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©2009, The McGraw-Hill Companies, All Rights Reserved 2-1 McGraw-Hill/Irwin Chapter Two Determination of Interest Rates

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-2 McGraw-Hill/Irwin Interest Rate Fundamentals Nominal interest rates: the interest rates actually observed in financial markets –affect the values (prices) of securities traded in money and capital markets –affect the relationships between spot and forward FX rates Nominal interest rates: the interest rates actually observed in financial markets –affect the values (prices) of securities traded in money and capital markets –affect the relationships between spot and forward FX rates

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-3 McGraw-Hill/Irwin Time Value of Money and Interest Rates The time value of money is based on the notion that a dollar received today is worth more than a dollar received at some future date –Simple interest: interest earned on an investment is not reinvested –Compound interest: interest earned on an investment is reinvested The time value of money is based on the notion that a dollar received today is worth more than a dollar received at some future date –Simple interest: interest earned on an investment is not reinvested –Compound interest: interest earned on an investment is reinvested

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-4 McGraw-Hill/Irwin Present Value of a Lump Sum Discount future payments using current interest rates to find the present value (PV) PV = FV t [1/(1 + r)] t = FV t (PVIF r,t ) PV = present value of cash flow FV t = future value of cash flow (lump sum) received in t periods r = interest rate per period t = number of years in investment horizon PVIF r,t = present value interest factor of a lump sum Discount future payments using current interest rates to find the present value (PV) PV = FV t [1/(1 + r)] t = FV t (PVIF r,t ) PV = present value of cash flow FV t = future value of cash flow (lump sum) received in t periods r = interest rate per period t = number of years in investment horizon PVIF r,t = present value interest factor of a lump sum

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-5 McGraw-Hill/Irwin Future Value of a Lump Sum The future value (FV) of a lump sum received at the beginning of an investment horizon FV t = PV (1 + r) t = PV(FVIF r,t ) FVIF r,t = future value interest factor of a lump sum The future value (FV) of a lump sum received at the beginning of an investment horizon FV t = PV (1 + r) t = PV(FVIF r,t ) FVIF r,t = future value interest factor of a lump sum

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-6 McGraw-Hill/Irwin Relation between Interest Rates and Present and Future Values Present Value (PV) Interest Rate Future Value (FV) Interest Rate

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-7 McGraw-Hill/Irwin Present Value of an Annuity The present value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon PMT = periodic annuity payment PVIFA r,t = present value interest factor of an annuity The present value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon PMT = periodic annuity payment PVIFA r,t = present value interest factor of an annuity

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-8 McGraw-Hill/Irwin Future Value of an Annuity The future value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon FVIFA r,t = future value interest factor of an annuity The future value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon FVIFA r,t = future value interest factor of an annuity

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-9 McGraw-Hill/Irwin Effective Annual Return Effective or equivalent annual return (EAR) is the return earned or paid over a 12-month period taking compounding into account EAR = (1 + r) c – 1 c = the number of compounding periods per year Effective or equivalent annual return (EAR) is the return earned or paid over a 12-month period taking compounding into account EAR = (1 + r) c – 1 c = the number of compounding periods per year

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-10 McGraw-Hill/Irwin Financial Calculators Setting up a financial calculator –Number of digits shown after decimal point –Number of compounding periods per year Key inputs/outputs (solve for one of five) N = number of compounding periods I/Y = annual interest rate PV = present value (i.e., current price) PMT = a constant payment every period FV = future value (i.e., future price) Setting up a financial calculator –Number of digits shown after decimal point –Number of compounding periods per year Key inputs/outputs (solve for one of five) N = number of compounding periods I/Y = annual interest rate PV = present value (i.e., current price) PMT = a constant payment every period FV = future value (i.e., future price)

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-11 McGraw-Hill/Irwin Loanable Funds Theory Loanable funds theory explains interest rates and interest rate movements Views level of interest rates in financial markets as a result of the supply and demand for loanable funds Domestic and foreign households, businesses, and governments all supply and demand loanable funds Loanable funds theory explains interest rates and interest rate movements Views level of interest rates in financial markets as a result of the supply and demand for loanable funds Domestic and foreign households, businesses, and governments all supply and demand loanable funds

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-12 McGraw-Hill/Irwin Supply and Demand of Loanable Funds Interest Rate Quantity of Loanable Funds Supplied and Demanded DemandSupply

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-13 McGraw-Hill/Irwin Shifts in Supply and Demand Curves change Equilibrium Interest Rates 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** Interest Rate

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-14 McGraw-Hill/Irwin Determinants of Interest Rates for Individual Securities i j * = f(IP, RIR, DRP j, LRP j, SCP j, MP j ) Inflation (IP) IP = [(CPI t+1 ) – (CPI t )]/(CPI t ) x (100/1) Real Interest Rate (RIR) and the Fisher effect RIR = i – Expected (IP) i j * = f(IP, RIR, DRP j, LRP j, SCP j, MP j ) Inflation (IP) IP = [(CPI t+1 ) – (CPI t )]/(CPI t ) x (100/1) Real Interest Rate (RIR) and the Fisher effect RIR = i – Expected (IP)

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-15 McGraw-Hill/Irwin Determinants of Interest Rates for Individual Securities (cont’d) Default Risk Premium (DRP) DRP j = i jt – i Tt i jt = interest rate on security j at time t i Tt = interest rate on similar maturity U.S. Treasury security at time t Liquidity Risk (LRP) Special Provisions (SCP) Term to Maturity (MP) Default Risk Premium (DRP) DRP j = i jt – i Tt i jt = interest rate on security j at time t i Tt = interest rate on similar maturity U.S. Treasury security at time t Liquidity Risk (LRP) Special Provisions (SCP) Term to Maturity (MP)

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-16 McGraw-Hill/Irwin Term Structure of Interest Rates: the Yield Curve Yield to Maturity Time to Maturity (a) (b) (c) (a) Upward sloping (b) Inverted or downward sloping (c) Flat

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-17 McGraw-Hill/Irwin Unbiased Expectations Theory Long-term interest rates are geometric averages of current and expected future short- term interest rates 1 R N = actual N-period rate today N = term to maturity, N = 1, 2, …, 4, … 1 R 1 = actual current one-year rate today E( i r 1 ) = expected one-year rates for years, i = 1 to N Long-term interest rates are geometric averages of current and expected future short- term interest rates 1 R N = actual N-period rate today N = term to maturity, N = 1, 2, …, 4, … 1 R 1 = actual current one-year rate today E( i r 1 ) = expected one-year rates for years, i = 1 to N

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-18 McGraw-Hill/Irwin Liquidity Premium Theory Long-term interest rates are geometric averages of current and expected future short- term interest rates plus liquidity risk premiums that increase with maturity L t = liquidity premium for period t L 2 < L 3 < …

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-19 McGraw-Hill/Irwin Market Segmentation Theory Individual investors and FIs have specific maturity preferences Interest rates are determined by distinct supply and demand conditions within many maturity segments Investors and borrowers deviate from their preferred maturity segment only when adequately compensated to do so Individual investors and FIs have specific maturity preferences Interest rates are determined by distinct supply and demand conditions within many maturity segments Investors and borrowers deviate from their preferred maturity segment only when adequately compensated to do so

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©2009, The McGraw-Hill Companies, All Rights Reserved 2-20 McGraw-Hill/Irwin Implied Forward Rates A forward rate (f) is an expected rate on a short-term security that is to be originated at some point in the future The one-year forward rate for any year N in the future is: A forward rate (f) is an expected rate on a short-term security that is to be originated at some point in the future The one-year forward rate for any year N in the future is:

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