APPENDIX G
Time Value of Money
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE G-1
(a) Interest = p X i X n
I = $6,000 X .05 X 12 years
(b) Future value factor for 12 periods at 5% is 1.79586 (from Table 1)
(1) Case A 5% 3 periods (2) Case A 3% 8 periods
Case B 6% 8 periods Case B 4% 12 periods
BRIEF EXERCISE G-3
FV = p X FV of 1 factor
BRIEF EXERCISE G-5
FV = p X FV of 1 factor + (p X FV of an annuity factor)
= ($8,000 X 2.40662) + ($1,000 X 28.13238)
BRIEF EXERCISE G-6
FV = p X FV of 1 factor
BRIEF EXERCISE G-7
(a) (b)
(1) 12% 7 periods
(2) 10% 20 periods
BRIEF EXERCISE G-8
(a) i = 10%
?
$25,000
0 1 2 3 4 5 6 7 8 9
BRIEF EXERCISE G-8 (Continued)
(b) i = 9%
? $25,000 $25,000 $25,000 $25,000 $25,000 $25,000
0 1 2 3 4 5 6
BRIEF EXERCISE G-9
i = 8%
? $900,000
0 1 2 3 4 5 6
BRIEF EXERCISE G-10
i = 6%
?
$450,000
0 1 2 3 4 5 6 7 8
BRIEF EXERCISE G-11
i = 8%
? $40,000 $40,000 $40,000 $40,000 $40,000 $40,000
0 1 2 3 4 14 15
BRIEF EXERCISE G-12
i = 5%
? $80,000 $80,000 $80,000 $80,000 $80,000 $80,000
0 1 2 3 4 5 6
BRIEF EXERCISE G-13
i = 5%
? $400,000
Diagram
for
Principal
0 1 2 3 4 19 20
i = 5%
? $22,000 $22,000 $22,000 $22,000 $22,000 $22,000
Diagram
for
Interest
0 1 2 3 4 19 20
BRIEF EXERCISE G-14
The bonds will sell at a discount (for less than $400,000). This may be proven
as follows:
Present value of principal to be received at maturity:
$400,000 X .31180 (PV of $1 due in 20 periods
at 6% from Table 3) …………………………………………………….. $124,720*
BRIEF EXERCISE G-15
i = 6%
? $75,000
Diagram
for
Principal
Diagram
for
0 1 2 3 4 5 6
i = 6%
BRIEF EXERCISE G-16
i = 4%
? $2,500,000
Diagram
for
Principal
0 1 2 3 4 14 15 16
i = 4%
? $75,000 $75,000 $75,000 $75,000 $75,000 $75,000 $75,000
Diagram
for
Interest
0 1 2 3 4 14 15 16
BRIEF EXERCISE G-17
i = 5%
? $48,850 $48,850 $48,850 $48,850 $48,850 $48,850
0 1 2 3 4 9 10
BRIEF EXERCISE G-18
i = ?
$4,765.50 $12,000
0 1 2 3 4 11 12
BRIEF EXERCISE G-19
i = 11%
$36,125 $75,000
n = ?
BRIEF EXERCISE G-20
i = ?
? $1,200 $1,200 $1,200 $1,200 $1,200 $1,200 $1,200 $1,200
0 1 2 3 4 5 6 14 15
$10,271.38
BRIEF EXERCISE G-21
i = 9%
$1,300 $1,300 $1,300 $1,300 $1,300 $1,300
$7,793.83 n = ?
BRIEF EXERCISE G-22
i = 9%
?
$2,700
$2,700
$2,700
$2,700
$2,700
$2,700
$2,700
0
1
2
3
4
5
6
7
BRIEF EXERCISE G-23
i = 11%
?
$25,000
$30,000
$40,000
0
1
2
3
Year 3 ($40,000 X .73119) =
To determine the present value of the future cash flows, discount the future
cash flows at 11%, using Table 3.
BRIEF EXERCISE G-24
10*
?
–18,000
0
50,000
N
I/YR.
PV
PMT
FV
10.76%
10
?
42,000
–6,500
0
N
I/YR.
PV
PMT
FV
8.85%
BRIEF EXERCISE G-26
40
?
178,000*
–8,400
0
N
I/YR.
PV
PMT
FV
(semiannual)
BRIEF EXERCISE G-27
(a)
Inputs:
7
7.35
?
16,000
0
Answer:
(b)
Inputs:
10
10.65
?
16,000**
200,000*
Answer:
BRIEF EXERCISE G-28
(a)
Note—set payments at 12 per year.
Inputs:
96
7.8
42,000
?
0
N
I
PV
PMT
FV
Answer:
–589.48
(b)
Inputs:
7.25
Answer: