APPENDIX A
Time Value of Money
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE A-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)
BRIEF EXERCISE A-2
(1) Case A 5% 3 periods (2) Case A 3% 8 periods
BRIEF EXERCISE A-3
FV = p X FV of 1 factor
BRIEF EXERCISE A-4
FV of an annuity of 1 = p X FV of an annuity factor
BRIEF EXERCISE A-5
FV = p X FV of 1 factor + (p X FV of an annuity factor)
BRIEF EXERCISE A-6
FV = p X FV of 1 factor
BRIEF EXERCISE A-7
(a) (b)
(1) 12% 7 periods
(2) 10% 20 periods
BRIEF EXERCISE A-8
(a) i = 10%
?
$25,000
0 1 2 3 4 5 6 7 8 9
Discount rate from Table 3 is .42410 (9 periods at 10%). Present value
BRIEF EXERCISE A-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 A-9
i = 8%
? $900,000
0 1 2 3 4 5 6
Discount rate from Table 3 is .63017 (6 periods at 8%). Present value of
BRIEF EXERCISE A-10
i = 6%
?
$450,000
0 1 2 3 4 5 6 7 8
Discount rate from Table 3 is .62741 (8 periods at 6%). Present value of
$450,000 to be received in 8 years discounted at 6% is therefore $282,334.50
BRIEF EXERCISE A-11
i = 8%
? $40,000 $40,000 $40,000 $40,000 $40,000 $40,000
0 1 2 3 4 14 15
BRIEF EXERCISE A-12
i = 5%
? $80,000 $80,000 $80,000 $80,000 $80,000 $80,000
0 1 2 3 4 5 6
Discount rate from Table 4 is 5.07569. Present value of 6 payments of $80,000
BRIEF EXERCISE A-13
i = 5%
? $400,000
Diagram
for
Principal
0 1 2 3 4 19 20
i = 5%
Present value of principal to be received at maturity:
$400,000 X 0.37689 (PV of $1 due in 20 periods
at 5% from Table 3) …………………………………………………….. $150,756*
Present value of interest to be received periodically
BRIEF EXERCISE A-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*
Present value of interest to be received periodically
BRIEF EXERCISE A-15
i = 6%
? $75,000
Diagram
for
Principal
0 1 2 3 4 5 6
Present value of principal to be received at maturity:
$75,000 X .70496 (PV of $1 due in 6 periods
at 6% from Table 3) ……………………………………………………. $52,872.00
Present value of interest to be received annually
over the term of the note: $3,000* X 4.91732
BRIEF EXERCISE A-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
Present value of principal to be received at maturity:
$2,500,000 X 0.53391 (PV of $1 due in 16 periods
at 4% from Table 3) ……………………………………………………. $1,334,775
BRIEF EXERCISE A-17
i = 5%
? $48,850 $48,850 $48,850 $48,850 $48,850 $48,850
0 1 2 3 4 9 10
BRIEF EXERCISE A-18
i = ?
$4,765.50 $12,000
0 1 2 3 4 11 12
Present value = Future value X Present value of 1 factor
$4,765.50 = $12,000 X Present value of 1 factor
BRIEF EXERCISE A-19
i = 11%
$36,125 $75,000
n = ?
Present value = Future value X Present value of 1 factor
$36,125 = $75,000 X Present value of 1 factor
BRIEF EXERCISE A-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
The 8.55948 for 15 periods is found in the 8% column in Table 4. Joanne
Quick will therefore earn a rate of return of 8%.
BRIEF EXERCISE A-21
i = 9%
$1,300 $1,300 $1,300 $1,300 $1,300 $1,300
$7,793.83 n = ?
Present value = Future amount X Present value of an annuity factor
BRIEF EXERCISE A-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
Discount rate from Table 4 is 5.03295. Present value of 7 payments of
$2,700 each discounted at 9% is therefore $13,588.97 ($2,700 X 5.03295).
BRIEF EXERCISE A-23
i = 11%
?
$25,000
$30,000
$40,000
0
1
2
3
To determine the present value of the future cash flows, discount the future
cash flows at 11%, using Table 3.
Year 1 ($25,000 X .90090) =
$22,522.50
Year 2 ($30,000 X .81162) =
Year 3 ($40,000 X .73119) =
Present value of future cash flows
$76,118.70
To achieve a minimum rate of return of 11%, Snyder Company should pay
BRIEF EXERCISE A-24
10*
?
–18,000
0
50,000
N
I/YR.
PV
PMT
FV
BRIEF EXERCISE A-25
10
?
42,000
–6,500
0
N
I/YR.
PV
PMT
FV
BRIEF EXERCISE A-26
40
?
178,000*
–8,400
0
N
I/YR.
PV
PMT
FV
(semiannual)
10.76%
BRIEF EXERCISE A-27
(a)
Inputs:
7
7.35
?
16,000
0
N
I
PV
PMT
FV
(b)
Inputs:
10
10.65
?
16,000**
200,000*
N
I
PV
PMT
FV
Answer:
Answer:
BRIEF EXERCISE A-28
(a)
Note—set payments at 12 per year.
Inputs:
96
7.8
42,000
?
0
N
I
PV
PMT
FV
(b)
Note—set payments to 1 per year.
Inputs:
5
7.25
8,000
?
0
N
I
PV
PMT
FV
Answer:
Answer: