Discounted cash flow methods

Rate of return and payback period calculations, described in the previous subsections, provide a good starting point for appraising an investment, but they ignore what is often termed the time value of money.

If you were offered the choice of accepting £100 now or in one year’s time, you would almost certainly take the money now to spend and enjoy the proceeds or perhaps invest and earn some interest. In contrast, if the choice were between £100 now and £200 in a year’s time you might well decide that it is better to wait and get the higher sum – assuming that you are confident the offer will still stand in a year and that you don’t have an urgent need for the money now. But if the choice were between £100 now and £110 or maybe £120 in a year’s time, the situation is less clear-cut.

Organisations have to take decisions like this one all the time and one way of making the decision is to look at the interest rate that could be earned on the money. Suppose that the interest rate on a savings account offered by a reliable and trustworthy bank is 3%.

Investing the £100 for one year would give

If the £103 is reinvested for a further year the result would be

You may recognise this processing as compounding. Calculating compound interest has the following general formula

where

P = the initial amount invested (the principal)

r = the percentage interest rate

n = the number of years.

Or in financial language you can say that if the interest rate is 3% the future value of £100 in one year is £103 and in two years is approximately £106, and so on.

The converse of this is known as the present value (PV) and, rearranging the above formula, the present value of £P in n years’ time is given by

Table 3 shows the present value of £1 receivable at the end of each year for periods ranging from 0 to 30 years and interest rates ranging from 0 to 10%. If you have access to a spreadsheet package, you might find it interesting to recreate this table yourself.

The principles of discounted cash flow (DCF) allow possible investments to be reviewed by using the table of present values (Table 3), or discount factors as they are also known, to determine the time in a project’s life when payments are made and when income is earned. The term discount rates is used rather than interest rates. You can think of the discount rate as being the rate of return or profit that a project will make. In general you can assume that a project will not go ahead if investing in it, which carries some risk, is estimated to give a lower rate of return than investing the money in a secure bank account.

The use of discounted cash flow is best illustrated by means of a worked example, as demonstrated in Activity 7.

In principle all DCF calculations can be performed in this way, but it can get long-winded for projects with long lifetimes, such as a reservoir or road. If it is clear that a cash flow will occur over a long period, it is possible to sum the discount factors and multiply this sum by the cash flow.

Table 6 shows the present value of £1 received annually for different time periods.