Principles of Corporate Finance_ 12th Edition

52 Part One Value

bre44380_ch03_046-075.indd 52 09/30/15 12:47 PM

A change in interest rates has only a modest impact on the value of near-term cash flows

but a much greater impact on the value of distant cash flows. Thus the price of long-term

bonds is affected more by changing interest rates than the price of short-term bonds. For

example, compare the two curves in Figure 3.2. The brown line shows how the price of the

three-year 4.25% bond varies with the interest rate. The blue line shows how the price of a

30-year 4.25% bond varies. You can see that the 30-year bond is much more sensitive to inter-

est rate fluctuations than the three-year note.

Duration and Volatility

Changes in interest rates have a greater impact on the prices of long-term bonds than on

those of short-term bonds. But what do we mean by “long-term” and “short-term”? A coupon

bond that matures in year 30 makes payments in each of years 1 through 30. It’s misleading

to describe the bond as a 30-year bond; the average time to each cash payment is less than

30 years.

the months following the issue, the financial crisis reached its peak. Lehman Brothers filed for

bankruptcy with assets of $691 billion, and the government poured money into rescuing Fannie

Mae, Freddie Mac, AIG, and a host of banks. As investors rushed to the safety of Treasury

bonds, prices soared. By mid-December the price of the 4.375s of 2038 had reached 138.05%

of face value and the yield had fallen to 2.5%. Anyone fortunate enough to have bought the

bond at the issue price would have made a capital gain of $1,380.50 − $963.80 = $416.70. In

addition, on August 15 the bond made its first coupon payment of $21.875 (this is the semian-

nual payment on the 4.375% coupon bond with a face value of $1,000). Our lucky investor

would therefore have earned a seven-month rate of return of 45.5%:

Rate of return =

coupon income + price change

__________________________

investment

=

$21.875 + 416.70

_______________

$963.80

= .455, or 45.5%

Suddenly, government bonds did not seem quite so boring as before.

● ● ● ● ●

Table 3.2 calculates the prices of two seven-year bonds. We assume annual coupon payments

and a yield to maturity of 4% per year. Take a look at the time pattern of each bond’s cash

payments and review how the prices are calculated:

Which of these two bonds is the longer-term investment? They both have the same final

maturity, of course. But the timing of the bonds’ cash payments is not the same. In the case of

the 3s, the average time to each cash flow is longer, because a higher proportion of the cash

flows occurs at maturity, when the face value is paid off.

Suppose now that the yield to maturity on each bond falls to 3%. Which bond would you

most like to own? The 3s, of course. Since they have the longer effective maturity, they should

benefit most from a fall in yields. Table 3.3 confirms that this is indeed the case:

The 9s have the shorter average maturity, and therefore a shift in interest rates has a more

muted effect on the price. That much is clear. However, it would be useful to have a precise

EXAMPLE 3.2^ ●^ Which Is the Longer-Term Bond?

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Try It! Figure 3.2:

How changes in

interest rates

affect long- and

short-term bonds