Chapter Two

1. Chapter Two Determinants of Interest Rates

2. Chapter Outline • Time Value of Money Review • Effective Rate vs. Quoted Rates • Loanable Funds Theory • Factors Affecting Nominal Interest Rates • Term Structure of Interest Rate • Forecasting Interest Rate

3. 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

4. 1. Time Value of Money Review • Compound interest vs. simple interest • Present Value and Future Value of Lump Sum and Annuity PV=FV (PVIFr,t)=FV(PVIFi/m,nm) PV=PMT (PVIFAr,t)=PMT(PVIFAi/m,nm) FV=PV (FVIFr,t)=PV(FVIF i/m, nm) FV=PMT(FVIFAr,t)= PMT(FVIFAi/m, nm)

5. 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(PVIFi/m,nm) • at 8% interest = $10,000(0.630170) = $6,301.70 • at 12% interest = $10,000(0.506631) = $5,066.31 • at 16% interest = $10,000(0.410442) = $4,104.42

6. 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 • FV = PV(FVIFi/m,nm) • at 8% interest = $10,000(1.586874) = $15,868.74 • at 12% interest = $10,000(1.973823) = $19,738.23 • at 16% interest = $10,000(2.436396) = $24,363.96

7. Relation between Interest Rates and Present and Future Values Present Value (PV) Future Value (FV) Interest Rate Interest Rate

8. 2. 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 r = period rate c = number of compounding periods per year

9. 3. 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

10. Supply and Demand of Loanable Funds Demand Supply Interest Rate Quantity of Loanable Funds

11. Funds Supplied and Demanded by Various Groups (in billions of dollars) Funds SuppliedFunds DemandedNet Households $34,860.7 $15,197.4 $19,663.3 Business - nonfinancial 12,679.2 30,779.2 -12,100.0 Business - financial 31,547.9 45061.3 -13,513.4 Government units 12,574.5 6,695.2 5,879.3 Foreign participants 8,426.7 2,355.9 6,070.8

12. Factors Shifting Demand & Supply Curve • Supply • Wealth • Risk of financial security • Near-term spending needs • Monetary expansion • Economic conditions • Demand • Utility derived from asset purchased with borrowed funds • Restrictiveness of nonprice conditions • Economic conditions

13. Effect on Interest rates from a Shift in the Demand Curve for or Supply curve 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

14. 4. 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)

15. Liquidity Risk • risk that a security can not be sold at a predictable price with low transaction cost on short notice • Special Provisions • taxability • Term to Maturity

16. Inflation and Interest Rates: The Fisher Effect • The nominal 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(p. 47): 3.49% - 1.60% = 1.89%

17. 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 for December 2003: DRPAaa = 5.66% - 4.01% = 1.65% DRPBaa = 6.76% - 4.01% = 2.75%

18. Liquidity Risk and Interest Rates The risk that a security need to be sold at low prices because of inactive trading LRPj = ijt - iTt

19. 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

20. Term to Maturity and Interest Rates: Yield Curve (a) Upward sloping (b) Inverted or downward sloping (c) Flat Yield to Maturity (a) (c) (b) Time to Maturity

21. 5. 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 generally demand a higher maturity premium

22. 6. 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 • Spot rate is the yield to maturity of a zero-coupon bond • __ • 1R2 = [(1 + 1R1)(1 + (2f1))]1/2 - 1 • where • 2 f1 = expected one-year rate for year 2, or the implied • forward one-year rate for next year