Introduction to Corporate Finance

4: Valuing Bonds

4-2c SeMIANNUAL COMPOUNDING

Many bonds make two interest payments per year rather than one, and some pay even more frequently.

Adjusting our bond-pricing framework to handle, for example, semiannual interest payments is easy. A bond

paying semiannual interest has twice as many coupon payments, but each payment is half as much compared

to the bond with annual payments. If the bond matures in n years and the annual coupon equals $C, then the

bond now makes 2n payments equal to $C ÷ 2. Similarly, if the bond’s annual yield to maturity equals r, we

replace that with a semiannual yield of r ÷ 2. This produces a modified version of Equation 4.2:^4

Eq. 4.3 P

CC C

0 12

2

1

2

2

1

2

2

1

=

+









+

+









+⋅+

+

rr r

...

22

1

2

22









+

+









nn

M

r

A slightly modified version of Equation 3.7 on page 90 expresses the equation above as a sum of the

present value of an ordinary annuity and the present value of a lump sum:

Eq. 4.3a P 0 =

C

r

2

2

1

1

1+

2

2





















×−





























r

n









• 
  

• 
  









M

r

n

1

2

2

example

Peterson Fishing Pty Ltd issues a three-year bond that offers a 6% coupon rate paid semiannually. This means
that the annual coupon equals $60, and there are two $30 payments each year. Suppose that 6% per year is
also the market’s required return on Peterson bonds. The market price of the bonds equals:

=















×− =

==

=+=

PV

PV

ofcoupons

$30

0.03

1

1

(1.03)

$162.5 2

ofprincipal

$1,000

(1.03)

$837.48

Priceofbond $162.52 $837.48 $1,000

6

6

In Excel, the solution is the same as with annual payments, except that the rate and the size of the payment
are cut in half, and the number of periods doubles. To calculate the price of Peterson’s bonds in Excel, simply
type = PV(0.03,6,–30,–1,000,0).

4 The yield to maturity on a bond is typically quoted like an annual percentage rate. That is, the bond’s annual YTM equals the semiannual yield
times 2. This implies that the effective annual YTM is slightly above the quoted YTM.

finance in practice

HOW MUCH HOUSE CAN YOU AFFORD?

Before they begin their home search, most

homebuyers, particularly first-time buyers, need

to estimate how expensive a home they can

afford. Many lenders require that the monthly

mortgage payment plus monthly payments for

property taxes and homeowner insurance cannot

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