If an individual behaves rationally, he/she would not value the opportunity to receive a specific amount of money now equally with the opportunity to have the same amount at some future date. Most individuals value the opportunity to receive money now higher than waiting for one or more years to receive the same amount. This phenomenon is referred to as an individual’s time preference for money.
Why is a shilling today worth more to you than a shilling a year from now?
Three reasons may be attributed to the individual’s time preference for money:
- Preference for consumption
- Investment opportunities
We live under risk and uncertainty. As an individual is not certain about future cash receipts, he prefers receiving cash now. Most people have subjective preference for present consumption either because of the urgency of their present wants or because of the risk of not being in a position to enjoy future consumption that may be caused by illness, death or inflation. Most individuals prefer present cash to future cash because of the available investment opportunity to which they can put present cash to earn additional cash. If a shilling is invested elsewhere it would earn a return on it, in the form of interest, dividends, or price appreciation. Central to the notion of the time value of money is the idea that the money can be invested elsewhere to earn a return. This return is what we call discount rate.
Time value of money is generally expressed by an interest rate. This rate will be positive even in the absence of any risk. For instance if interest rate is 5% it implies that an investor can forego the opportunity of receiving shs. 100 if he/she is offered shs. 105 after one year. Thus the individual is indifferent between shs. 100 and shs. 105 a year from now as he considers the two amounts equivalent in value. In reality, an investor will be exposed to some degree of risk. Therefore he would require a rate of return from the investment which compensates him for both time and risk. His required rate of return will be:
Required rate of return = Risk free rate + Risk premium
The risk free premium compensates for time while risk premium compensates for risk.
Knowledge of the required rate of return or simply the interest rate help an individual or a firm to make decisions. It permits individual or the firm to convert different amounts offered at different times to amounts of equivalent value in the present, a common point of reference.
- Principle: Amount of money borrowed by a borrower now (also called the present value of the money borrowed)
- Interest: A fee paid by the borrower for the privilege of using the money borrowed for some period of time.
- Future value: total amount (principle + interest) to be repaid to the lender at the end of the period of time that the money was borrowed.
There are two types of interest: Simple and compound interest.
- Simple interest: a percentage of the amount borrowed (i.e. principle) is paid to the lender each year (or a fraction of a year)
- Compound interest: in each compounding period (e.g. month, year) a percentage of the amount borrowed plus a percentage of the total interest accumulated is paid to the lender at the end of the compounding period.
In the case of simple interest, the amount of interest paid is based only on the amount borrowed, whereas in a compound interest scenario the amount of interest paid is based on the amount borrowed/invested plus the interest accumulated in the account.
Simple interest formula where P is principle, r is the annual interest rate and t is the length of the loan, measured in years.
The total accumulated amount A (or future value) paid by the borrower to the lender is
Examples: Suppose you invest Kshs. 1000 at 8% simple interest, how much money will be in the account after:
- 5 years
- 6 months
In addition to the initial investment earning interest, the interest earned in each year itself earns interest in the future years.
Assume an investor has shs. 50,000 in the bank earning 6% interest for the foreseeable future.
At the end of one year the 50,000 will be worth 53,000 (i.e. 50,000+interest rate of 6% on 50,000).Thus the future value at the end of year 1
At the end of year 2, the deposit would have grown further to shs. 56,180 (i.e 53,000+interest rate of 6% on 53,000). Thus future value at the end of year 2
Compound interest formula:
Example: Suppose you invest Kshs. 100,000 at 8% compound interest, calculate the future value at the end of 5 years.
When we want to solve for future value of any amount of cash, we refer to the finanncial tables which give precalculated future value factor and multiply by the amount. From the tables, the future value interest factor for a shilling compounded at 8% for 5 years is 1.4693.