Copyright © 2015 by McGraw-Hill Education. All rights reserved. Chapter Two Determinants of Interest Rates

2-2 Interest Rate Fundamentals Nominal interest rates: the interest rates actually observed in financial markets Used to determine fair present value and prices of securities Two components: Opportunity cost Adjustments for individual security characteristics Nominal interest rates: the interest rates actually observed in financial markets Used to determine fair present value and prices of securities Two components: Opportunity cost Adjustments for individual security characteristics

Real Riskless Interest Rates Additional purchasing power required to forego current consumption What causes differences in nominal and real interest rates? If you wish to earn a 3% real return and prices are expected to increase by 2%, what rate must you charge? Irving Fisher first postulated that interest rates contain a premium for expected inflation. Additional purchasing power required to forego current consumption What causes differences in nominal and real interest rates? If you wish to earn a 3% real return and prices are expected to increase by 2%, what rate must you charge? Irving Fisher first postulated that interest rates contain a premium for expected inflation. 2-3

2-4 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

2-5 Supply and Demand of Loanable Funds Interest Rate Quantity of Loanable Funds Supplied and Demanded DemandSupply

2-6 Key Interest Rates Over Time

Net Supply & Demand of Funds in U.S. in

Determinants of Household Savings 1. Interest rates and tax policy 2. Income and wealth: the greater the wealth or income, the greater the amount saved, 3. Attitudes about saving versus borrowing, 4. Credit availability, the greater the amount of easily obtainable consumer credit the lower the need to save, 5. Job security and belief in soundness of entitlements. 1. Interest rates and tax policy 2. Income and wealth: the greater the wealth or income, the greater the amount saved, 3. Attitudes about saving versus borrowing, 4. Credit availability, the greater the amount of easily obtainable consumer credit the lower the need to save, 5. Job security and belief in soundness of entitlements. 2-8

Determinants of Foreign Funds Invested in the U.S. 1. Relative interest rates and returns on global investments 2. Expected exchange rate changes 3. Safe haven status of U.S. investments 4. Foreign central bank investments in the U.S. 1. Relative interest rates and returns on global investments 2. Expected exchange rate changes 3. Safe haven status of U.S. investments 4. Foreign central bank investments in the U.S. 2-9

Determinants of Foreign Funds Invested in the U.S. Source: Economist,

Federal Government Demand for Funds 2-11 Source: CBO 2013 report,

Federal Government Demand for Funds Federal debt held by the public was $11.9 trillion in 2013 (71% of GDP) and is projected to grow to $21.0 trillion by 2024 (78% of projected 2020 GDP) Large potential for crowding out and/or dependence on foreign investment Federal debt held by the public was $11.9 trillion in 2013 (71% of GDP) and is projected to grow to $21.0 trillion by 2024 (78% of projected 2020 GDP) Large potential for crowding out and/or dependence on foreign investment 2-12

Federal Government Demand for Funds Total Federal Debt was $16.7 trillion in 2013 and is projected to grow to $27.0 trillion by 2024 Interest expense is projected to grow as well, amount depends on spending and interest rates Total Federal Debt was $16.7 trillion in 2013 and is projected to grow to $27.0 trillion by 2024 Interest expense is projected to grow as well, amount depends on spending and interest rates 2-13

Business Demand for Funds Level of interest rates: When the cost of loanable funds is high businesses finance internally, Expected future profitability vs. risk: The greater the number of profitable projects available to businesses, Expected economic growth Level of interest rates: When the cost of loanable funds is high businesses finance internally, Expected future profitability vs. risk: The greater the number of profitable projects available to businesses, Expected economic growth 2-14

2-15 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

Factors that Cause Supply and Demand Curves to Shift 2-16

Factors that Cause Supply and Demand Curves to Shift 2-17

Factors that Cause Supply and Demand Curves to Shift 2-18

2-19 Determinants of Interest Rates for Individual Securities i j * = f(IP, RFR, DRP j, LRP j, SCP j, MP j ) Inflation (IP) IP = [(CPI t+1 ) – (CPI t )]/(CPI t ) x (100/1) Real risk-free interest rate (RFR) and the Fisher effect RFR = i – Expected (IP) i j * = f(IP, RFR, DRP j, LRP j, SCP j, MP j ) Inflation (IP) IP = [(CPI t+1 ) – (CPI t )]/(CPI t ) x (100/1) Real risk-free interest rate (RFR) and the Fisher effect RFR = i – Expected (IP)

2-20 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)

2-21 DRPs over Time

2-22 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

2-23 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

2-24 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 < …<L N 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 < …<L N

2-25 UET vs. Liquidity Premium Theory

2-26 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

2-27 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:

2-28 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, most common 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, most common

2-29 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

2-30 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

2-31 Relation between Interest Rates and Present and Future Values Present Value (PV) Interest Rate Future Value (FV) Interest Rate

2-32 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

2-33 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

2-34 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 per period ) 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 per period ) c – 1 c = the number of compounding periods per year

2-35 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)