The time value of money
When people undertake to set aside money for investment something has to be given up now. For instance, if someone buys bonds in a firm or lends via commercial paper there is a sacrifice of present consumption.
One of the incentives to save is the possibility of gaining a higher level of future consumption. Therefore, it is apparent that compensation is required to induce people to make a consumption sacrifice. Compensation will be required for at least three things:• Impatience to consume. Individuals generally prefer to have £1 today than £1 in five years' time. To put this formally: the utility of £1 now is greater than £1 received five years hence. Individuals are predisposed towards impatience to consume, thus they need an appropriate reward to begin the saving process. The rate of exchange between certain future consumption and certain current consumption is the pure rate of interest - this occurs even in a world of no inflation and no risk. If you lived in such a world you might be willing to sacrifice £100 of consumption now if you were compensated with £102 to be received in one year. This would mean a pure rate of interest of 2%.
• Inflation. The price of time (or the interest rate needed to compensate for impatience to consume) exists even when there is no inflation, simply because people generally prefer consumption now to consumption later. If there is inflation then the providers of finance will have to be compensated for that loss in purchasing power as well as for time.
• Risk. The promise of the receipt of a sum of money some years hence generally carries with it an element of risk; the payout may not take place or the amount may be less than expected. Risk simply means that the future return has a variety of possible values.
Thus, the issuer of a security, whether it be a share, a bond or a certificate of deposit, must be prepared to compensate the investor for impatience to consume, inflation and risk involved, otherwise no one will be willing to buy the security.
A further factor (which, to a large extent, could be seen as a form of risk) is that once the lender has committed the funds to a borrower for a set period of time they have to face the problem that at some point they may need the funds. With some investments there are ways of releasing the money - converting the instrument to cash - quickly, at low transaction cost and with certainty over the amount that would be released - either by insisting that the borrower repays on request or from selling the right to receive interest, etc. to another investor in a market - high liquidity and therefore low liquidity risk. If lenders/investors do not have access to easy and quick liquidity (high liquidity risk) then they are likely to demand an additional return in compensation.If Mrs Ann Investor is considering a ˆ1,000 one-year investment she will require compensation for three elements of time value. First, a return of 2% is required for the pure time value of money. Second, inflation is anticipated to be 3% over the year. At time zero (t0) ˆ1,000 buys one basket of goods and services. To buy the same basket of goods and services at time t1 (one year later) ˆ1,030 is needed. To compensate the investor for impatience to consume and inflation the investment needs to generate a return of 5.06%, that is:
(1 + 0.02)(1 + 0.03) - 1 = 0.0506 = 5.06%
The figure of 5.06% may be regarded here as the risk-free return (RFR), the interest rate that is sufficient to induce investment assuming no uncertainty about cash flows. Investors tend to view lending to highly reputable governments through the purchase of bills as the nearest they are going to get to riskfree investing because these institutions have an almost unlimited ability to raise income from taxes or to create money with minimal likelihood of default. This applies only if the country has a reputation for good financial management - Greece had a troublesome 2011-15; between 2011 and 2014 bonds from Spain, Portugal and Ireland were also thought to be risky investments.
When investors doubt the soundness of government finances, this has the effect of pushing up the interest rates governments have to pay to allow for the risk of default (non-payment) way beyond the normal RFR accorded a reputable eurozone government, such as Germany.The RFR forms the bedrock for time value of money calculations as the pure time value and the expected inflation rate affect all investments equally. Whether the investment is in property, bonds, shares or a factory, if expected inflation rises from 3% to 5% then the investor's required return on all investments will increase by 2%.
However, different investment categories carry different degrees of uncertainty about the outcome of the investment. For instance, an investment on the Russian stock market, with its high volatility, may be regarded as more risky than the purchase of a bond in Unilever, with its steady growth prospects. Investors require different risk premiums on top of the RFR to reflect the perceived level of extra risk. Thus:
Required return (Time value of money) = RFR + risk premium
In the case of Mrs Ann Investor, the risk premium pushes up the total return required to, say, 10%, thus giving full compensation for all three elements of the time value of money.
The interest rates quoted in the financial markets are (theoretically) sufficiently high to compensate for all three elements - whether investors sometimes over- or under-price bonds, etc. and thus yields are pushed irrationally low or high is a different matter.
Leaving the idea of irrationality to one side, a ten-year loan to a reputable government (such as the purchase of a bond) currently paying 5% will be offering some of this as compensation for time preference and a little for risk, but the majority of that interest is likely to be compensation for future inflation. The same elements apply to the cost of capital for a business; when it issues financial securities, the returns offered include a large element of inflation and risk compensation.
The nominal rate of interest is the rate quoted by lenders and includes the inflation element. The real rate of interest removes inflation.
Real rate of interest = Nominal rate of interest - Inflation