Principles of Corporate Finance_ 12th Edition

62 Part One Value

bre44380_ch03_046-075.indd 62 09/30/15 12:47 PM

The formula for converting nominal cash flows in a future period t to real cash flows today is

Real cash flow at date t = _______________________nominal cash flow at date t

(1 + inflation rate)t

For example, suppose you invest in a 20-year Treasury strip, but inflation over the 20 years

averages 6% per year. The strip pays $1,000 in year 20, but the real value of that payoff is only

1,000/1.06^20 =  $311.80. In this example, the purchasing power of $1 today declines to just

over $.31 after 20 years.

These examples show you how to get from nominal to real cash flows. The journey from

nominal to real interest rates is similar. When a bond dealer says that your bond yields 10%,

she is quoting a nominal interest rate. That rate tells you how rapidly your money will grow,

say over one year:

However, with an expected inflation rate of 6%, you are only 3.774% better off at the end

of the year than at the start:

Thus, we could say, “The bond offers a 10% nominal rate of return,” or “It offers a 3.774%

expected real rate of return.”

The formula for calculating the real rate of return is:

1 + rreal = (1 + rnominal)/(1 + inflation rate)

In our example, 1  + rreal  =  1.10/1.06  =  1.03774. A common rule of thumb states that

rreal = rnominal − inflation rate. In our example this gives rreal = .10 − .06 = .04, or 4%. This is

not a bad approximation to the true real interest rate of 3.774%. But when inflation is high, it

pays to use the full formula.

Indexed Bonds and the Real Rate of Interest

Most bonds are like our U.S. Treasury bonds; they promise you a fixed nominal rate of inter-

est. The real interest rate that you receive is uncertain and depends on inflation. If the infla-

tion rate turns out to be higher than you expected, the real return on your bonds will be lower.

You can nail down a real return, however. You do so by buying an indexed bond that makes

cash payments linked to inflation. Indexed bonds have been around in many other countries

for decades, but they were almost unknown in the United States until 1997, when the U.S.

Treasury began to issue inflation-indexed bonds known as TIPS (Treasury Inflation-Protected

Securities).^11

Invest Current Dollars Receive Dollars in Year 1 Result

$1,000 → $1,100 10% nominal rate of return

Invest Current Dollars

Expected Real Value

of Dollars in Year 1 Result

$1,000 → $1,037.74 (=1,100/1.06) 3.774% expected real

rate of return

(^11) Indexed bonds were not completely unknown in the United States before 1997. For example, in 1780 American Revolutionary
soldiers were compensated with indexed bonds that paid the value of “five bushels of corn, 68 pounds and four-seventh parts of a
pound of beef, ten pounds of sheep’s wool, and sixteen pounds of sole leather.”