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##### Chapter Two

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**Chapter Two**Determinants of Interest Rates**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**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**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 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 = $1,254.40**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**Calculating Present Value (PV) of a Lump Sum**PV = FVn(1/(1 + i/m))nm = FVn(PVIFi/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**Calculation of Present Value (PV) of an Annuity**nm PV = PMT (1/(1 + i/m))t = PMT(PVIFAi/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**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(PVIFAi/m,nm) at 8% interest - = $10,000(18.913926) = $189,139.26 at 12% interest - = $10,000(16.935542) = $169,355.42 at 16% interest - = $10,000(15.246963) = $152,469.63**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**Future Values Equations**• FV of lump sum equation • FVn = PV(1 + i/m)nm = PV(FVIF i/m, nm) • FV of annuity payment equation • (nm-1) • FVn = PMT (1 + i/m)t = PMT(FVIFAi/m, mn) • (t = 1)**Relation between Interest Rates and Present and Future**Values Present Value (PV) Future Value (FV) Interest Rate Interest Rate**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)4 - 1 = 8.24% At 12% interest - EAR = (1 + .12/4)4 - 1 = 12.55%**Discount Yields**Money market instruments (e.g., Treasury bills and commercial paper) that are bought and sold on a discount basis idy = [(Pt - Po)/Pf](360/h) Where: Pf = Face value Po = Discount price of security**Single Payment Yields**Money market securities (e.g., jumbo CDs, fed funds) that pay interest only once during their lives: at maturity ibey = ispy(365/360)**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**Supply of Loanable Funds**Demand Supply Interest Rate Quantity of Loanable Funds Supplied and Demanded**Funds Supplied and Demanded by Various Groups (in billions**of dollars) Funds SuppliedFunds Demanded Households $31,866.4 $ 6,624.4 Business -- nonfinancial 7,400.0 30,356.2 Business -- financial 27,701.9 29,431.1 Government units 6,174.8 10,197.9 Foreign participants 6,164.8 2,698.3**Determination of Equilibrium Interest Rates**D S Interest Rate I H i E I L Q Quantity of Loanable Funds Supplied and Demanded**Effect on Interest rates from a Shift in the Demand Curve**for or Supply curve of Loanable Funds Increased supply of loanable funds Increased demand for loanable funds DD* Interest Rate SS SS DD DD SS* i** E* E i* E i* E* i** Q* Q** Q* Q** Quantity of Funds Supplied Quantity of Funds Demanded**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 (continued)**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**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% - 2.70% = 2.38%**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 DRPj = ijt - iTt Example: DRPAaa = 7.55% - 6.35% = 1.20% DRPBbb = 8.15% - 6.35% = 1.80%**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. im = ic(1 - ts - tF) Where: ic = Interest rate on a corporate bond im = Interest rate on a municipal bond ts = State plus local tax rate tF = Federal tax rate**Term to Maturity and Interest Rates: Yield Curve**(a) Upward sloping (b) Inverted or downward sloping (c) Humped (d) Flat Yield to Maturity (a) (d) (c) (b) Time to Maturity**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**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 __ R2 = [(1 + R1)(1 + (f2))]1/2 - 1 where f2 = expected one-year rate for year 2, or the implied forward one-year rate for next year