Principles of Corporate Finance_ 12th Edition

64 Part One Value

bre44380_ch03_046-075.indd 64 09/30/15 12:47 PM

This is Fisher’s theory: A change in the expected inflation rate causes the same proportion-

ate change in the nominal interest rate; it has no effect on the required real interest rate. The

formula relating the nominal interest rate and expected inflation is

1 + rnominal = (1 + rreal) (1 + i)

where rreal is the real interest rate that consumers require and i is the expected inflation rate.

In our example, the prospect of inflation causes 1 + rnominal to rise to 1.03 × 1.05 = 1.0815.

Not all economists would agree with Fisher that the real rate of interest is unaffected by

the inflation rate. For example, if changes in prices are associated with changes in the level of

industrial activity, then in inflationary conditions I might want more or less than 103 apples in

a year’s time to compensate me for the loss of 100 today.

We wish we could show you the past behavior of interest rates and expected inflation.

Instead we have done the next best thing and plotted in Figure 3.8 the return on Treasury bills

(short-term government debt) against actual inflation for the United States, U.K., and Ger-

many. Notice that since 1953 the return on Treasury bills has generally been a little above the

rate of inflation. Investors in each country earned an average real return of between 1% and

2% during this period.

Look now at the relationship between the rate of inflation and the Treasury bill rate. Fig-

ure 3.8 shows that investors have for the most part demanded a higher rate of interest when

inflation was high. So it looks as if Fisher’s theory provides a useful rule of thumb for finan-

cial managers. If the expected inflation rate changes, it is a good bet that there will be a cor-

responding change in the interest rate. In other words, a strategy of rolling over short-term

investments affords some protection against uncertain inflation.

◗ FIGURE 3.7

The green line shows the real

yield on long-term TIPS issued

by the U.S. government. The

brown line shows the yield on

long-term nominal bonds.

1

2

3

4

5

6

Interest rat

e, %

22

21

0

10-year real interest rate

10-year nominal interest rate

Jan-03July-

03

Jan-04July-

04

Jan-05July-

05

Jan-06July-

06

Jan-07July-

07

Jan-08July-

08

Jan-09July-

09

Jan-10July-10Jan-11July-11Jan-12July-12Jan-13July-13Jan-14July-14

3-6 The Risk of Default

Corporate Bonds and Default Risk

Look at Table 3.6, which shows the yields to maturity on a sample of corporate bonds. Notice

that the bonds all mature in 2017, but their yields to maturity differ dramatically. With a yield

of over 20%, the bonds of Alpha Natural Resources appeared to offer a mouth-watering rate

of return. However, the company had been operating at a loss and had substantial debts. Inves-

tors foresaw that there was a good chance that the company would go bankrupt and that they

would not get their money back. Thus the payments promised to the bondholders represent a