Question

On January 1, Brothers Corporation issues $10,000,000 of 6%, 15 year bonds, with interest paid semi-annually. The market rate of interest is 8%.

Before we calculate the price, let’s answer a few basis questions which will be important in determining the price.

1. What is the face amount of the bond offering?

2. What will the actual semi-annual interest payment be?

3. What interest rate is used to compute the present value? Face interest rate or market rate?

4. How many interest periods will there be in this bond offering?

5. Based upon the facts provided, will these bonds be sold at a “discount”, “par” or “premium”?

Hint: Look at the interest rate relationship. This will help you anticipate your answer!

Calculate the issue price and bond proceeds of the bond using the present value method? As you should recall from the notes, text and videos, the present value (price) of a bond is based upon the present value of the repayment of the bond in the future and the present value of the future interest payments. Show your work!

Answer 1

Coupon rate per period (6%/2)	3.00%
Face value of bond	$        10,000,000
Market rate per period (8%/2)	4.00%
Interest paid (10000000*3%)	$              300,000
Interest paid on	Semi annually
Number of period (15*2)	30
Market rate is used to compute the present value
Bond will be sold at discount.	a discount
Coupoun rate of 3% per semiannual period is less than the market rate of 4% .

Final answer:

Market rate per period used for PV factor.
Market rate per period		4.00%
Period	PV factor	PVA factor
1	0.96154	0.96154
2	0.92456	1.88609
3	0.88900	2.77509
4	0.85480	3.62990
5	0.82193	4.45182
6	0.79031	5.24214
7	0.75992	6.00205
8	0.73069	6.73274
9	0.70259	7.43533
10	0.67556	8.11090
11	0.64958	8.76048
12	0.62460	9.38507
13	0.60057	9.98565
14	0.57748	10.56312
15	0.55526	11.11839
16	0.53391	11.65230
17	0.51337	12.16567
18	0.49363	12.65930
19	0.47464	13.13394
20	0.45639	13.59033
21	0.43883	14.02916
22	0.42196	14.45112
23	0.40573	14.85684
24	0.39012	15.24696
25	0.37512	15.62208
26	0.36069	15.98277
27	0.34682	16.32959
28	0.33348	16.66306
29	0.32065	16.98371
30	0.30832	17.29203

	Amount	Multiply: PV factor	Present value
Face value	$        10,000,000	0.30832	$    3,083,200
Interest paid	$              300,000	17.29203	$    5,187,609
Issue price of bonds (Total of above)			$    8,270,809
Less: face value of Bond			$ 10,000,000
Discount on Bond payable			$    1,729,191

Answer might be minor different due to rounding of PV factor.