### INTRODUCTION

To illustrate how inflation should be handled in Investment Appraisal we shall take a simple example, under two different scenarios – an environment with no inflation and an environment where inflation is present:

**No Inflation**– suppose you are considering the purchase of a television for RWF1,000. I am undertaking a simple one-year project and I require RWF1,000. I approach you and guarantee you a return of 5% on your investment. Your investment will have grown to RWF1,050 at the end of the year and, in theory, because there has been no inflation the price of the television should still be RWF1,000. Thus, you have made RWF50 in the process and also got your television. Therefore, you have achieved aof 5%.__real return__**Inflation (assume 20% per annum)**– using the same example as number 1. If you had given me the RWF1,000 this would be worth RWF1,050 at the end of the year but the price of the television would probably have risen to RWF1,200 (+20%) because of inflation, so you would not be able to afford it. The value of your savings has been eroded because of inflation – you have got a return of 5% in money terms but inflation has been running at 20%. Therefore, you have not got a__real__of 5% – this is only a__return__. In this instance, with inflation of 20% you would require a nominal (money) return of 26% in order to obtain a real return of 5%.__nominal (or money) return__

Obviously, there is a link between the nominal (or money) rate of return (**26%**), the real rate of return (**5%**) and the rate of inflation (**20%**). This relationship may be expressed as follows:

#### (1 + Nominal Rate) (1 + Real Rate) = ————————– (1 + Inflation Rate)

Using the figures in the above example:

** 1.26 **

#### ——- = 1.05

##### 1.20

** **

If you have any two variables you can find the third. For example, if you require a real return of 5% from an investment and you estimate inflation to be 20% you can work out the required nominal return at 26% as follows:

** (1 + Real Rate) x (1 + Inflation Rate) = (1 + Nominal Rate) (1.05) x (1.20) = (1.26) **

** **

### REAL v NOMINAL (MONEY) DISCOUNT RATES

Now that you know the difference between a real and a nominal rate of return (or discount rate) which rate should be used in discounting the cash flows of a project? This really depends on how the **cash flows** are expressed. They can be stated either as:

**Real Cash Flows**– stated in today‟s prices and**exclude**any allowance for inflation.**Nominal/Money Cash Flows**– these**include**an allowance for inflation and are stated in the actual RWF‟s receivable/payable.

As a very simple illustration, an examination question might state (amongst other things)

….”materials for the project cost RWF10 per unit in terms of today‟s prices. Inflation is expected to run at the rate of 10% per annum and the project will last for three years.”

The rules for handling inflation are quite straightforward:

If the cash flows are expressed in **real terms** (today‟s money), use the **real** **discount** rate.

If the cash flows are expressed in **money terms** (the actual number of RWF that will be received/paid on the various future dates), use the **nominal/money discount rate. **

No matter which approach is used you should get the same result.

So which approach should be used? In most cases it is probably best to inflate the cash flows to money cash flows and then discount at the money required rate of return. Among the reasons for suggesting this are:

Different inflation rates may apply to different variables. For example, raw materials may inflate at 5% per annum, labour at 3% per annum etc. Thus, in converting a money rate to a real rate, which inflation rate do you divide by – 5% or 3%?

When converting a money rate to a real rate you often end up with fractions. For example, where the money rate of return is 15% and inflation is expected to be 5% per annum, this translates to a real rate of 9.52%. This rate may be difficult to handle as Discount Tables tend to be produced for whole numbers only.

When taxation is included in the appraisal capital allowances are based on **original**, rather than replacement cost and do not change in line with changing prices. Therefore, if the cash flows are left in terms of present day prices and discounted at the real discount rate it would understate the company‟s tax liability.

### HANDLING DIFFERENT INFLATION RATES

Where different inputs inflate at different rates the best approach is to inflate each element by the appropriate inflation rate and then to discount the net cash flows (which are now in money terms) by the money rate of return.

### GENERAL CONSIDERATIONS – INFLATION

**Planning**– more difficult**Project Appraisal**– another complication**Interest Rates**– higher nominal rates**Capital**– additional capital required**Borrowings**– extra borrowings => increased financial risk for shareholders **Nature of Borrowings**– long v short; fixed v floating; foreign borrowings?**Selling Prices**– can increase in costs be passed on?**Impact on Customers**– delayed payment; bad debts; liquidations etc.