Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Chapter Two Determinants of Interest Rates

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Calculation of Simple Interest Value = Principal + Interest Example: $1,000 to invest for a period of two years at 12 percent Value = $1,000 + $1,000(.12)(2) = $1,240 Value = Principal + Interest Example: $1,000 to invest for a period of two years at 12 percent Value = $1,000 + $1,000(.12)(2) = $1,240

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Value of Compound Interest Value = Principal + Interest + Compounded interest Value = $1,000 + $1,000(12)(2) + $1,000(12)(2) = $1,000[1 + 2(12) + (12) 2 ] = $1,000(1.12) 2 = $1, Value = Principal + Interest + Compounded interest Value = $1,000 + $1,000(12)(2) + $1,000(12)(2) = $1,000[1 + 2(12) + (12) 2 ] = $1,000(1.12) 2 = $1,254.40

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Present Values 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 a single cash payment received at the end of some investment horizon –annuity a series of equal cash payments received at fixed intervals over the investment horizon 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 a single cash payment received at the end of some investment horizon –annuity a series of equal cash payments received at fixed intervals over the investment horizon PVs decrease as interest rates increase

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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 n = number of years in investment horizon m = number of compounding periods in a year 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 n = number of years in investment horizon m = number of compounding periods in a year PVIF = present value interest factor of a lump sum

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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 i = simple annual interest n = number of years in investment horizon m = number of compounding periods in a year 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 i = simple annual interest n = number of years in investment horizon m = number of compounding periods in a year PVIFA = present value interest factor of an annuity

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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 quarter for the next 6 years in exchange for a fixed payment today. PV = PMT(PVIFA i/m,nm ) at 8% interest - = $10,000( ) = $189, at 12% interest - = $10,000( ) = $169, at 16% interest - = $10,000( ) = $152, You are offered a security investment that pays $10,000 on the last day of every quarter for the next 6 years in exchange for a fixed payment today. PV = PMT(PVIFA i/m,nm ) at 8% interest - = $10,000( ) = $189, at 12% interest - = $10,000( ) = $169, at 16% interest - = $10,000( ) = $152,469.63

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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 = 1) 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 = 1)

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Relation between Interest Rates and Present and Future Values Present Value (PV) Interest Rate Future Value (FV) Interest Rate

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Equivalent Annual Return (EAR) Rate returned over a 12-month period taking the compounding of interest into account EAR = (1 + i/m) m - 1 At 8% interest - EAR = (1 +.08/4) = 8.24% At 12% interest - EAR = (1 +.12/4) = 12.55% Rate returned over a 12-month period taking the compounding of interest into account EAR = (1 + i/m) m - 1 At 8% interest - EAR = (1 +.08/4) = 8.24% At 12% interest - EAR = (1 +.12/4) = 12.55%

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Discount Yields Money market instruments (e.g., Treasury bills and commercial paper) that are bought and sold on a discount basis i dy = [(P t - P o )/P f ](360/h) Where: P f = Face value P o = Discount price of security Money market instruments (e.g., Treasury bills and commercial paper) that are bought and sold on a discount basis i dy = [(P t - P o )/P f ](360/h) Where: P f = Face value P o = Discount price of security

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Single Payment Yields Money market securities (e.g., jumbo CDs, fed funds) that pay interest only once during their lives: at maturity i bey = i spy (365/360) Money market securities (e.g., jumbo CDs, fed funds) that pay interest only once during their lives: at maturity i bey = i spy (365/360)

Copyright © 2001 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 © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Supply of Loanable Funds Interest Rate Quantity of Loanable Funds Supplied and Demanded DemandSupply

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Funds Supplied and Demanded by Various Groups (in billions of dollars) Funds Supplied Funds Demanded Households $31,866.4 $ 6,624.4 Business -- nonfinancial 7, ,356.2 Business -- financial 27, ,431.1 Government units 6, ,197.9 Foreign participants 6, ,698.3 Funds Supplied Funds Demanded Households $31,866.4 $ 6,624.4 Business -- nonfinancial 7, ,356.2 Business -- financial 27, ,431.1 Government units 6, ,197.9 Foreign participants 6, ,698.3

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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**

Copyright © 2001 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 © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Liquidity Risk –risk that a security can not be sold at a predictable price with low transaction cost on short notice Special Provisions –taxability –convertibility –callability Time 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 –convertibility –callability Time to Maturity

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Inflation and Interest Rates: The Fischer Effect The interest rate should compensate an investor for both expected inflation and the opportunity cost of foregone consumption (the real rate component) i = Expected (IP) + RIR Example: 5.08% % = 2.38% The interest rate should compensate an investor for both expected inflation and the opportunity cost of foregone consumption (the real rate component) i = Expected (IP) + RIR Example: 5.08% % = 2.38%

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 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: DRP Aaa = 7.55% % = 1.20% DRP Bbb = 8.15% % = 1.80% 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: DRP Aaa = 7.55% % = 1.20% DRP Bbb = 8.15% % = 1.80%

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin 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 © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill /Irwin Term to Maturity and Interest Rates: Yield Curve Yield to Maturity Time to Maturity (a) (b) (c) (d) (a) Upward sloping (b) Inverted or downward sloping (c) Humped (d) Flat

Copyright © 2001 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 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 demand a higher maturity premium

Copyright © 2001 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 _ _ R 2 = [(1 + R 1 )(1 + (f 2 ))] 1/2 - 1 where f 2 = 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 _ _ R 2 = [(1 + R 1 )(1 + (f 2 ))] 1/2 - 1 where f 2 = expected one-year rate for year 2, or the implied forward one-year rate for next year