Introduction to Corporate Finance

4: Valuing Bonds

Inflation and Interest rates

One of the main factors causing interest rate movements is inflation, which is a rise in the prices of

goods and services. When investors buy financial assets, they expect these investments to provide a

return that exceeds the inflation rate. This is important, because people want a better standard of living

from saving and investing their money. If asset returns only keep up with inflation, then investors are not

better off for investing their funds. To illustrate, say you want to expand your DVD collection. You have

$150 to spend, and each DVD costs $15, so you can purchase 10 new DVDs. Or suppose you save your

money and invest it in an asset earning a 10% return. You reason that after one year, you will have $165

($150 × 1.10), and with that you can buy 11 DVDs rather than 10. But imagine that, while your money

is invested, the price of DVDs increases by 10%, from $15 to $16.50. Thus, at the end of the year, your

$165 enables you to purchase just 10 DVDs – exactly what you could have purchased a year earlier. In

real terms, you are no better off at the end of the year than you were at the start.

The lesson is that bond yields must offer investors a positive real return. The real return on an investment

plus the inflation rate approximately equals the stated or nominal return. Mathematically, if r equals the nominal

interest rate, i equals the inflation rate, and rreal equals the real rate, the nominal interest rate formula is:

Eq. 4.4

rir

ririr

real

real real

(1+=)( 1 ++)(1 )

=+ +×

Notice that the last term in the previous equation is the product of the inflation rate and the real

interest rate. When both of these rates are relatively low, their product is very small, so we often ignore

that term and simply express the nominal interest rate as (approximately) the sum of the inflation rate

and the real interest rate:

Eq. 4.4a r ≈ i + rreal

In the DVD example, the nominal rate of return on your investment is 10%, but so is the inflation

rate, so the investment’s real return is zero. To earn a positive real return, the nominal return on the

investment would need to be greater than 10%.

example

The approximation in Equation 4.4 is relatively accurate
as long as neither the real rate nor the inflation rate is
very high. For example, in the second quarter of 2014,
the nominal interest rate on government bonds in Spain
was about 2.75%, and the rate of inflation averaged
about 0.25%. Plug these values into Equation 4.4 and
solve for the real interest rate:

(1 + 0.0275) = (1 + 0.0025)(1 + rreal)
rreal = 0.0249 or 2.49%

This is almost exactly equal to the approximate
value for the real rate obtained from Equation 4.4a:

0.0275 = 0.0025+ rreal
rreal = 0.0250 or 2.50%
Now consider the situation in India, where the
inflation rate stood around 6.5% on average in 2014.
Suppose an investment in India offered a nominal

return of 9%, so the approximate real return from

Equation 4.4a would be 2.50%, the same real return

offered on Spanish bonds at the time:

0.09 = 0.0650+ rreal

rreal = 0.0250 or 2.50%

However, if we use Equation 4.4 to find the

exact value of the real interest rate, we find that the

approximation in Equation 4.4a overstates the real

rate by more than two-thirds of a percentage point:

(1 + 0.09) = (1 + 0.065)(1 + rreal)

rreal = 0.0235 or 2.35%

In most cases, Equation 4.4a provides a

reasonably close approximation for the real rate

of return, but be aware that the quality of that

approximation declines as the inflation rate or the

real interest rate rises.

real return

The inflation-adjusted return;

approximately equal to

the difference between an

investment’s stated or nominal

return and the inflation rate

nominal return

The stated return offered by

an investment; includes the

real return plus any additional

return due to expected inflation