Fundamentals of Financial Management (Concise 6th Edition)

210 Part 3 Financial Assets

calculated in Section 7-3. This higher value occurs because each interest payment

is received somewhat faster under semiannual compounding.

Alternatively, when we know the price of a semiannual bond, we can easily

back out the bond’s nominal yield to maturity. In the previous example, if you

were told that a 15-year bond with a 10% semiannual coupon was selling for

$1,523.26, you could solve for the bond’s periodic interest rate as follows:

N I/YR PV PMT FV

50 1000

= 2.5

30 –1,523.26

Output:

Inputs:

In this case, enter N = 30, PV = $1523.26, PMT = 50, and FV = 1000; then press the

I/YR key to obtain the interest rate per semiannual period, 2.5%. Multiplying by 2,

we calculate the bond’s nominal yield to maturity to be 5%.^11

SEL

F^ TEST Describe how the annual payment bond valuation formula is changed to

evaluate semiannual coupon bonds and write the revised formula.

Hartwell Corporation’s bonds have a 20-year maturity, an 8% semiannual

coupon, and a face value of $1,000. The going interest rate (rd) is 7% based on

semiannual compounding. What is the bond’s price? ($1,106.78)

(^11) We can use a similar process to calculate the nominal yield to call for a semiannual bond. The only di! erence
would be that N should represent the number of semiannual periods until the bond is callable and FV should be
the bond’s call price rather than its par value.
(^12) An immediate increase in rates from 10% to 15% would be quite unusual, and it would occur only if something
quite bad were revealed about the company or happened in the economy. Smaller but still signi" cant rate
increases that adversely a! ect bondholders do occur fairly often.
(^13) You would have an accounting (and tax) loss only if you sold the bond; if you held it to maturity, you would not
have such a loss. However, even if you did not sell, you would still have su! ered a real economic loss in an
opportunity cost sense because you would have lost the opportunity to invest at 15% and would be stuck with a
10% bond in a 15% market. In an economic sense, “paper losses” are just as bad as realized accounting losses.
7-7 ASSESSING A BOND’S RISKINESS
In this section, we identify and explain the two key factors that impact a bond’s
riskiness. Once those factors are identi! ed, we differentiate between them and
discuss how you can minimize these risks.
7-7a Interest Rate Risk
As we saw in Chapter 6, interest rates " uctuate over time and when they rise, the
value of outstanding bonds decline. This risk of a decline in bond values due to an
increase in interest rates is called interest rate risk (or interest rate price risk). To
illustrate, refer back to Allied’s bonds; assume once more that they have a 10%
annual coupon; and assume that you bought one of these bonds at its par value,
$1,000. Shortly after your purchase, the going interest rate rises from 10 to 15%.^12
As we saw in Section 7-3, this interest rate increase would cause the bond’s price
to fall from $1,000 to $707.63; so you would have a loss of $292.37 on the bond.^13
Since interest rates can and do rise, rising rates cause losses to bondholders; people
or! rms who invest in bonds are exposed to risk from increasing interest rates.
Interest Rate (Price)
Risk
The risk of a decline in a
bond’s price due to an
increase in interest rates.
Interest Rate (Price)
Risk
The risk of a decline in a
bond’s price due to an
increase in interest rates.