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The Level of Interest Rates Chapter 4 FIN 221 1 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 What are Interest Rates? • Interest rates are: 1. The price of borrowing money for the use of its purchasing power (it is the rental price of money). 2. To a borrower, they are penalty for consuming income before it is earned. 3. To a lender , they are reward for postponing current consumption until the maturity of the loan. 4. Interest rates serve an Allocative Function in the economy. They allocate funds between SSUs and DSUs and among financial markets. Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 2 Determine the interest Rate in the LR • Two Main factors effect on interest rate on deposits: 1- Return on investment (upper limit on interest rate can be paid to savers) 2- positive time preference for consumption (how much consumption consumers are willing to forgo at different interest rate levels) • Equilibrium real interest rate is the intersection point between demand for funds (Investment curve) and supply of funds (Saving curve) 3 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 • Factors effect on return on investment then on demand for fund. So demand curve will shift either to the right or to the left: 1. 2. 3. 4. 5. Productivity Technology taxes, expected risk expected sales • Factor effect on supply of funds. so supply of funds curve will shift either rightward or leftward: 1. Consumer attitude (propensity to save) 2. personal Income, 3. personal income tax 4 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 • Examples: 1- draw an equilibrium position between demand and supply of funds indicating the equilibrium interest rate. 2- show and explain the effects of the following on equilibrium position: a) Improvement in technology b) increase in taxes on business c) increase in taxes on personal income d) expect more sales in the future e) Increase in real interest rate f) Decrease propensity to save g) Expect less risk in the future h) Discover a new machine that will increase the productivity i) The economy will enter a recession stage that will effect on income and sales 5 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Determine the Interest Rate in the SR (Theory of Loanable Funds) • In the short run, interest rate depends on the supply of and the demand for loanable funds. • The supply of and the demand for loanable funds depend on productivity and thrift. 6 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Sources of Demand and Supply of Loanable Funds • Sources of Supply loanable Funds Consumer savings. Business savings Government savings Central bank, changing quantity of money. • Sources of Demand Loanable Funds Business investment. Consumer credit purchase. Government budget deficit. 7 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Factors effect on Supply of Loanable Funds 1. Real Interest rate (Movement) 2. Change in Quantity Supplied of Money 3. Change in the Income tax 4. Change in GOV. Budget (from Deficit to Surplus Position) 5. Change in Saving Rate 6. Change in Business Savings 8 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Factors effect on Demand for Loanable Funds 1. Real Interest rate 2. Change in future expected Profits 3. Change in GOV. Budget (from surplus to deficit position) 4. Change in Taxes 9 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Excess Supply Excess Demand 10 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Movement Versus Shifting of SL / DL • Changes in interest rate brings changes in quantity of LFs demanded and supplied, and thus movements along the SL and DL curves. • Changes in factor (s) other than the interest rate will change the supply / demand for LFs. There will be a shift in the supply and demand curves, and as a result a new equilibrium occurs. • In summary, 1. If SL only increases, ………………….. 2. If DL only increases, ……………………… 3. If both SL and DL increase, …………….. Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 4.11 If both SL and DL decrease, ………………. Price Expectations and Interest Rate • Increase prices leads to decrease purchasing power. • To avoid decrease in purchasing power, compensation should be added. • Example: An SSU and a DSU plan to exchange money and financial claims for a period of one year. Both agreed that a fair rental price for the money is 5% and both anticipate an 8% inflation rate during the year. What would be the contract rate on the loan ?To answer this question we need to discuss the Fisher Effect. 12 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 The Fisher Effect : The Fisher Effect Theory states that the nominal interest rate (contract rate) includes real interest rate (interest rate without inflation) and expected annual inflation rate. The Fisher Equation is expressed as: (1+ i ) = (1+r) ( 1+ ΔPe ) Where : i = the observed nominal rate of interest. r = real rate of interest in the absence of price level changes ( interest rate where no inflation exists). ΔPe = expected annual change in commodity prices (expected annual rate of inflation). 13 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Solving the Fisher Equation for (i), we obtain the following equation: 1 + i = 1 + ΔPe + r + r Δpe 1 – 1 + i = r + ΔPe + r ΔPe i = r + ΔPe + r Δpe The final term of the Fisher equation (r ΔPe )is approximately equal to zero. So, in many situations it is dropped from the equation without creating a critical error. The equation without the final term is referred to as the Approximate Fisher Equation and is stated as : i = r + Δpe Note 1 : the nominal interest rate includes: (1) the real interest rate and (2) the anticipated change in price level over the life of the contract.` Note 2: if Δpe equals ZERO, nominal interest rate (i) = real interest Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 14 (r ). rate Example 1: If real interest rate is 5%, actual inflation last year was 7%, and expected inflation for the coming year is 9%. What is the current level of nominal interest rate? Example 2: In Example 1, what compensation would a lender require for lending BD 1000 for 1 year? Example 3: If the real interest rate is 6%, actual inflation for the last year was 5%, and expected inflation is 9% , according to the fisher effect, what is the current level of nominal interest rate? 15 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Example 4: If you believe that the real of interest is 5% and the expected inflation rate is 4%, what is the nominal interest rate? 16 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 The Realized Real Rate The Fisher equation is based on expected inflation rate. The actual rate of inflation may be different from the anticipated rate. This may lead to the realized rate of return on a loan to be different from the nominal interest rate agreed on at the time of the loan contract. The realized (actual) real rate is calculated as : r = i - ΔPa, Where; r = is the realized real rate of return, i = the nominal interest rate, and ΔPa = is the actual rate of inflation. 17 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Example 1 An investor earned 12% last year, a year when actual inflation was 9% and was expected to have been 6%. The investor realized real return rate was: Example 2: No. 9 Page 103 An investor buys a 1 –year Treasury security with a promised yield of 10%. The investor expected the annual rate of inflation to be 6%; however, the actual rate turned out to be 10%. What were the expected and the realized real rates of return for the investor? • expected real rate = • realized real rate = 18 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Example 3 In example 2, assume the actual rate of inflation turned out to be 12%. What was the realized real rate? Notice: The realized real rate may be Positive, Zero or Negative. 1. If nominal interest rate (i) > actual inflation, then realized real rate is ………………. 2. If nominal interest rate (i) = actual inflation then realized real rate is ………………. 3. if nominal interest rate (i) ˂ actual inflation then realized real rate is ………………. 19 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Example 4: If actual inflation turns out to be less than expected inflation, would you rather have been a borrower or a lender? why? Example 5: Magdy lends a 1 –year security to Fahmy with a promised yield of 10%. The investor expected the annual rate of inflation to be 6%; however, the actual rate turned out to be 10%. Who is benefit in this situation? 20 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4 Forecasting Interest Rate • Two are used by economists to forecast interest rate: 1. Economic Models 2. Flow of Funds Approach • 21 Dr. Hisham Abdelbaki - FIN 221 - Ch. 4