**Nominal vs. Real Rates of Returns**

**How should the rate of inflation be taken into account in the capital budgeting decisions?**

We should be consistent in treating inflation. Since the discount rate is market determined, and it is therefore stated in nominal terms; then the cash flows should also be expressed in nominal terms. In other words, cash flows should reflect effect of inflation, when they are discounted by the inflation affect of inflation, when they are discounted by the inflation affected discount rate. We shall elaborate this point in the following section.

Suppose a person-we call him john, deposit 100$ in the HSBC bank for one year at 10% rate of interest. This means that the bank agrees to return 110$ to john after a year, irrespective of how much goods or services this money can buy for him. The sum of 110$ is stated in nominal terms-the impact of inflation not separated. Thus, 10% is a nominal rate of return on john’s investment. Let us assume that the rate of inflation is expected to be 7% next year. What does the rate of inflation imply? It means that prices prevailing today will rise by 7% next year. In other words, a 7% rate of inflation implies that what can be bought for 1$ now can be bought for 1.07$ next year. We can thus say that the purchasing power of 1.07$ next year is the same as that of 1$ today. What is the purchasing power of 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. The 110$ next year and 102.80$ today are equivalent in terms of the purchasing power if then rate of inflation is 7%. The 110$ is expressed in nominal terms since they have not been adjusted for the effect of inflation. On the other hand, the 102.80$ are in real terms since they have been adjusted for the effect of inflation. Our investor, john, thus earns, 10% nominal rate of return, but only 2.8% 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 recognized in the economic theory, is called the Fisher’s effect. It may be stated as follows:

**Nominal discount rate = (1 + Real discount rate) X (1 + Inflation rate) – 1**

**K = (1 + K)(1 + Alpha) – 1**

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