Question

On June 30, 2018, Singleton Computers issued 8% stated rate bonds with a face amount of $200 million. The bonds mature on June 30, 2033 (15 years). The market rate of interest for similar bond issues was 7% (3.5% semiannual rate). Interest is paid semiannually (4.0%) on June 30 and December 31, beginning on December 31, 2018.

1. Determine the price of the bonds on June 30, 2018.
2. Calculate the interest expense Singleton reports in 2018 for these bonds using the effective interest method.

Answer 1

Answer

1. Price of the bond is $$218,392,000

2. Interest expense of 2018 is $7,643,720.00

Explanation

1.

Issue price is computed using the equation given below:

Issue price = [Annual interest × PVIFA (r, n)] + [Face value × PVIF (r, n)]

                 = [($200,000,000 × 4%) × PVIFA (3.5%, 30)] + [$200,000,000 × PVIF (3.5%, 30)]

                  = ($8,000,000 × 18.392) + ($200,000,000 × 0.35628)

                  = $147,136,000 + $71,256,000

                  = $218,392,000

Hence the issue price of the bond is $218,392,000.

2.

To determine interest expense using the effective-interest method, we may use the following table:

Period	Opening balance (A)	Interest expense (B = A * 3.5%)	Semi-Annual Payment (C)	Reduction in liability (D = C-B)	Closing Balance (E = A-D)
1	21,83,92,000.00	76,43,720.00	80,00,000.00	3,56,280.00	21,80,35,720.00
2	21,80,35,720.00	76,31,250.20	80,00,000.00	3,68,749.80	21,76,66,970.20
3	21,76,66,970.20	76,18,343.96	80,00,000.00	3,81,656.04	21,72,85,314.16
4	21,72,85,314.16	76,04,986.00	80,00,000.00	3,95,014.00	21,68,90,300.15
5	21,68,90,300.15	75,91,160.51	80,00,000.00	4,08,839.49	21,64,81,460.66
6	21,64,81,460.66	75,76,851.12	80,00,000.00	4,23,148.88	21,60,58,311.78
7	21,60,58,311.78	75,62,040.91	80,00,000.00	4,37,959.09	21,56,20,352.69
8	21,56,20,352.69	75,46,712.34	80,00,000.00	4,53,287.66	21,51,67,065.04
9	21,51,67,065.04	75,30,847.28	80,00,000.00	4,69,152.72	21,46,97,912.31
10	21,46,97,912.31	75,14,426.93	80,00,000.00	4,85,573.07	21,42,12,339.24
11	21,42,12,339.24	74,97,431.87	80,00,000.00	5,02,568.13	21,37,09,771.12
12	21,37,09,771.12	74,79,841.99	80,00,000.00	5,20,158.01	21,31,89,613.11
13	21,31,89,613.11	74,61,636.46	80,00,000.00	5,38,363.54	21,26,51,249.57
14	21,26,51,249.57	74,42,793.73	80,00,000.00	5,57,206.27	21,20,94,043.30
15	21,20,94,043.30	74,23,291.52	80,00,000.00	5,76,708.48	21,15,17,334.82
16	21,15,17,334.82	74,03,106.72	80,00,000.00	5,96,893.28	21,09,20,441.54
17	21,09,20,441.54	73,82,215.45	80,00,000.00	6,17,784.55	21,03,02,656.99
18	21,03,02,656.99	73,60,592.99	80,00,000.00	6,39,407.01	20,96,63,249.98
19	20,96,63,249.98	73,38,213.75	80,00,000.00	6,61,786.25	20,90,01,463.73
20	20,90,01,463.73	73,15,051.23	80,00,000.00	6,84,948.77	20,83,16,514.96
21	20,83,16,514.96	72,91,078.02	80,00,000.00	7,08,921.98	20,76,07,592.99
22	20,76,07,592.99	72,66,265.75	80,00,000.00	7,33,734.25	20,68,73,858.74
23	20,68,73,858.74	72,40,585.06	80,00,000.00	7,59,414.94	20,61,14,443.80
24	20,61,14,443.80	72,14,005.53	80,00,000.00	7,85,994.47	20,53,28,449.33
25	20,53,28,449.33	71,86,495.73	80,00,000.00	8,13,504.27	20,45,14,945.06
26	20,45,14,945.06	71,58,023.08	80,00,000.00	8,41,976.92	20,36,72,968.13
27	20,36,72,968.13	71,28,553.88	80,00,000.00	8,71,446.12	20,28,01,522.02
28	20,28,01,522.02	70,98,053.27	80,00,000.00	9,01,946.73	20,18,99,575.29
29	20,18,99,575.29	70,66,485.14	80,00,000.00	9,33,514.86	20,09,66,060.42
30	20,09,66,060.42	70,33,812.11	80,00,000.00	9,66,187.89	19,99,99,872.54

Hence, the interest expense of 2018 is $7,643,720.00