Present and Future Values
Article Index
Present and Future Values
Net Present Value NPV
Irregular time periods
Regular cashflows
Key points

The principles of present and future value apply even if the cash flow is irregular. The calculations are just a matter of breaking down the cashflow calculations into simple steps,

### Now available as a print book

The draft chapters are still available on the website

# Financial Functions ### Now available as a print book

The draft chapters are still available on the website

Spreadsheets take the hard work out of calculations, but you still need to know how to do them. Financial Functions with a spreadsheet is all about understanding and reasoning, using a spreadsheet to do the actual calculation.

1. Understanding Percentages
Percentages are something familiar to us all - but they present many pitfalls that need to be avoided.

2. Interest Simple and Compound
We explore the idea of borrowing money for a specified rate of interest or earning interest on an investment. The ideas of Present and Future Value PV and FV are introduced.

3. Effective Interest Rates
We explore the idea of the `effective’ annual interest rate and then on to the Effective Interest Rate/Annual Percentage Rate, the much quoted EIR or APR.

4. Introduction to Cashflow - Savings Plans
In the first of three chapters covering the way in which interest rate affects cashflow we explore savings - but first we introduce some general ideas that apply equally to annuities and repayment loans.

5. Cashflow Continued - Annuities
We move on to annuities in the second of three chapters devoted to exploring the way in which interest rate affects

6. Exploring Repayment Loans
Repayment loans are the subject of the last of three chapters which look at the effects of regular cashflows.

7. Present and Future Values
The principles of present and future value apply even if the cash flow is irregular. The calculations are just a matter of breaking down the cash flow calculations into simple steps.

8. Investment Analysis
How is it possible to evaluate investments that generate irregular cashflows? We explore how NPV can be used to make investment decisions.

9. Advanced Investment Analysis IRR and MIRR
The IRR is perhaps the most complicated of the measures of the value of an investment with an irregular cash flow. Understanding exactly what it means is a good step toward making correct use of it.

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## Chapter Seven

In earlier chapters we have examined how money behaves under some particularly simple situations - a single deposit or loan accruing interest and the effect of a regular cashflow on the same.

In real life cashflows are often irregular both in time and in amount. This makes it difficult to evaluate the worth of an investment or the cost of a loan that involves irregular payments. However all is not lost because there are a range of methods that can be used to compare such investments and loans.

In this and the next chapter we examine the ideas of the present and future value of money and see how these ideas can be used to make judgements about the worth of an investment.

## The time value of money

The most important thing to realise when evaluating an investment is that money now is worth more than money in the future - even if you ignore the action of inflation.

The reason is that money that you have now can be invested and can earn a safe rate of interest. If you are deprived of a sum of money until a later date then you have to take into account the loss of interest. You can think of this as an opportunity cost of not having the money.

If the prevailing ‘no risk’ interest rate is I% then \$PV will grow to \$FV given by:

` FV = PV*(1+I)^n`

in n time periods.

The present value grows into the future value by the action of compound interest. This relationship can be turned the other way about and we can say that the future value can be discounted back to its equivalent present value.

This relationship between Future Value and Present Value is fundamental to the measurement of the time value of money.

If you are to receive a sum of money in the future then what ever it is worth then it is only worth the equivalent present value now.

That is, all Future Values should be reduced to their corresponding Present Values before their worth can be assessed using:

`PV=FV/(1+I)^n`

You can think of this as reducing future sums of money by a discount factor of 1/(1+I)^n to allow for the effect of interest.

For example, if you are to receive \$100 in 5 years time, i.e. FV=500 and n=5*12, the Present Value is:

` PV=500/(1+0.08/12)^(5*12)=355.60`

So if you were offered \$500 in 5 years time or \$355.60 now there would be no reason to prefer one or the other on purely financial grounds.

It is in this sense that the present value and the future value represent the same amount of wealth - one will become the other by the action of time and interest.

## The safe interest rate

Of course the equivalence of FV and PV does depend on the interest rate that you choose to use in the formula and this adds a degree of arbitrariness into the comparison.

In practice you should use an interest rate that makes the comparison meaningful to you. For example, there is no point in using an interest rate that is not accessible to you or to the sum of money under consideration.

So using a high rate that can only be obtained by large deposits isn’t reasonable in most cases, neither is a high risk rate. You should in general choose an interest rate that is readily obtainable and regarded as a safe investment.

There is another problem in that safe interest rates may vary over the period of the calculation and so alter the present value. However factors that alter the ‘safe’ interest rate also tend to affect the return on every type of investment and so the alter the future value in the same way as the present value!

As a result the present value still provides an excellent way of comparing different investment opportunities.

## Interest rates and inflation

The effect of inflation on interest rates and investments is a very general concern and it could be discussed in almost any chapter of this book. However it is particularly relevant to a discussion of the time value of money.

If we are discounting future cash amounts to allow for the ‘natural’ growth in money due to the availability of a safe interest rate, then why not also discount to adjust for inflation?

This is a perfectly reasonable procedure and something that can be done quite easily if you have an estimate of the inflation rate. If you receive \$F n years in the future then its deflated value now is simply:

` P=F/(1-R)^n`

where R is the effective annual inflation rate.

Notice that this calculation has nothing at all to do with the mechanism by which the future sum of money is acquired. It could be the promised cash lump sum received as part of a pension, or the accumulated growth of an investment.

The calculation of the deflated value is identical in form to the calculation of the present value. This raises the question of how the two are related and whether or not we should also deflate as well as discount the future value?

The deflated value takes account of the loss of purchasing power of money. That is having \$F in the future will allow you to buy the same goods that having \$P today would do. The present value on the other hand does not take into account the purchasing power of money, only the lost investment revenue due to not receiving money for n years.

The point is that inflation does not directly alter the amount of money that you need to invest now to receive a another sum in n years time. In this sense inflation does not affect the concept or method of calculation of the present value nor the relationship between present and future value.

That is

• the present value of a future cash sum is not affected by inflation even though the purchasing power of the future value is.

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