The factor 10.83471 or its approximate is then located in the “Future value of 1” table by reading down the 10% column to the 25period line; thus, 25 is the unknown number of years Jafr
Trang 1SOLUTIONS TO B EXERCISES
E61B (5–10 minutes)
E62B (5–10 minutes)
Principal 10,000
(b) Interest compounded annually—Future value of
X
$10,000 Total withdrawn $21,589.20
(c) Interest compounded semiannually—Future
X $10,000 Total withdrawn $21,911.20
Trang 2(a) $14,000 X 1.33823 = $18,735.22
(b) $14,000 X .46651 = $6,531.14
(c) $14,000 X 27.15211 = $380,129.54
(d) $14,000 X 7.46944 = $104,572.16
E64B (15–20 minutes)
(a) Future value of an ordinary
annuity of $12,000 a period
Future value of an annuity
(b) Present value of an ordinary
annuity of $7,500 for 30
Present value of annuity
due of $7,500 for 30 periods
gives $91,188.08) (c) Future value of an ordinary
annuity of $6,000 a period
Future value of an annuity
due of $6,000 a period
(d) Present value of an ordinary
Trang 3at 10% $14,372.36 (Or see Table 65)
E65B (10–15 minutes)
(a) $50,000 X 5.33493 = $266,746.50.
(b) $50,000 X 8.85137 = $442,568.50.
(c) ($50,000 X 3.16986 X .56447 = $89,464.54.
or (6.14457 – 4.35526) X $50,000 = $89,465.50 (difference of $0.96 due
to rounding).
E66B (15–20 minutes)
(a) Future value of $20,000 @ 5% for 20 years
(b) Future value of an ordinary annuity of
$2,000,000 at 6% for 10 years
(c) $80,000 discounted at 6% for 10 years:
Accept the cash bonus of $50,000.
Trang 4(a) $500,000 X .21455 = $107,275.00
+ $50,000 X 9.81815 = 490,907.50
$598,182.50
+ $50,000 X 8.51356 = 425,678.00
$499,998.00
The answer should be $500,000; the above computation is off by $2 due
to rounding.
+ $50,000 X 7.46944 = 373,472.00
$425,307.00
E68B (10–15 minutes)
(a) Present value of an ordinary annuity of 1
(b) Fund balance at June 30, 2017 Future amount of ordinary annuity at 10% $190,191.60 = $40,980.74 4.64100 for 4 years
Amount of each of four contributions is $40,980.74
Trang 5The rate of interest is determined by dividing the future value by the present value and then find the factor in the FVF table with n = 2 that approximate that number:
E610B (10–15 minutes)
value of $2,000,000 by $184,592, which is 10.83471—the value $1 would accumulate to at 10% for the unknown number of interest periods. The factor 10.83471 or its approximate is then located in the “Future value of 1” table by reading down the 10% column to the 25period line; thus, 25
is the unknown number of years Jafri must wait to for his two million.
of $2,000,000 by the present investment of $365,392, which is 5.47357— the amount $1 would accumulate to in 15 years at an unknown interest rate. The factor or its approximate is then located in the “Future value of 1” table by reading across the 15period line to the 12% column; thus, 12% is the interest rate Jones must earn for her investment to gow to two million.
Trang 6(a) Total payments – Amount owed today = Total interest
$488,235.90 (10 X $48,823.59) – $300,000 = $188,235.90
manufacturer’s 10% rate determined below.
= 6.14557—Inspection of the 10period row reveals a rate
of 10%.
E612B (10–15 minutes)
Building A—PV = $1,500,000.
Building B—
Rent X (PV of annuity due of 25 periods at 8%) = PV
$125,000 X 11.52876 = PV
$1,441,095.00 = PV
Building C—
Rent X (PV of ordinary annuity of 25 periods at 8%) = PV
$21,000 X 10.67478 = PV
$224,170.38 = PV
Answer: Lease Building B since the present value of its net cost is the
smallest.
Trang 7Time diagram:
Loyd Inc.
$5,000,000
0 1 2 3 28 29 30
n = 30 Formula for the interest payments:
PV – OA = $275,000 (17.29203)
PV – OA = $4,755,308.25
Formula for the principal:
PV = FV (PVF n, i )
PV = $5,000,000 (0.30832)
PV = $1,541,600
The selling price of the bonds = $4,755,308.25 + $1,541,600 = $6,296,908.25.
Trang 8i = 8%
R =
0 1 2 15 16 24 25
n = 15 n = 10
PV – OA = $2,800,000 (10.67478 – 8.55948)
PV – OA = $2,800,000 (2.11530)
PV – OA = $5,922,840
OR
Time diagram:
i = 8%
R =
0 1 2 15 16 24 25
Trang 9(i) Present value of the expected annual pension payments at the end of the
15 th year:
PV – OA = $2,800,000 (6.71008)
PV – OA = $18,788,224
(ii) Present value of the expected annual pension payments at the beginning
of the current year:
PV = $18,788,224 (0.31524)
PV = $5,922,800*
*$40 difference due to rounding.
The company’s pension obligation (liability) is $5,922,800.
Trang 10i = 4%
0 1 2 n = ?
FVF( n, 4% ) = $1,000,000 ÷ $525,000
= 1.9048 reading down the 4% column, 1.9048 corresponds to approximately
16 ½ years.
amount to establish the foundation.
0 1 2 5 6
= $200,000 (1.26532)
= $253,064—Thus, the amount needed from the annuity:
$1,000,000 – $253,064 = $746,936.
$? $? $? FV = $746,936
0 1 2 5 6
Trang 11Amount to be repaid on March 1, 2023:
Time diagram:
i = 5% per 6 months
3/1/13 3/1/14 3/1/15 3/1/21 3/1/21 3/1/23
n = 20 6month periods
FV = $200,000 (2.65330)
FV = $530,660
Amount of annual contribution to retirement fund:
Time diagram:
i = 8%
R R R R R FV – AD =
R = ? ? ? ? ? $530,660
3/1/18 3/1/19 3/1/20 3/1/21 3/1/22 3/1/23
Trang 12i = 10%
R R R
PV – OA = $250,000 ? ? ?
0 1 24 25
n = 25
$250,000 = R (9.07704)
R = $27,542.02 E618B (10–15 minutes)
Time diagram:
i = 6%
PV – OA = ? $200,000 $200,000 $200,000 $200,000 $200,000
0 1 2 8 9 10
n = 10
Trang 13$200,000, since the present value of those payments ($1,472,018) is less than the alternative immediate cash payment of $1,500,000.
Trang 14i = 6%
PV – AD = ?
R =
$200,000 $200,000 $200,000 $200,000 $200,000
0 1 2 8 9 10
n = 10 Formula:
The recommended method of payment would be the immediate cash payment
of $1,500,000, since that amount is less than the present value of the 10 annual payments of $200,000 ($1,560,338).
Trang 15Outflow X
$3,950
Outflow X
$5,650
Outflow X
$2,300
Trang 16
Factor,
E622B (15–20 minutes)
expected cash flows as a fair value estimate.
Estimate X
Factor,
n = 6, I = 4% Present Value
$ 1,520,000 X 5.24214 $ 7,968,053
The fair value estimate of the trade name is less than the carrying value; thus, an impairment is recorded.
the expected future cash flows associated with the trade name. This fair