Interest rates is the amount charged by a lender or borrower, which is expressed as a percentage of the principal. In simple terms, it is the cost of borrowing Money or the return for investing Money. For example, a bank will charge interest on an amount loaded out to a customer, or a charge on an overdrawn bank account. Equally, a bank will also pay interest on a customer with a positive bank balance. It is important to note that interest vary depending on the type and provider of borrower. Interest is the price borrowers must pay to Lenders to obtain the use of Money over a certain period of time. Simple interest = P (principal) x I (annual interest rate) X N (number of years) Compound interest is defined as the total amount of principal and interest in future (or the future value) less principal amount of present value ( or present value). Compound interest = P (principal) x [ ( 1 + (interest rate) n (months)) – 1] Future value is defined as the value of an asset (or cash) in the future that is equivalent to a specific sum today. Simple annual interest = Original investment x ( 1 + interest rate * number of years)) Interest compounded annually = Original investment x ( ( 1 + interest rate ) ^ number of years) Real interest rate helps to reflect the value in real terms. It is defined as the interest rate, adjusted to remove the effects of inflation, which reflects the real cost of funds to the borrower and moreover, the real yield to the lender. Real interest rate = Nominal interest rate – Inflation (expected or actual) Example: An individual is earning 4% interest per year on their savings account. Inflation is currently set at 3% per year. In order to calculate the real interest rate: 4% - 3% = 1%. This means that the individual’s purchasing power increases by 1% a year. Nominal interest rate is the interest rate before taking into account inflation. This is the rate quoted in loan / deposit agreements. The formula is as follows, which helps to link with real interest rate: ( 1 + Nominal Interest rate ) = ( 1 + real interest rate) ( 1 + inflation rate) There are three such theories that discuss interest rates: 1. The classical theory 2. The loanable funds theory 3. The keynesian. The Classical Theory This theory is associated primarily with academics such as Ricardo and Fisher. It is a static theory, which considers the rate of interest a real phenomenon in that it is determined by real factors. It is the supply of savings and the deman of investment which determines the equilibrium rate of interest. Aggregate saving is the difference between the total national income and the total consumption expenditure. It is important to note that savings may be effected by individuals, households, businesses and governments. The Loanable funds theory This theory makes some modifications to the classical theory model. This is through the interest paid in Money terms on Money loans and assets. However, interest rate here has nothing to do with the levels of Money and prices. Commercial banks are a more efficient channel of savings into the best investment outlets. Keynesian Often referred to as “Keynes’ Liquidity Preference Theory of Interest Rate Determination”, argues that the determinants of the equilibirum interest rate are ‘monetary’ factors only. In Keynes’ analysis, the demand and supply of money are the determinants of interest rate. Keynes argues that interest is the price paid to borrow funds. In his theory, an assumption is made that people like to keep cash rather than invest it in assets. Therefore, there is a preference for liquid cash. Moreover, as cash is the most liquid asset, thus people prefer to keep cash. In his model, Keynes argues that the demand and supply of money are the primary determinants of cash. Demand for money is defined as the demand to hold an asset. This desire can arise for the following three reasons – Fırstly, the transaction demand for money refers to the day-to-day transactions. Thus factors such as income and spending quantities come into play. Individuals with higher income, tend to have more liquid cash. The second is precautionary demand for money. With this, there is uncertainty. This refers to holding cash balances in case of unforseen future contingencies i.e. illness or death. Again, individuals with more income tend to have more liquid cash to keep in their bank accounts. Finally, speculative demand for money. This motive refers to an individual’s desire to hold one’s assets in liquid form to take advantage of market movements. This is in relation to any uncertainty in the future and / or changes in interest rates. Individuals hold money so that they are able to deal in bonds / securities, where interest rates fluctuate. For example, if bond prices are expected to rise (or interest rates are expected to fall), people will now buy bonds and sell when prces rise. In this instance, keeping cash in bond terms is more favourable. Total demand for money is made up of the sum of these three – D.Money = Transaction Demand of Money + Precautionary Demand of Monday + Speculative Demand of Money It is important to understand what Keynes’ refers to as the ‘liquidity trap’. The figure below shows the liquidity preference curve. It can be observed that at a minimum rate of interest, r-min, the curve is perfectly elastic. However, there is a ceiling of interest rate, r-r-max. Note, interest rate cannot rise above the ceiling. Thus, interest rates are only able to fluctuate between r-max and r-min. Money supply is different in that it is determined by the policy of the central bank of that particular country. In the graph above, SM is shown as perfectly elastic as this is provided directly by the institition. Present-Worth Analysis Blank & Traquin (2012) present the concept as the “future amount of money converted to its equivalent value now has a present worth (PW) that is always less that tha of the future cash flow”. Present worth is often referred to as discounted cash flow (DCF), and the interest rate as the discount rate. For any interest rate greater than zero, then all present / future factors have to have a value less than 1.0. This is the reason why it is referred to as discounted cash flow. To better explain this concept, we need to develop it using projects. Once a project is viable, then alternatives are formulated; mutually exclusive or independent. Each are evaluated differently. Mutually exclusive is defined as the only one can be selected, whereas, Independent, more than one can be selected. Please note that in some cases doing nothing is also an option. In this case, the project maintains it current approach; no new costs are introduced, nor revenues or savings. Example: Selection of Alternatives by Present worth For the example projects below, which should be selected if they are (a) mutually exclusive; (b) independent? Project ID Present Worth A $30,000 B $12,500 C $-4,000 D $2,000 Solution: (a) Select numerically largest PW: alternative A (b) Select all with PW > 0; projects A, B & D Present-worth analysis is “based on cash flow equivalance along with the payback period” (Park, 2008). PW helps to analyse how cashflows are discounted for a project into a single present value. Thus making it one of the most efficient analysis methods used toda for determining whether to move forward with a project. The Minimum attractive rate of return (MARR) is the interest rate at which a firm can always earn/borrow money (Park, 2008). This is usually determined by management; it is the rate at which PW should be calcualted. Formula to calculate present worth is as follows: