Question

Your broker faxed to you the following information about two annual coupon bonds that you are considering as a potential investment.​ Unfortunately, your fax machine is blurring some of the​ items, and all you can read from the fax on the two different bonds is the​ following. Fill in the missing data from the information that the broker sent.

What is the price of the IBM coupon bond?

Features   IBM Coupon Bond   AOL Coupon Bond
Face value (Par)   1,000   5,000
Coupon Rate   8.5%  
Yield to maturity   7.5%   9.5%
Years to maturity   15   20
Price       4,339.07

Answer 1

Price of IBM coupon bond:

Bond value is arrived at calculating sum of the present value of all the cash flows from a bond which is periodic coupon payment plus the principal at maturity.

Formula is:

—п F 1-(1+r) Воnd Price 3D С* (1+r)" r

C = periodic coupon payment in dollar terms;
r = rate of interest in market which is nothing but YTM (Yield to maturity);
n = no of years (or periods in case of more than 1 coupon payments during a year);
F = Future value to be received at maturity

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Now since the question is not clear about the coupon payment frequency we will consider annual as well as semi-annual both:

1) Annual coupon payments:

Details provided:

IBM
Face Value	$1,000
Coupon Rate	8.50%
YTM	7.50%
Years to Maturity	15 Years
Coupon Frequency	Annual
Coupon amount	$85

Coupon amount = Face Value * Coupon %

Below tables gives details as per formula:

F	1,000
YTM	0.075
n	15
C	85
Price	-1,088.27

When you input above values in the bond price formula you will get price of $ -1,088.27

As you see, this is an investment hence the value is negative depicting the outflow in order to purchase the bond.

Alternatively you can use excel function- PV - to calculate this:

=PV(rate,nper,pmt,fv)

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2) Semi-annual coupon payments:

Details provided:

IBM
Face Value	$1,000
Coupon Rate	8.50%
YTM	7.50%
Years to Maturity	15 Years
Coupon Frequency	Annual
Coupon amount	$85

Below tables gives details as per formula:

F	1,000
YTM	0.0375
n	30
C	42.5
Price	-1,089.15

When you input above values in the bond price formula you will get price of $ -1,089.15

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Coupon rate on this security (8.5%) is higher than the market rate of 7.5% which reflects in the price of security when compared with the par value. Since it is offering higher coupon, it is trading at a premium.