Question

Company A issued a 5 year 4.5% coupon bond with a stated value (par) of $12,000,000 on September 30, 2019 when the market rate of interest (yield to maturity) was 3.75%. The bond pays interest semiannually.

1. What is the price of the bond?

2. Now assume the above bond was settled (purchased) on 12/31/2019.

a. What is the cash (dirty) price of the bond?

b. What is the ask (quote or clean) price of the bond?

Answer 1

The answer may be minor differences due to the rounding of the PV factor.

Part

Coupon rate per semiannual (4.5%/2)	2.250%
Market rate per semiannual (3.75%/2)	1.875%
Number of semiannual period (5*2)	10
Cash Interest Paid (12000000*2.250%)	$                270,000
Present value of interest (270000*9.04161693)	$             2,441,237
Present value of principal (12000000*0.83046968)	$             9,965,636
Price of the bond	$          12,406,873

Period	PV factor @ 1.875%
1	0.98159509
2	0.96352892
3	0.94579526
4	0.92838799
5	0.91130109
6	0.89452868
7	0.87806496
8	0.86190426
9	0.84604099
10	0.83046968
Total	9.04161693

Part 2

Price of the bond	$          12,406,873
Face value of bond	$          12,000,000
Premium on bond payable	$                406,873

Interest payment (Credit Cash) = Face value of bond * Coupon rate = $270,000
Interest Expense (Debit Interest Expense) = book value of Bond for previous period * 1.875%
Amortization of bond premium (Debit Bond Premium) = Interest payment - Interest Expense
Credit Balance in Bond premium = Credit Balance in Bond premium for previous period - Amortization of bond premium
Credit Balance in Bond Payable = Face value of bond
Book value of Bond = Credit Balance in Bond premium + Credit Balance in Bond Payable
Bond Premium Amortization Table
Credit Balance in Bond premium at end of retirement of bond payable must be Zero.
Period	Date	Interest payment (Cash paid) @ 6%	Interest Expense @ 1.875%	Amortization of bond premium	Credit Balance in Bond premium	Credit Balance in Bond Payable	Book (carrying) value of Bond
0	Sep 30, 2019				$        406,873	$        12,000,000	$        12,406,873
1	Mar 31, 2020	$        270,000	$        232,629	$        37,371	$        369,502	$        12,000,000	$        12,369,502
2	Sep 30, 2020	$        270,000	$        231,928	$        38,072	$        331,430	$        12,000,000	$        12,331,430
3	Mar 31, 2021	$        270,000	$        231,214	$        38,786	$        292,644	$        12,000,000	$        12,292,644
4	Sep 30, 2021	$        270,000	$        230,487	$        39,513	$        253,131	$        12,000,000	$        12,253,131
5	Mar 31, 2022	$        270,000	$        229,746	$        40,254	$        212,877	$        12,000,000	$        12,212,877
6	Sep 30, 2022	$        270,000	$        228,991	$        41,009	$        171,869	$        12,000,000	$        12,171,869
7	Mar 31, 2023	$        270,000	$        228,223	$        41,777	$        130,091	$        12,000,000	$        12,130,091
8	Sep 30, 2023	$        270,000	$        227,439	$        42,561	$          87,531	$        12,000,000	$        12,087,531
9	Mar 31, 2024	$        270,000	$        226,641	$        43,359	$          44,172	$        12,000,000	$        12,044,172
10	Sep 30, 2024	$        270,000	$        225,828	$        44,172	$                     0	$        12,000,000	$        12,000,000

Bond was settled (purchased) on 12/31/2019.
1 Oct 2019 to 31, Dec 2019	3 Months
Accrued interest payable for three months (12000000*4.50%*3/12)	$                135,000
Premium on bond payable as of Sep 30, 2019	$                406,873
Less: Amortization of premium for 3 months (37371/2)	$                   18,686
Premium on bond payable as of Dec 31, 2019	$                388,187
Face value of bond	$          12,000,000
Add: Premium on bond payable as of Dec 31, 2019	$                388,187
Ask (quote or clean) price of the bond	$          12,388,187
Ask (quote or clean) price of the bond	$          12,388,187
Add: Accrued interest payable for three months	$                135,000
Cash (dirty) price of the bond	$          12,523,187