Brief Exercise 14–1
$30,000,000 x
face
amount
6%
annual
rate
6/12
x
=
$900,000
fraction of the
annual period
cash
interest
Brief Exercise 14–2
Interest
$ 2,000,000 ¥
Principal
$80,000,000
Present value (price) of the bonds
x
x
23.11477*
0.30656**
=
=
$46,229,540
24,524,800
$70,754,340
¥ [5 ÷ 2] % x $80,000,000
* Present value of an ordinary annuity of $1: n = 40, i = 3%. (Table 4)
** Present value of $1: n = 40, i = 3%. (Table 2)
Brief Exercise 14–3
The price will be the present value of the periodic cash interest payments (face
amount times stated rate) plus the present value of the principal payable at
maturity. Both interest and principal are discounted to present value at the market
rate of interest for securities of similar risk and maturity. When the stated rate and
the market rate are the same, the bonds will sell at face value, $75 million in this
instance.
Brief Exercise 14–4
Interest
$ 2,500,000 ¥
Principal
$100,000,000
Present value (price) of the bonds
x
x
27.35548*
0.45289**
=
=
¥ [5 ÷ 2] % x $100,000,000
* Present value of an ordinary annuity of $1: n = 40, i = 2%. (Table 4)
** Present value of $1: n = 40, i = 2%. (Table 2)
$ 68,388,700
45,289,000
$113,677,700
Brief Exercise 14–5
Interest will be the effective rate times the outstanding balance:
4% x $82,218,585 = $3,288,743
Brief Exercise 14–6
Interest will be the effective rate times the outstanding balance:
June 30
Interest expense (2% x $69,033,776) ................................
Discount on bonds payable (difference) .................
Cash (1.5% x $80,000,000) .......................................
December 31
Interest expense (2% x [$69,033,776 + 180,676]) ..........
Discount on bonds payable (difference) .................
Cash (1.5% x $80,000,000).......................................
1,380,676
180,676
1,200,000
1,384,289
184,289
1,200,000
Interest expense for the year: $1,380,676 + 1,384,289 = $2,764,965
Brief Exercise 14–7
Interest will be a plug figure:
$80,000,000 – 69,033,776 = $10,966,224 discount
$10,966,224 ÷ 40 semiannual periods = $274,156 reduction each period
June 30
Interest expense (to balance) .............................................
Discount on bonds payable (difference) .................
Cash (1.5% x $80,000,000) .......................................
December 31
Interest expense (to balance) .............................................
Discount on bonds payable (difference) .................
Cash (1.5% x $80,000,000) .......................................
1,474,156
274,156
1,200,000
1,474,156
274,156
1,200,000
Interest expense for the year: $1,474,156 + 1,474,156 = $2,948,312
Brief Exercise 14–8
Interest will be the effective rate times the outstanding balance:
June 30
Cash (1.5% x $80,000,000) ..........................................
Discount on investment in bonds (difference) ...........
Interest revenue (2% x $69,033,776) ............................
1,200,000
180,676
December 31
Cash (1.5% x $80,000,000) ..........................................
Discount on investment in bonds (difference) ...........
Interest revenue (2% x [$69,033,776 + 180,676]) ......
1,200,000
184,289
1,380,676
1,384,289
Brief Exercise 14–9
Interest
$6,000¥ x 2.72325 *
Principal
$300,000 x 0.86384 **
Present value (price) of the note
=
=
$ 16,340
259,152
$275,492
¥ 2% x $300,000
* Present value of an ordinary annuity of $1: n = 3, i = 5%. (Table 4)
** Present value of $1: n = 3, i = 5%. (Table 2)
Equipment (price determined above) ................................
Discount on notes payable (difference) ..........................
Notes payable (face amount) ......................................
275,492
24,508
300,000
Brief Exercise 14–10
$300,000 ÷ 2.72325 =
amount
of loan
(from Table 4)
n = 3, i = 5%
$110,162
installment
payment
Helpful, but not required:
Cash
Payment
1
2
3
110,162
110,162
110,162
Effective
Interest
5% x Outstanding Balance
.05 (300,000) =
.05 (204,838) =
.05 (104,918) =
15,000
10,242
5,246
Decrease in Outstanding
Balance
Balance
Balance Reduction
95,162
99,920
104,918*
300,000
204,838
104,918
0
* rounded
Interest expense (5% x ($300,000 – [$110,162 – 5% x $300,000]))
Note payable (difference) ...............................................
Cash (payment determined above) .................................
10,242
99,920
110,162
EXERCISE 14–9
1. Price of the bonds at January 1, 2013
Interest
$18,000¥ x 6.87396 *
Principal
$600,000 x 0.75941 **
Present value (price) of the bonds
=
=
$123,731
455,646
$579,377
¥ 3% x $600,000
* Present value of an ordinary annuity of $1: n = 8, i = 3.5% (Table 4)
** Present value of $1: n = 8, i = 3.5% (Table 2)
2. January 1, 2013
Cash (price determined above) ...........................
Discount on bonds (difference) .......................
Bonds payable (face amount) .......................
579,377
20,623
600,000
3. Amortization schedule
Cash
Payment
3% x Face Amount
1
2
3
4
5
6
7
8
18,000
18,000
18,000
18,000
18,000
18,000
18,000
18,000
144,000
*rounded
.035
.035
.035
.035
.035
.035
.035
.035
Effective
Increase in Outstanding
Interest
Balance
Balance
3.5% x Outstanding Balance Discount Reduction
(579,377)
(581,655)
(584,013)
(586,453)
(588,979)
(591,593)
(594,299)
(597,099)
=
=
=
=
=
=
=
=
20,278
20,358
20,440
20,526
20,614
20,706
20,800
20,901*
2,278
2,358
2,440
2,526
2,614
2,706
2,800
2,901
164,623
20,623
579,377
581,655
584,013
586,453
588,979
591,593
594,299
597,099
600,000
Exercise 14–9 (concluded)
4. June 30, 2013
Interest expense (3.5% x $579,377) ....................
Discount on bonds payable (difference) ......
Cash (3% x $600,000)...................................
December 31, 2013**
Interest expense (3.5% x [$579,377 + 2,278]) ....
Discount on bonds payable (difference) ......
Cash (3% x $600,000)...................................
20,278
2,278
18,000
20,358
2,358
18,000
5. Liability at December 31, 2013
Bonds payable (face amount) .....................................
Less: discount ..........................................................
Initial balance, January 1, 2013 ...............................
June 30, 2013 discount amortization ....................
Dec. 31, 2013 discount amortization ....................
December 31, 2013 net liability ..............................
$600,000
(20,623)
$579,377
2,278
2,358
$584,013
6. Interest expense for year ended December 31, 2013
June 30, 2013 interest expense ................................
Dec. 31, 2013 interest expense ................................
Interest expense for 2013 .........................................
7. December 31, 2016
Interest expense (3.5% x $597,099) ....................
Discount on bonds payable (difference) ......
Cash (3% x $600,000)...................................
$20,278
20,358
$40,636
20,901*
2,901
18,000
* rounded value from amortization schedule
Bonds payable .....................................................
Cash ..........................................................
600,000
600,000