The simple truths from the tables
Although made redundant by spreadsheet functions or the use of appropriate formulae, traditional tables are informative with regard to the effect of time and rates. Table 11.2 gives the factors for compounding an amount invested today - time 0. The longer the money is invested the higher the factor, but the increase is not linear, because interest is earned on the interest earned - hence the term 'compounding'. It is the effect of charging interest on interest as well as on the original capital.
Table 11.2 shows what an amount invested now (time zero) will be worth at a time in the future, assuming a constant annual rate. This is the basic compound interest table and the arithmetic of this underlies all the other tables and representations of the 'time value of money'.
Table 11.2 also clearly shows that the higher the rate and the longer the term of investment the better the 'project'. It also makes a point ignored or misunderstood by many investors, that a small decrease in rate of return will have a significant effect on terminal values. For example, a rate falling
TABLE 11.2 The factors for compounding an amount invested today - time 0
TABLE 11.3 Discount factors
from 5 to 4 per cent decreases the 50-year terminal value from 11.47 to 7.11, a fall in the terminal value of 38 per cent.
The discount factors shown in Table 11.3 are those used in typical cash flow discounting. These factors are simply the inverse of those found in Table 11.2 - the one base table!
What the factors reveal is that with commonly demanded rates of 10 per cent plus, inflows after 5 and certainly after 10 years have a low impact on present values. A simple truth is that for many investments or projects, if they do not work in 10 years they never will, or more likely the risks of waiting for the long-term cash inflows will be too high. The truth of the arithmetic gives the lie to the fact that governments believe that the private sector will assume risks in long-term projects - they would be foolish to do so. Table 11.2 also points to an answer to the often asked question 'Over what period should we appraise?' - the answer is 10 years or in fact possibly just 5. If a project does not 'work' in 5 years, it never will!
The table also affirms the point that banks will not lend for general business activities (projects) over periods in excess of 7 or 10 years - the further away the repayments the lower their worth today and the higher the risk.
Table 11.2, the base table, can be restructured to present annual worths or values, effectively the average annual payment required to repay a loan or mortgage at the rate and number of years specified (Table 11.4).
TABLE 11.4 Annual worths or values
A point to note is that over a sufficiently long period (20 years plus), the interest rate is the significant element - the repayment of the original capital is insignificant. This does not mean that you can borrow as much as you like - you still have to pay the interest on the capital borrowed!
