CHAPTER 6
SOLUTIONS TO B EXERCISES
E6-1B (5–10 minutes)
Rate of Interest
Number of Periods
1.
a.
8%
8
c.
5%
6%
c.
4%
E6-2B (5–10 minutes)
(a)
Simple interest of $800 per year X 10 ………………………
$ 8,000
Principal ………………………………………………………………..
10,000
Total withdrawn ……………………………………………..
$18,000
1 @ 8% for 10 periods …………………………………….
value of 1 @ 4% for 20 periods …………………………..
2.19112
E6-3B (10–15 minutes)
(a)
(b)
(c)
(d)
E6-4B (15–20 minutes)
(a)
Future value of an ordinary
annuity of $12,000 a period
(b)
periods at 8%
$84,433.35
($7,500 X 11.25778)
Factor (1 + .08)
X 1.08
due of $7,500 for 30 periods
at 8%
(Or see Table 6-5 which
Present value of an ordinary
annuity of $7,500 for 30
gives $91,188.08)
(c)
for 15 periods at 8%
($6,000 X 27.15211)
Factor (1 + .08)
Future value of an ordinary
annuity of $6,000 a period
for 15 periods at 8%
(d)
Present value of an ordinary
annuity of $3,000 for 6
periods at 10%
$13,065.78
($3,000 X 4.35526)
Factor (1 + .10)
X 1.10
Present value of an annuity
date of $3,000 for 6 periods
at 10%
$14,372.36
(Or see Table 6-5)
E6-5B (10–15 minutes)
(a)
$50,000 X 5.33493 = $266,746.50.
E6-6B (15–20 minutes)
(a)
Future value of $20,000 @ 5% for 20 years
($20,000 X 2.65330) = …………………………………..
$ 53,066.00
(b)
Future value of an ordinary annuity of
($2,000,000 X 13.18079) ………………………………..
(c)
$80,000 discounted at 6% for 10 years:
Accept the cash bonus of $50,000.
E6-7B (12–17 minutes)
(a)
$500,000 X .21455
=
$107,275.00
+ $50,000 X 9.81815
=
490,907.50
$598,182.50
(b)
$500,000 X .14864
=
=
425,678.00
$499,998.00
(c)
$500,000 X .10367
=
+ $50,000 X 7.46944
=
373,472.00
$425,307.00
E6-8B (10–15 minutes)
(a)
3.16986
(b)
Fund balance at June 30, 2017
Future amount of ordinary annuity at 10%
E6-9B (10 minutes)
The 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:
(a) The number of interest periods is calculated by first dividing the future
value of $2,000,000 by $184,592, which is 10.83471—the value $1 would
(b) The unknown interest rate is calculated by first dividing the future value
of $2,000,000 by the present investment of $365,392, which is 5.47357—
E6-11B (10–15 minutes)
(a) Total payments – Amount owed today = Total interest
$488,235.90 (10 X $48,823.59) – $300,000 = $188,235.90
E6-12B (10–15 minutes)
Building A—PV = $1,500,000.
Building B—
Building C—
Rent X (PV of ordinary annuity of 25 periods at 8%) = PV
$21,000 X 10.67478 = PV
$224,170.38 = PV
E6-13B (15–20 minutes)
Time diagram: Loyd Inc.
PV = ? i = 4%
PV – OA = ? Principal
$5,000,000
Interest
Formula for the interest payments:
PV – OA = R (PVF – OAn, i)
Formula for the principal:
PV = FV (PVFn, i)
PV = $5,000,000 (PVF30, 4%)
E6-14B (15–20 minutes)
Time diagram: i = 8%
R =
PV – OA = ? $2,800,000 $2,800,000 $2,800,000
Formula: PV – OA = R (PVF – OAn, i)
PV – OA = $2,800,000 (PVF – OA25–15, 8%)
OR
Time diagram: i = 8%
R =
PV – OA = ? $2,800,000 $2,800,000 $2,800,000
E6-14B (Continued)
(i) Present value of the expected annual pension payments at the end of the
15th year:
PV – OA = R (PVF – OAn, i)
(ii) Present value of the expected annual pension payments at the beginning
of the current year:
PV = FV (PVF – OAn, i)
The company’s pension obligation (liability) is $5,922,800.
E6-15B (15–20 minutes)
(a) i = 4%
PV = $525,000 FV = $1,000,000
0 1 2 n = ?
(b) By setting aside $200,000 now, Lee can gradually build the fund to an
amount to establish the foundation.
PV = $200,000 FV = ?
$? $? $? FV = $746,936
0 1 2 5 6
E6-16B (10–15 minutes)
Amount to be repaid on March 1, 2023:
Time diagram:
i = 5% per 6 months
PV = $200,000 FV = ?
n = 20 6-month periods
Formula: FV = PV (FVFn, i)
Amount of annual contribution to retirement fund:
Time diagram: i = 8%
R R R R R FV – AD =
R = ? ? ? ? ? $530,660
E6-17B (10–15 minutes)
Time diagram: i = 10%
R R R
PV – OA = $250,000 ? ? ?
n = 25
Formula: PV – OA = R (PV – OAn, i)
$250,000 = R (PVF – OA25, 10%)
E6-18B (10–15 minutes)
Time diagram: i = 6%
PV – OA = ? $200,000 $200,000 $200,000 $200,000 $200,000
n = 10
Formula: PV – OA = R (PVF – OAn, i%)
The recommended method of payment would be the 10 annual payments of
$200,000, since the present value of those payments ($1,472,018) is less than
the alternative immediate cash payment of $1,500,000.
E6-19B (10–15 minutes)
Time diagram: i = 6%
PV – AD = ?
R =
$200,000 $200,000 $200,000 $200,000 $200,000
Formula:
Using Table 6-4 Using Table 6-5
PV – AD = R (PVF – OAn, i) PV – AD = R (PVF – ADn, i)
The recommended method of payment would be the immediate cash payment
E6-20B (5–10 minutes)
(a) Estimated
Cash Probability Expected
Outflow X Assessment = Cash Flow
$2,800 30% $ 840
(b) Estimated
Cash Probability Expected
Outflow X Assessment = Cash Flow
(c) Estimated
Cash Probability Expected
Outflow X Assessment = Cash Flow
E6-21B (10–15 minutes)
Estimated
Cash Probability Expected
Outflow X Assessment = Cash Flow
$ 500 10% $ 50
E6-22B (15–20 minutes)
(a) This exercise determines the present value of an ordinary annuity or
expected cash flows as a fair value estimate.
Cash flow Probability Expected
Estimate X Assessment = Cash Flow
$1,000,000 30% $ 300,000
(b) This fair value is based on unobservable inputs—Houston’s own data on
the expected future cash flows associated with the trade name. This fair
value estimate is considered Level 3.