BRIEF EXERCISE D-2
(1) a.
b.
6%
4%
3 periods
8 periods
(2) a.
b.
5%
3%
8 periods
12 periods
BRIEF EXERCISE D-4
FV of an annuity of 1 = p X FV of an annuity factor
= $78,000 X 12.57789
= $981,075.42
BRIEF EXERCISE D-6
FV = p X FV of 1 factor
= $34,000 X 1.53862
= $52,313.08
BRIEF EXERCISE D-8
(a)
i = 10%
?
$28,000
0
1
2
3
4
5
6
7
8
9
Discount rate from Table 3 is .42410 (9 periods at 10%). Present
value
of $28,000 to be received in 9 years discounted at 10% is
therefore $11,874.80 ($28,000 X .42410).
(b)
i = 9%
?
0
$28,000 $28,000 $28,000 $28,000 $28,000 $28,000
1
2
3
4
5
6
Discount rate from Table 4 is 4.48592 (6 periods at 9%). Present
value of 6 payments of $28,000 each discounted at 9% is therefore
$125,605.76 ($28,000 X 4.48592).
BRIEF EXERCISE D-9
i = 9%
?
$750,000
0
1
2
3
4
5
Discount rate from Table 3 is .64993 (5 periods at 9%). Present value
of $750,000 to be received in 5 years discounted at 9% is therefore
$487,447.50 ($750,000 X .64993). Chaffee Company should therefore
invest $487,447.50 to have $750,000 in five years.
BRIEF EXERCISE D-11
i = 5%
?
0
$45,000 $45,000 $45,000 $45,000
1
2
3
4
$45,000 $45,000
14
15
Discount rate from Table 4 is 10.37966. Present value of 15 payments
of $45,000 each discounted at 5% is therefore $467,084.70 ($45,000 X
10.37966). Arthur Company should pay $467,084.70 for this annuity
contract.
BRIEF EXERCISE D-13
i = 4%
?
$300,000
Diagram
for
Principal
0
1
2
3
4
19
20
i = 4%
?
$13,500 $13,500 $13,500 $13,500
$13,500 $13,500
Diagram
for
Interest
0
1
2
3
4
19
20
Present value of principal to be received at maturity:
$300,000 X 0.45639 (PV of $1 due in 20 periods
at 4% from Table 3) .............................................................. $136,917.00
Present value of interest to be received periodically
over the term of the bonds: $13,500 X 13.59033
(PV of $1 due each period for 20 periods at 4%
from Table 4)......................................................................... 183,469.45
Present value of bonds ............................................................... $320,386.45
BRIEF EXERCISE D-14
The bonds will sell at a discount (for less than $300,000). This may be
proven as follows:
Present value of principal to be received at maturity:
$300,000 X .37689 (PV of $1 due in 20 periods
at 5% from Table 3) .............................................................. $113,067.00
Present value of interest to be received periodically
over the term of the bonds: $13,500 X 12.46221
(PV of $1 due each period for 20 periods at 5%
from Table 4)......................................................................... 168,239.83
Present value of bonds ............................................................... $281,306.83
BRIEF EXERCISE D-17
i = 10%
?
0
$3,300 $3,300 $3,300 $3,300 $3,300 $3,300 $3,300 $3,300
1
2
3
4
5
6
7
8
Discount rate from Table 4 is 5.33493. Present value of 8 payments of
$3,300 each discounted at 10% is therefore $17,605.27 ($3,300 X
5.33493). Mark Barton should not purchase the tire retreading machine
because the present value of the future cash flows is less than the
$18,000 purchase price of the retreading machine.
BRIEF EXERCISE D-20
i=?
$4,172.65
0
$10,000
1
2
3
4
14
15
Present value = Future value X Present value of 1 factor
$4,172.65 = $10,000 X Present value of 1 factor
Present value of 1 factor = $4,172.65 ÷ $10,000 = .41727
The .41727 for 15 periods is found in the 6% column. Colleen Mooney
will receive a 6% return.
BRIEF EXERCISE D-23
i = 11%
$1,000 $1,000 $1,000 $1,000 $1,000 $1,000
$5,146.12
n=?
Present value = Annuity amount X Present value of an annuity factor
$5,146.12= $1,000 X Present value of an annuity factor
Present value of an annuity factor = $5,146.12 ÷ $1,000 = 5.14612
The 5.14612 at an interest rate of 11% is shown in the 8-year row.
Therefore, Patty will receive 8 payments.