©2007, The McGraw-Hill Companies, All Rights Reserved 2-1 McGraw-Hill/Irwin Chapter Two Determinants of Interest Rates

©2007, The McGraw-Hill Companies, All Rights Reserved 2-2 McGraw-Hill/Irwin 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

©2007, The McGraw-Hill Companies, All Rights Reserved 2-3 McGraw-Hill/Irwin Time Value of Money and Interest Rates Assumes the basic notion that a dollar received today is worth more than a dollar received at some future date Compound interest –interest earned on an investment is reinvested Simple interest –interest earned on an investment is not reinvested Assumes the basic notion that a dollar received today is worth more than a dollar received at some future date Compound interest –interest earned on an investment is reinvested Simple interest –interest earned on an investment is not reinvested

©2007, The McGraw-Hill Companies, All Rights Reserved 2-4 McGraw-Hill/Irwin Calculation of Simple Interest Value = Principal + Interest (year 1) + Interest (year 2) Example: $1,000 to invest for a period of two years at 12 percent Value = $1,000 + $1,000(.12) + $1,000(.12) = $1,000 + $1,000(.12)(2) = $1,240 Value = Principal + Interest (year 1) + Interest (year 2) Example: $1,000 to invest for a period of two years at 12 percent Value = $1,000 + $1,000(.12) + $1,000(.12) = $1,000 + $1,000(.12)(2) = $1,240

©2007, The McGraw-Hill Companies, All Rights Reserved 2-5 McGraw-Hill/Irwin Value of Compound Interest Value = Principal + Interest + Compounded interest Value = $1,000 + $1,000(.12) + $1,000(.12) + $1,000(.12) = $1,000[1 + 2(.12) + (.12) 2 ] = $1,000(1.12) 2 = $1, Value = Principal + Interest + Compounded interest Value = $1,000 + $1,000(.12) + $1,000(.12) + $1,000(.12) = $1,000[1 + 2(.12) + (.12) 2 ] = $1,000(1.12) 2 = $1,254.40

©2007, The McGraw-Hill Companies, All Rights Reserved 2-6 McGraw-Hill/Irwin Present Value of a Lump Sum PV function converts cash flows received over a future investment horizon into an equivalent (present) value by discounting future cash flows back to present using current market interest rate –lump sum payment –annuity PVs decrease as interest rates increase PV function converts cash flows received over a future investment horizon into an equivalent (present) value by discounting future cash flows back to present using current market interest rate –lump sum payment –annuity PVs decrease as interest rates increase

©2007, The McGraw-Hill Companies, All Rights Reserved 2-7 McGraw-Hill/Irwin Calculating Present Value (PV) of a Lump Sum PV = FV n (1/(1 + i/m)) nm = FV n (PVIF i/m,nm ) where: PV = present value FV = future value (lump sum) received in n years i = simple annual interest rate earned n = number of years in investment horizon m = number of compounding periods in a year i/m = periodic rate earned on investments nm = total number of compounding periods PVIF = present value interest factor of a lump sum PV = FV n (1/(1 + i/m)) nm = FV n (PVIF i/m,nm ) where: PV = present value FV = future value (lump sum) received in n years i = simple annual interest rate earned n = number of years in investment horizon m = number of compounding periods in a year i/m = periodic rate earned on investments nm = total number of compounding periods PVIF = present value interest factor of a lump sum

©2007, The McGraw-Hill Companies, All Rights Reserved 2-8 McGraw-Hill/Irwin 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

©2007, The McGraw-Hill Companies, All Rights Reserved 2-9 McGraw-Hill/Irwin Calculation of Present Value (PV) of an Annuity nm PV = PMT  (1/(1 + i/m)) t = PMT(PVIFA i/m,nm ) t = 1 where: PV = present value PMT = periodic annuity payment received during investment horizon i/m = periodic rate earned on investments nm = total number of compounding periods PVIFA = present value interest factor of an annuity nm PV = PMT  (1/(1 + i/m)) t = PMT(PVIFA i/m,nm ) t = 1 where: PV = present value PMT = periodic annuity payment received during investment horizon i/m = periodic rate earned on investments nm = total number of compounding periods PVIFA = present value interest factor of an annuity

©2007, The McGraw-Hill Companies, All Rights Reserved 2-10 McGraw-Hill/Irwin Calculation of Present Value of an Annuity You are offered a security investment that pays $10,000 on the last day of every year for the next 6 years in exchange for a fixed payment today. PV = PMT(PVIFA i/m,nm ) at 8% interest - = $10,000( ) = $46, If the investment pays on the last day of every quarter for the next six years at 8% interest - = $10,000( ) = $189, You are offered a security investment that pays $10,000 on the last day of every year for the next 6 years in exchange for a fixed payment today. PV = PMT(PVIFA i/m,nm ) at 8% interest - = $10,000( ) = $46, If the investment pays on the last day of every quarter for the next six years at 8% interest - = $10,000( ) = $189,139.26

©2007, The McGraw-Hill Companies, All Rights Reserved 2-11 McGraw-Hill/Irwin Future Values Translate cash flows received during an investment period to a terminal (future) value at the end of an investment horizon FV increases with both the time horizon and the interest rate Translate cash flows received during an investment period to a terminal (future) value at the end of an investment horizon FV increases with both the time horizon and the interest rate

©2007, The McGraw-Hill Companies, All Rights Reserved 2-12 McGraw-Hill/Irwin Future Values Equations FV of lump sum equation FV n = PV(1 + i/m) nm = PV(FVIF i/m, nm ) FV of annuity payment equation (nm-1) FV n = PMT  (1 + i/m) t = PMT(FVIFA i/m, mn ) (t = 0) FV of lump sum equation FV n = PV(1 + i/m) nm = PV(FVIF i/m, nm ) FV of annuity payment equation (nm-1) FV n = PMT  (1 + i/m) t = PMT(FVIFA i/m, mn ) (t = 0)

©2007, The McGraw-Hill Companies, All Rights Reserved 2-13 McGraw-Hill/Irwin 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 –at 8% interest = $10,000( ) = $15, –at 12% interest = $10,000( ) = $19, –at 16% interest = $10,000( ) = $24, –at 16% interest compounded semiannually = $10,000( ) = $25, You invest $10,000 today in exchange for a fixed payment at the end of six years –at 8% interest = $10,000( ) = $15, –at 12% interest = $10,000( ) = $19, –at 16% interest = $10,000( ) = $24, –at 16% interest compounded semiannually = $10,000( ) = $25,181.70

©2007, The McGraw-Hill Companies, All Rights Reserved 2-14 McGraw-Hill/Irwin Calculation of the Future Value of an Annuity You invest $10,000 on the last day of every year for the next six years, –at 8% interest = $10,000( ) = $73, If the investment pays you $10,000 on the last day of every quarter for the next six years, –FV = $10,000( ) = $304, If the annuity is paid on the first day of each quarter, –FV = $10,000( ) = $310, You invest $10,000 on the last day of every year for the next six years, –at 8% interest = $10,000( ) = $73, If the investment pays you $10,000 on the last day of every quarter for the next six years, –FV = $10,000( ) = $304, If the annuity is paid on the first day of each quarter, –FV = $10,000( ) = $310,303.00

©2007, The McGraw-Hill Companies, All Rights Reserved 2-15 McGraw-Hill/Irwin Relation between Interest Rates and Present and Future Values Present Value (PV) Interest Rate Future Value (FV) Interest Rate

©2007, The McGraw-Hill Companies, All Rights Reserved 2-16 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 Where 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 Where c = number of compounding periods per year

©2007, The McGraw-Hill Companies, All Rights Reserved 2-17 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

©2007, The McGraw-Hill Companies, All Rights Reserved 2-18 McGraw-Hill/Irwin Supply of Loanable Funds Interest Rate Quantity of Loanable Funds Supplied and Demanded DemandSupply

©2007, The McGraw-Hill Companies, All Rights Reserved 2-19 McGraw-Hill/Irwin 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

©2007, The McGraw-Hill Companies, All Rights Reserved 2-20 McGraw-Hill/Irwin Determination of Equilibrium Interest Rates Interest Rate Quantity of Loanable Funds Supplied and Demanded D S I H i I L E Q

©2007, The McGraw-Hill Companies, All Rights Reserved 2-21 McGraw-Hill/Irwin Effect on Interest rates from a Shift in the Demand Curve for or Supply curve of Loanable Funds 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**

©2007, The McGraw-Hill Companies, All Rights Reserved 2-22 McGraw-Hill/Irwin Factors Affecting Nominal Interest Rates Inflation Real Interest Rate Default Risk Liquidity Risk Special Provisions Term to Maturity Inflation Real Interest Rate Default Risk Liquidity Risk Special Provisions Term to Maturity

©2007, The McGraw-Hill Companies, All Rights Reserved 2-23 McGraw-Hill/Irwin Inflation and Interest Rates: The Fisher Effect The 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: 3.49% % = 1.89% The 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: 3.49% % = 1.89%

©2007, The McGraw-Hill Companies, All Rights Reserved 2-24 McGraw-Hill/Irwin 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%

©2007, The McGraw-Hill Companies, All Rights Reserved 2-25 McGraw-Hill/Irwin 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

©2007, The McGraw-Hill Companies, All Rights Reserved 2-26 McGraw-Hill/Irwin Term Structure of Interest Rates Unbiased Expectations Theory Liquidity Premium Theory Market Segmentation Theory Unbiased Expectations Theory Liquidity Premium Theory Market Segmentation Theory

©2007, The McGraw-Hill Companies, All Rights Reserved 2-27 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 _ _ 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 _ _ 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