Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-1 Chapter Two Determinants of Interest Rates

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-2 Chapter Outline 1.Time Value of Money Review 2.Effective Rate vs. Quoted Rates 3.Loanable Funds Theory 4.Factors Affecting Nominal Interest Rates 5.Term Structure of Interest Rate 6.Forecasting Interest Rate 1.Time Value of Money Review 2.Effective Rate vs. Quoted Rates 3.Loanable Funds Theory 4.Factors Affecting Nominal Interest Rates 5.Term Structure of Interest Rate 6.Forecasting Interest Rate

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-3 Interest Rate Fundamentals Nominal interest rates - the interest rate actually observed in financial markets –directly affect the value (price) of most securities traded in the market –affect the relationship between spot and forward FX rates Nominal interest rates - the interest rate actually observed in financial markets –directly affect the value (price) of most securities traded in the market –affect the relationship between spot and forward FX rates

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Time Value of Money Review 1.Compound interest vs. simple interest 2.Present Value and Future Value of Lump Sum and Annuity PV=FV (PVIF r,t )=FV(PVIF i/m,nm ) PV=PMT (PVIFA r,t )=PMT(PVIFA i/m,nm ) FV=PV (FVIF r,t )=PV(FVIF i/m, nm ) FV=PMT(FVIFA r,t )= PMT(FVIFA i/m, nm ) 1.Compound interest vs. simple interest 2.Present Value and Future Value of Lump Sum and Annuity PV=FV (PVIF r,t )=FV(PVIF i/m,nm ) PV=PMT (PVIFA r,t )=PMT(PVIFA i/m,nm ) FV=PV (FVIF r,t )=PV(FVIF i/m, nm ) FV=PMT(FVIFA r,t )= PMT(FVIFA i/m, nm )

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-5 Calculating Present Value of a Lump Sum You are offered a security investment that pays $10,000 at the end of 6 years in exchange for a fixed payment today. PV = FV(PVIF i/m,nm ) at 8% interest = $10,000( ) = $6, at 12% interest = $10,000( ) = $5, at 16% interest = $10,000( ) = $4, You are offered a security investment that pays $10,000 at the end of 6 years in exchange for a fixed payment today. PV = FV(PVIF i/m,nm ) at 8% interest = $10,000( ) = $6, at 12% interest = $10,000( ) = $5, at 16% interest = $10,000( ) = $4,104.42

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-6 Calculation of Future Value of a Lump Sum You invest $10,000 today in exchange for a fixed payment at the end of six years FV = PV(FVIF i/m,nm ) at 8% interest = $10,000( ) = $15, at 12% interest = $10,000( ) = $19, at 16% interest = $10,000( ) = $24, You invest $10,000 today in exchange for a fixed payment at the end of six years FV = PV(FVIF i/m,nm ) at 8% interest = $10,000( ) = $15, at 12% interest = $10,000( ) = $19, at 16% interest = $10,000( ) = $24,363.96

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-7 Relation between Interest Rates and Present and Future Values Present Value (PV) Interest Rate Future Value (FV) Interest Rate

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Effective or Equivalent Annual Return (EAR) Rate earned over a 12 – month period taking the compounding of interest into account. EAR = (1 + r) c – 1 Wherer = period rate c = number of compounding periods per year Rate earned over a 12 – month period taking the compounding of interest into account. EAR = (1 + r) c – 1 Wherer = period rate c = number of compounding periods per year

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Loanable Funds Theory A theory of interest rate determination that views equilibrium interest rates in financial markets as a result of the supply and demand for loanable funds

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-10 Supply and Demand of Loanable Funds Interest Rate Quantity of Loanable Funds DemandSupply

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-11 Funds Supplied and Demanded by Various Groups (in billions of dollars) Funds Supplied Funds Demanded Net Households $34,860.7 $15,197.4 $19,663.3 Business - nonfinancial 12, , ,100.0 Business - financial 31, ,513.4 Government units 12, , ,879.3 Foreign participants 8, , ,070.8 Funds Supplied Funds Demanded Net Households $34,860.7 $15,197.4 $19,663.3 Business - nonfinancial 12, , ,100.0 Business - financial 31, ,513.4 Government units 12, , ,879.3 Foreign participants 8, , ,070.8

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-12 Factors Shifting Demand & Supply Curve Supply –Wealth –Risk of financial security –Near-term spending needs –Monetary expansion –Economic conditions Demand –Utility derived from asset purchased with borrowed funds –Restrictiveness of nonprice conditions –Economic conditions Supply –Wealth –Risk of financial security –Near-term spending needs –Monetary expansion –Economic conditions Demand –Utility derived from asset purchased with borrowed funds –Restrictiveness of nonprice conditions –Economic conditions

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-13 Effect on Interest rates from a Shift in the Demand Curve for or Supply curve Increased supply of loanable funds Quantity of Funds Supplied Interest Rate DD SS SS* E E* Q* i* Q** i** Increased demand for loanable funds Quantity of Funds Demanded DD DD* SS E E* i* i** Q*Q**

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Factors Affecting Nominal Interest Rates Inflation –continual increase in price of goods/services Real Interest Rate –nominal interest rate in the absence of inflation Default Risk –risk that issuer will fail to make promised payment Inflation –continual increase in price of goods/services Real Interest Rate –nominal interest rate in the absence of inflation Default Risk –risk that issuer will fail to make promised payment (continued)

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-15 Liquidity Risk –risk that a security can not be sold at a predictable price with low transaction cost on short notice Special Provisions –taxability Term to Maturity Liquidity Risk –risk that a security can not be sold at a predictable price with low transaction cost on short notice Special Provisions –taxability Term to Maturity

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-16 Inflation and Interest Rates: The Fisher Effect The nominal interest rate should compensate an investor for both expected inflation and the opportunity cost of foregone consumption, the real rate component i = RIR + Expected(IP) or RIR = i – Expected(IP) Example(p. 47): 3.49% % = 1.89% The nominal interest rate should compensate an investor for both expected inflation and the opportunity cost of foregone consumption, the real rate component i = RIR + Expected(IP) or RIR = i – Expected(IP) Example(p. 47): 3.49% % = 1.89%

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-17 Default Risk and Interest Rates The risk that a security’s issuer will default on that security by being late on or missing an interest or principal payment DRP j = i jt - i Tt Example for December 2003: DRP Aaa = 5.66% % = 1.65% DRP Baa = 6.76% % = 2.75% The risk that a security’s issuer will default on that security by being late on or missing an interest or principal payment DRP j = i jt - i Tt Example for December 2003: DRP Aaa = 5.66% % = 1.65% DRP Baa = 6.76% % = 2.75%

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-18 Liquidity Risk and Interest Rates The risk that a security need to be sold at low prices because of inactive trading LRP j = i jt - i Tt The risk that a security need to be sold at low prices because of inactive trading LRP j = i jt - i Tt

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-19 Tax Effects: The Tax Exemption of Interest on Municipal Bonds Interest payments on municipal securities are exempt from federal taxes and possibly state and local taxes. Therefore, yields on “munis” are generally lower than on equivalent taxable bonds such as corporate bonds. i m = i c (1 - t s - t F ) Where: i c = Interest rate on a corporate bond i m = Interest rate on a municipal bond t s = State plus local tax rate t F = Federal tax rate Interest payments on municipal securities are exempt from federal taxes and possibly state and local taxes. Therefore, yields on “munis” are generally lower than on equivalent taxable bonds such as corporate bonds. i m = i c (1 - t s - t F ) Where: i c = Interest rate on a corporate bond i m = Interest rate on a municipal bond t s = State plus local tax rate t F = Federal tax rate

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 2-20 Term to Maturity and Interest Rates: Yield Curve Yield to Maturity Time to Maturity (a) (b) (c) (a) Upward sloping (b) Inverted or downward sloping (c) Flat

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Term Structure of Interest Rates Unbiased Expectations Theory –at a given point in time, the yield curve reflects the market’s current expectations of future short-term rates Liquidity Premium Theory –investors will only hold long-term maturities if they are offered a premium to compensate for future uncertainty in a security’s value Market Segmentation Theory –investors have specific maturity preferences and will generally demand a higher maturity premium Unbiased Expectations Theory –at a given point in time, the yield curve reflects the market’s current expectations of future short-term rates Liquidity Premium Theory –investors will only hold long-term maturities if they are offered a premium to compensate for future uncertainty in a security’s value Market Segmentation Theory –investors have specific maturity preferences and will generally demand a higher maturity premium

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Forecasting Interest Rates Forward rate is an expected or “implied” rate on a security that is to be originated at some point in the future using the unbiased expectations theory Spot rate is the yield to maturity of a zero-coupon bond _ _ 1 R 2 = [(1 + 1 R 1 )(1 + ( 2 f 1 ))] 1/2 - 1 where 2 f 1 = expected one-year rate for year 2, or the implied forward one-year rate for next year Forward rate is an expected or “implied” rate on a security that is to be originated at some point in the future using the unbiased expectations theory Spot rate is the yield to maturity of a zero-coupon bond _ _ 1 R 2 = [(1 + 1 R 1 )(1 + ( 2 f 1 ))] 1/2 - 1 where 2 f 1 = expected one-year rate for year 2, or the implied forward one-year rate for next year