 × .909 = $6,181.20
5. If you invest $9,000 today, how much will you have
a. In 2 years at 9 percent?
b. In 7 years at 12 percent?
c. In 25 years at 14 percent?
d. In 25 years at 14 percent (compounded semiannually)?
9-5. Solution:
a.
2
(1 )
$9,000 (1.09)
$10,692.90
n
FV PV i
FV
FV
= ´ +
= ´
=
b.
2
(1 )
$9,000 (1.12)
$19,896.13
n
FV PV i
FV
FV
= ´ +
= ´
=
c.
25
(1 )
$9,000 (1.14)
$235,157.24
n
FV PV i
FV
FV
= ´ +
= ´
=
d.
50
(1 )
$9,000 (1.07)
$265,113.23
n
FV PV i
FV
FV
= ´ +
= ´
=
Calculator Solution:
(a)
N I/Y PV PMT FV
(b)
N I/Y PV PMT FV
Answer: $19,896.13
(c)
N I/Y PV PMT FV
(d)
N I/Y PV PMT FV
Appendix A
FV = PV × FVIF
a. $9,000 × 1.188 = $ 10,692
b. $9,000 × 2.211 = $ 19,899
6. Present value (LO9-3) Your aunt offers you a choice of $20,100 in 20 years or $870 today.
If money is discounted at 17 percent, which should you choose?
9-6. Solution:
20
1
(1 )
1
$20,100 (1.17)
$869.92
n
PV FV
i
PV
PV
= ´ +
= ´
=
Take the $870 today instead of $20,100 in 20 years.
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Calculator Solution:
N I/Y PV PMT FV
Appendix B
7. Present Value (LO9-3) Your uncle offers you a choice of $105,000 in 10 years or $47,000
today. If money is discounted at 9 percent, which should you choose?