Chapter 5 © 2003 South-Western/Thomson Learning Interest Rates and Bond Prices

Slide 2 Learning Objectives  Why the interest rate represents the time value of money  What are compounding and discounting  Why interest rates and bond prices are inversely related

Slide 3 Learning Objectives  The major determinants of interest rates  The relationship between nominal and real interest rates  How interest rates fluctuate over the business cycle

Slide 4 The Time Value of Money  Money represents purchasing power …  Short of funds for goods or services? 1. Borrow now and purchase now 2. Save now and purchase later  The higher the interest rates  the less appealing is #1  the more appealing is #2

Slide 5 The Time Value of Money Lending in present ENABLES  Spending in the future the sum of what is lent plus the interest earned Borrowing in future ENABLES  Spending in the present, but requires paying back in the future what is borrowed plus interest

Slide 6 Compounding and Discounting  Compounding Future Values  What is the future value of money lent (or borrowed) today AMOUNT REPAID = PRINCIPAL + INTEREST INTEREST = PRINCIPAL x INTEREST RATE amount of interest

Slide 7 Compounding and Discounting substituting equation into yields AMOUNT REPAID = PRINCIPAL + ( PRINCIPAL x INTEREST RATE ) AMOUNT REPAID = PRINCIPAL x ( 1 + i ) V 1 = V 0 ( 1 + i )

Slide 8 Compounding and Discounting V 1 = the funds to be received by the lender at the end of one year V 0 = the funds lent now This is present value

Slide 9 Compounding and Discounting In the second year V 2 = V 0 (1 + i ) 2 V n = V 0 (1 + i ) n

Slide 10 Discounting: Present Values  Discounting is backward-looking What is the PRESENT VALUE of money to be received (or paid) in the future? expressed V 0 = V n / (1 + i ) n

Slide 11 Discounting: Present Values RECAP  Compounding: finding the value of a future sum.  Discounting: finding the present value of a future sum  Future value: V n of a sum, V 0 invested today for n years is V 0 ( 1 + i ) n  Present value: V 0, of the sum V n, to be received in n years is V n / ( 1 + i ) n

Slide 12 Interest Rates, Bond Prices, and Present Value To compute the present value of each coupon payment and the present value of the final repayment of the face value on the maturity date. P = the price (present value) of the bond C = the coupon payment on the bond (C1 in year 1, C2 in year 2 etc. F = the face or par value of the bond i = the interest rate n = the number of years to maturity (on a five-year bond, n=5) P = C 1 / ( 1 + i ) 1 + C 2 / ( 1 + i ) 2 + … + C n / ( 1 + i ) n + F / ( 1 + i ) n

Slide 13 Interest Rates, Bond Prices, and Present Value  Discount from par - raises the yield on the bond, called the yield to maturity  Premium above par – a price above par value There is an inverse relationship between the price of outstanding bonds trading in the secondary market and the prevailing level of market interest rates. If bond prices are rising, then interest rates are falling, and vice versa.

Slide 14 Interest Rates, Bond Prices, and Present Value  The price of the bond is the discounted value of the future stream of income over the life of the bond.  When the interest rate increases, the price of the bond decreases.  When the interest rate decreases, the price of the bond increases. RECAP

Slide 15 Determinants of Interest Rates  Demand for loanable funds –  downward-sloping demand curve indicates that DSU’s are willing to borrow more at lower interest rates  Supply of loanable funds – originates  The household, business, government and foreign SSUs who are prepared to lend  The Fed, which, in its ongoing attempts to manage the economy’s performance, supplies reserves

Slide 16 Exhibit 5–3 The Supply of and Demand for Funds

Slide 17 Determinants of Interest Rates  Changes in the demand for loanable funds  Movements in gross domestic product (GMP)  When GMP rises  Firms & households become more willing and able to borrow  Firms expand inventory & engage in investment spending  Households willing to borrow, increased incomes, and/or improved employment outlook

Slide 18 Exhibit 5–4 A Shift in the Demand for Funds

Slide 19 Determinants of Interest Rates  Changes in the demand for loanable funds  Increase their purchases of goods and services, particularly  Auto  Durable goods  Houses Items that require financing + Easier to make the interest and principal payments on new debt + Increase in anticipated productivity of capital investment Lead to a greater demand for capital investment & hence increase the demand for loanable funds

Slide 20 Determinants of Interest Rates  Changes in the supply of funds  Monetary policy  Disequilibrium – the quantity supplied of funds exceeds the quantity demanded  As interest rates fall, DSUs & SSUs revise their borrowing and lending plans  Increase in the money supply will lower the interest rates  Decrease in the money supply will raise the interest rates

Slide 21 A Shift in the Supply of Funds The interest rate is a positive function of income or GDP, Y and negative function of the money supply, M i = f ( Y +,M ¯ )

Slide 22 Exhibit 5–5 A Shift in the Supply of Funds

Slide 23 Determinants of Interest Rates  The demand for loanable funds originates from DSUs  The quantity demanded is inversely related to the interest rate  The supply of loanable funds originates from SSUs and from Fed  The quantity supplied is directly related to the interest rate  If the money supply increases, the supply of loanable funds increases and the interest rate falls: i = f ( Y +,M ¯ ) RECAP

Slide 24 Inflation and Interest Rates  Lenders are concerned about  Nominal interest  Inflation

Slide 25 Inflation and Interest Rates  Nominal interest rate is not an adequate measure of the real return on an interest- bearing financial asset unless there is assurance of price stability.  Appropriate measure is the real interest rate, which is the return on the asset corrected for changes in the purchasing power of money.

Slide 26 Inflation and Interest Rates Money illusion is said to occur when investors react to nominal changes even though no changes in real interest rates or other real variables have occurred. i = r + p e The equation says that nominal interest rate has parts: a real interest rate, r, and an inflation premium i = r - p e

Slide 27 Inflation and Interest Rates  Major price indexes  Consumer Price Index (CPI) CPI is designed to measure changes in the cost of goods and services purchased by a typical urban consumer  Producer Price Index (PPI) PPI measures the changes in the cost of goods and services purchased by a typical producer  Inflation rate is generally measured by the percentage change in one of these price indexes.

Slide 28 Inflation and Interest Rates Expectations of inflation affect portfolio choices that help determine the demand and supply of loanable funds i = f ( Y +,M ¯, p + e ) Nominal interest rate is positively related to the expected inflation rate

Slide 29 Inflation and Interest Rates  The nominal interest rate is the real interest rate plus the expected inflation rate  Money illusion occurs when investors react to nominal changes when no real changes occurred  If expected inflation increases, the nominal interest rate will rise  Nominal interest rates are correlated with expected inflation i = f ( Y +,M ¯, p + e ) RECAP

Slide 30 The Cyclical Movement of Interest Rates  Stages of the business cycle are the recession trough, expansion, and peak  Interest rates tend to fluctuate pro- cyclically-that is, they move with the business cycle, rising during expansions and falling during recessions