# The time value of money and required rates

## What is meant by 'rate'?

The arithmetic of appraisal requires the use of a 'rate', conventionally expressed as a percentage and used in discounting cash flows. The rate should be called the discount rate as the exercise is one of using the arithmetic of discounting future cash flows at the given discount rate to express the cash flows in comparable terms - today's £s, \$s or other currencies.

## What (discount) rate should be used?

The rate used for discounting purposes is a fundamental element of all appraisal exercises. In practice, for the majority of cases, those appraising the investment or capex proposal simply have to follow the company process and use the set company corporate discount rate. The rate of return demanded often seems high, thus it can frustrate plans for investment. Investment is killed off by demanding too high a rate, and there is much evidence, especially in the United Kingdom, that there has been a history of demanding high rates of return, with the result that there has been a lower level of investment in capital equipment and tangible assets in comparison with the rest of the world.

But there is also the point that demonstrably successful companies in the United States and the United Kingdom are those that progress by demanding high rates of return from investment. They hold to demanding high rates (in comparison with the prevailing nominal money market rates) and deliver good returns to shareholders which, if retained and not paid out as dividends, lead to further high return on investment. Before outlining the matters to consider when selecting an appropriate rate for a particular business or project, it is important to consider other uses and meanings of the word 'rate':

- Interest rate. This is the rate normally associated with the cost of borrowing, typically a bank loan. The rate may be fixed or variable over the life or term of the loan.

- Discount rate. This is the rate used for the exercise of discounting - it could be the interest rate as above if, say, the investment was funded entirely by a bank loan, but is more likely to be derived from an entity's cost of capital.

- Cost of capital (rate). In its simplest form this is the weighted average cost of capital (funding) of a business and an example is given below. The average, weighted rate requires a knowledge of the cost of borrowing and cost of equity or shareholders' funds. The cost of borrowing or loans will normally be quite clear - defined loan interest rates. The cost of equity may be more difficult to determine, but often markets will give an indication of what is expected.

- Hurdle rate. A rate chosen to ration the amount of cash expended in a specified period. The rate should obviously be higher than a business's cost of capital or borrowing rates. The rate can be increased if too many

projects meet a given hurdle rate. The rate thus has little to do with the cost of money to the business concerned or in a particular economy.

- Real rate. This is the hypothetical or theoretical cost of money, excluding any compensation for the eroding effects of inflation.

- Nominal rate. This is the cost of money, which includes an allowance for the effect of inflation and currency or other risks - it is the rate which would normally have to be paid to banks.

- Required rate. This is the preferred term when using rates for the arithmetic of appraisals. The use of the word 'required' implies that while this rate must be met, its source also needs to be defined.

The example below demonstrates the principles.

CASE EXAMPLE Determining the weighted average cost of capital (WACC)

A business has 100,000 capital invested and employed and is funded 75 per cent by equity (share capital and retained profits) and 25 per cent by borrowings (loans). In this example the cost of equity has been set at a rate of 16 per cent and there is only one rate for the loan capital-8 per cent. There would more likely be a portfolio of loans and an average cost of loan capital would have to be calculated.

The weighted averaging exercise yields a WACC of 14 per cent (Table 11.5). Logic dictates that if the capital employed in the business can yield a minimum of 14 per cent return, both the lenders and the equity investors will have their demanded returns met.

TABLE 11.5 Calculating weighted average cost of capital

There are, of course, many issues to consider, for example the effects of taxation, changes in interest rates and the effects of inflation or deflation. The simple arithmetic and thus logic of the WACC calculation will hold true. One obvious aspect of the model is that should borrowing increase relevant to equity (higher leverage or gearing), there will be a lower WACC (Table 11.6).

TABLE 11.6 Calculating weighted average cost of capital higher leverage or gearing

This would permit investments that do not or cannot make such high returns; however, it is more likely that investors will look for high-return projects, resulting in the investors receiving even higher returns - their returns having been 'geared up'(Table 11.7).

TABLE 11.7 Calculating the equity return from a highly leveraged investment

If the investment yields 14 per cent, and hopefully better, the effect is that equity investors will gain an effective return of 32 per cent. Having an optimum level of gearing is obviously important-the arithmetic points to as near 100 per cent as is possible! What is an appropriate level of leverage or gearing is a subject about which there are many diverse views, and these are covered in more detail in Chapter 12 on capital structure.