The time value of money

Ask your friends how much money they would need to be offered in one year's time to make them indifferent between that amount and a guaranteed ￡1,000 now. The answer will vary from individual to individual, and will also vary geographically.

Any rational individual will prefer certain money now rather than uncertain money in the future. This is known as the “time value of money”. Even though you do not realise it, when answering the question above, you are implicitly thinking about important concepts such as opportunity cost, inflation and risk. For example, by how much are prices rising, how much satisfaction you would gain from spending the money now and what is the likelihood of the future payment not occurring? In order to determine the future amount that will make us indifferent, an investor will require compensation for these three elements.

The eagerness to spend the ￡1,000 now is the most difficult to quantify, but for inflation and risk it is easy to assign numerical values. Assume that inflation is 5% p.a. and we attach an amount of 3% to the eagerness to consume. In order to reward an investor for these two factors the required return would need to be:

(1 + 0.05) × (1 + 0.03) – 1 = 8.15%

The closest investment we have that simply rewards investors for loss of consumption and inflation, with no risk, is a short-term government security. In Chapter 2 we referred to such an asset as the risk-free rate.

However, physical investments such as building an office block or manufacturing a new product, and financial investments such as buying shares or bonds, carry with them a degree of risk. Investors therefore demand a “risk premium” beyond the risk-free rate when making investments with uncertain outcomes. We have already seen in section 2.7 that when determining the expected return on an asset we use the security market line:

E(Ri) = Rf + βi[E(Rm) – Rf]

More generally we can write:

required return = risk-free rate + risk premium

Therefore, when we are attempting to compare different amounts of money at different points in time, we need to take into consideration the eagerness to spend, inflation and risk.