Question

The selling price for a bond with a $1,000 par value and a 9 percent annual coupon rate is $1,100. It will mature in 14 years, and annual coupon payments are made at the end of each year. Present annual yields on similar bonds are 10 percent. Please answer or calculate the following questions:

1.   Are the bonds selling at par value, discount or premium? Explain

2.   Are the bonds selling in the primary or secondary market? Explain

3.   Mention two reason why a corporate or government issue bonds

4.   Calculate the bond yield to maturity. Show procedure.

5.   Determine the price of the bond given the required rate of return. Show procedure.

6.   Would you buy the bond? Explain

Answer 1

1. Because theprice is higher than the par value, the bond is selling at a premium and not at the par value. Had the price been 1000, then it would have been selling at par.

2. Bonds are selling in the secondary market, when the bonds are issued for the first time by the company then the bonds sells in the primary market. After that when the bonds are resold between investors, they are sold in the secondary market.

3. Bonds are issued to raise debt capital because interest rate is tax deductible. So the issuers would like to benefit from the the tax shield. Further, at times, the cost of raising debt in the market is lower than raising capital vial bank loan, so this is another reason why issuers raise debt capital.

4.   YTM is the rate at which the sum of PV of the cashflows equal the price.

YTM can be calculated using either a financial calculator or excel or through hit and trial:

Using Excel we get the YTM = 7.80% rounded to two decimal places

Year	CF	Discount Factor	Discounted CF
1	$       90.00	1/(1+0.0780101893426601)^1=	0.927635017	0.927635016705892*90=	$       83.49
2	$       90.00	1/(1+0.0780101893426601)^2=	0.860506724	0.86050672421894*90=	$       77.45
3	$       90.00	1/(1+0.0780101893426601)^3=	0.798236169	0.798236169496369*90=	$       71.84
4	$       90.00	1/(1+0.0780101893426601)^4=	0.740471822	0.740471822426011*90=	$       66.64
5	$       90.00	1/(1+0.0780101893426601)^5=	0.686887591	0.686887591366395*90=	$       61.82
6	$       90.00	1/(1+0.0780101893426601)^6=	0.637180982	0.637180982292235*90=	$       57.35
7	$       90.00	1/(1+0.0780101893426601)^7=	0.591071391	0.591071391153334*90=	$       53.20
8	$       90.00	1/(1+0.0780101893426601)^8=	0.54829852	0.548298519806898*90=	$       49.35
9	$       90.00	1/(1+0.0780101893426601)^9=	0.508620907	0.508620906580887*90=	$       45.78
10	$       90.00	1/(1+0.0780101893426601)^10=	0.471814563	0.471814563173127*90=	$       42.46
11	$       90.00	1/(1+0.0780101893426601)^11=	0.43767171	0.437671710191187*90=	$       39.39
12	$       90.00	1/(1+0.0780101893426601)^12=	0.405999604	0.405999604194898*90=	$       36.54
13	$       90.00	1/(1+0.0780101893426601)^13=	0.37661945	0.376619449619919*90=	$       33.90
14	$ 1,090.00	1/(1+0.0780101893426601)^14=	0.349365389	0.349365389439938*1090=	$     380.81
				Price= Sum of all Discounted CF	$ 1,100.00

Using Financial calculator, the YTM can be calculated through the following input. N=14, PV = -1100, PMT = 90, FV = 1000, CPT i/y

5.   Determine the price of the bond given the required rate of return. Show procedure.

If discount rate is 10% the price is calculated as follows:

Year	CF	Discount Factor	Discounted CF
1	$       90.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*90=	$   81.82
2	$       90.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*90=	$   74.38
3	$       90.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*90=	$   67.62
4	$       90.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*90=	$   61.47
5	$       90.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*90=	$   55.88
6	$       90.00	1/(1+0.1)^6=	0.56447393	0.564473930053777*90=	$   50.80
7	$       90.00	1/(1+0.1)^7=	0.513158118	0.513158118230706*90=	$   46.18
8	$       90.00	1/(1+0.1)^8=	0.46650738	0.466507380209733*90=	$   41.99
9	$       90.00	1/(1+0.1)^9=	0.424097618	0.424097618372485*90=	$   38.17
10	$       90.00	1/(1+0.1)^10=	0.385543289	0.385543289429531*90=	$   34.70
11	$       90.00	1/(1+0.1)^11=	0.350493899	0.350493899481392*90=	$   31.54
12	$       90.00	1/(1+0.1)^12=	0.318630818	0.318630817710357*90=	$   28.68
13	$       90.00	1/(1+0.1)^13=	0.28966438	0.289664379736688*90=	$   26.07
14	$ 1,090.00	1/(1+0.1)^14=	0.263331254	0.26333125430608*1090=	$ 287.03
				Price= Sum of all Discounted CF	$ 926.33

6.   The bond should not be bought, because it is over valued.

At the given YTM of 10% its value should be  $926.33, however the current market price is 1100 so buying it wont be profitable.