Capital Budgeting - Real Vs Nominal Interest Rates

Real Vs
Nominal
Interest Rates

Inflation affects both cash flows and the discount rate.
If inflation is ignored, the project’s Net Present Value (NPV)
may be either overstated or understated.
To handle inflation properly, you must match the type of
cash flows with the correct discount rate.
Inflation in Capital Budgeting

Suppose a person—we call him Jose, deposits Rs. 100 in the State Bank of India for
one year at 10 per cent rate of interest.
This means that the bank agrees to return Rs. 110 to Jose after a year, irrespective of
how much goods or services this money can buy for him.
The sum of Rs. 110 is stated in nominal terms—the impact of inflation not separated.
Thus, 10 per cent is a nominal rate of return on Jose’s investment.
Let us assume that the rate of inflation is expected to be 7 per cent next year.
What does the rate of inflation imply? It means that prices prevailing today will rise by
7 per cent next year.
In other words, a 7 per cent rate of inflation implies that what can be bought for Re 1
now can be bought for Rs.1.07 next year.
We can thus say that the purchasing power of Rs.1.07 next year is the same as that of
Rs.1.00 today.
What is the purchasing power of Rs.110 received next year?
It is `110/1.07 = `102.80; that is, the `110 received next year can buy goods worth
`102.80 now.
Concept

The `110 next year and `102.80 today are equivalent in terms of the purchasing power if
the rate of inflation is 7 per cent.
The Rs.110 is expressed in nominal terms since they have not been adjusted for the effect
of inflation.
On the other hand, the Rs.102.80 are in real terms since they have been adjusted for the
effect of inflation.
Our investor, Jose, thus earns, 10 per cent nominal rate of return, but only 2.8 per cent real
rate of return.
It should be noted that the rate of inflation is an expected rate; therefore, the real rate of
return is also expected.
The actual rate of inflation may be different from the expected rate.
The opportunity cost of capital of a firm or project is generally market determined and is
based on expected future returns.
It is, therefore, usually expressed in nominal terms and reflects the expected rate of
inflation.
The opportunity cost of capital or the discount rate is a combination of the real rate (say,
K) and the expected inflation rate (let us call it, alpha). This relationship, long ago
recognised in the economic theory, is called the Fisher’s effect.

If a firm expects a 10 per cent real rate of return from an investment project under
consideration and the expected inflation rate is 7 per cent, the nominal required rate of
return on the project would be:
k=( In practice, it is customary to add the real rate and the expected inflation rate to
obtain the nominal required rate of return: k = K + a.
Nominal discount rate can be used to derive the real rate of return (K):
It may be stated as follows:

Suppose a firm is considering a project with the following cash flows,
on the assumption that prices and costs increase at the same rate,
the firm follows the practice of stating cash flows at the prices of
period zero.
Example

This means that cash flows are expressed in real terms. The firm’s opportunity cost of
capital, which is market determined and is expressed in nominal terms, is 14 per cent.
Can the project’s real cash flows be discounted at the 14% nominal rate of discount?
Clearly the answer is no! It would be inconsistent to discount the real cash flows of the
project by the nominal discount rate. If we do so, the NVP of the project, as calculated
below, will be biased:
The project shows a negative NPV and, therefore, would be rejected. But a bias has
entered into the analysis. The cash flows are in real terms while the discount rate is in
nominal terms. For a correct analysis, two alternatives are available:
 either the cash flows should be converted into nominal terms and then
discounted at the nominal required rate of return or
 the discount rate should be converted into real terms and used to
discount the real cash flows.

Let us assume that in our example
the rate of inflation is expected to be
7 per cent. Thus, the cash flows in
nominal terms will be:
Alternatively, we can find out the real
discount rate and discount the cash flows
without converting them into nominal
terms. The real discount rate
will be:

Notice that the results under both alternatives are same. The project’s NPV is positive,
so accept it. Always remember: Discount nominal cash flows at nominal discount rate;
or discount real cash flows at real discount rate. The NPV formula can be written as
follows when cash flows and discount rates are expressed in nominal terms:
where K is the real discount rate, α is the expected inflation rate and Ct is the series of
real cash flows, using Equation (5) in the example, we get:

Thus it is obvious that when the expected inflation rate is
properly reflected in the cash flow estimates and the discount
rate, the resulting NPV is stated both in real and nominal terms,7
and it is free of inflation bias.
Since the inflation factor in the numerator and denominator
of Equation (15) is same, the formula becomes:

Two Types of Values
Type Description Includes Inflation?
Nominal (or Money)
values
Actual rupees expected
to be received/spent in
the future
❌ No
Real values
Expressed in today’s
purchasing power
(adjusted for inflation)
✅ Yes

Two Types of Discount Rates
Type Formula Used With
Nominal Discount Rate (i)
Reflects both real return
and inflation
Nominal Cash Flows
Real Discount Rate (r)
Reflects only the real rate
of return (excluding
inflation)
Real Cash Flows

Brigham, Eugene F. & Ehrhardt, Michael C. –
Financial Management: Theory and Practice
Reference

Capital Budgeting - Real Vs Nominal Interest Rates

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