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Chapter Two

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.

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Chapter Two

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  1. Chapter Two Determinants of Interest Rates McGraw-Hill/Irwin

  2. 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 McGraw-Hill/Irwin

  3. 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 McGraw-Hill/Irwin

  4. Calculation of Simple Interest Value = Principal + Interest (year 1) + Interest (year 2) Example: $1,000 to invest for a period of two years at 12 percent Value = $1,000 + $1,000(.12) + $1,000(.12) = $1,000 + $1,000(.12)(2) = $1,240 McGraw-Hill/Irwin

  5. Value of Compound Interest Value = Principal + Interest + Compounded interest Value = $1,000 + $1,000(.12) + $1,000(.12) + $1,000(.12) = $1,000[1 + 2(.12) + (.12)2] = $1,000(1.12)2 = $1,254.40 McGraw-Hill/Irwin

  6. Present Value of a Lump Sum • 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 • annuity • PVs decrease as interest rates increase McGraw-Hill/Irwin

  7. 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 rate earned n = number of years in investment horizon m = number of compounding periods in a year i/m = periodic rate earned on investments nm = total number of compounding periods PVIF = present value interest factor of a lump sum McGraw-Hill/Irwin

  8. 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 McGraw-Hill/Irwin

  9. 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 horizon i/m = periodic rate earned on investments nm = total number of compounding periods PVIFA = present value interest factor of an annuity McGraw-Hill/Irwin

  10. Calculation of Present Value of an Annuity You are offered a security investment that pays $10,000 on the last day of every year for the next 6 years in exchange for a fixed payment today. PV = PMT(PVIFAi/m,nm) at 8% interest - = $10,000(4.622880) = $46,228.80 If the investment pays on the last day of every quarter for the next six years at 8% interest - = $10,000(18.913926) = $189,139.26 McGraw-Hill/Irwin

  11. 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 McGraw-Hill/Irwin

  12. 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 = 0) McGraw-Hill/Irwin

  13. 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 • 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 • at 16% interest compounded semiannually • = $10,000(2.518170) = $25,181.70 McGraw-Hill/Irwin

  14. Calculation of the Future Value of an Annuity • You invest $10,000 on the last day of every year for the next six years, • at 8% interest = $10,000(7.335929) = $73,359.29 • If the investment pays you $10,000 on the last day of every quarter for the next six years, • FV = $10,000(30.421862) = $304,218.62 • If the annuity is paid on the first day of each quarter, • FV = $10,000(31.030300) = $310,303.00 McGraw-Hill/Irwin

  15. Relation between Interest Rates and Present and Future Values Present Value (PV) Future Value (FV) Interest Rate Interest Rate McGraw-Hill/Irwin

  16. 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 c = number of compounding periods per year McGraw-Hill/Irwin

  17. 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 McGraw-Hill/Irwin

  18. Supply of Loanable Funds Demand Supply Interest Rate Quantity of Loanable Funds Supplied and Demanded McGraw-Hill/Irwin

  19. 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 McGraw-Hill/Irwin

  20. Determination of Equilibrium Interest Rates D S Interest Rate I H i E I L Q Quantity of Loanable Funds Supplied and Demanded McGraw-Hill/Irwin

  21. 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 McGraw-Hill/Irwin

  22. Factors Affecting Nominal Interest Rates • Inflation • Real Interest Rate • Default Risk • Liquidity Risk • Special Provisions • Term to Maturity McGraw-Hill/Irwin

  23. Inflation and Interest Rates: The Fisher Effect The 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: 3.49% - 1.60% = 1.89% McGraw-Hill/Irwin

  24. 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% McGraw-Hill/Irwin

  25. 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 McGraw-Hill/Irwin

  26. Term Structure of Interest Rates • Unbiased Expectations Theory • Liquidity Premium Theory • Market Segmentation Theory McGraw-Hill/Irwin

  27. 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 __ 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 McGraw-Hill/Irwin

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