1 / 31

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.

colby-freeman
Download Presentation

Chapter Two

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter Two Determinants of Interest Rates

  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

  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

  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

  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

  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 • 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

  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

  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

  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

  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

  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

  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)

  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

  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

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

  16. Equivalent Annual Return (EAR) If you invest in a security that matures in 75 days and offers a 7% annual interest rate: EAR = (1 + i/(365/h))365/h - 1 =(1 + (.07)/(365/75))365/75 - 1 = 7.20%

  17. Discount Yields Money market instruments (e.g., Treasury bills and commercial paper) that are bought and sold on a discount basis idy = [(Pf - Po)/Pf](360/h) Where: Pf = Face value Po = Discount price of security

  18. 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)

  19. 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

  20. Supply of Loanable Funds Demand Supply Interest Rate Quantity of Loanable Funds Supplied and Demanded

  21. Funds Supplied and Demanded by Various Groups (in billions of dollars) Funds SuppliedFunds DemandedNet Households $30,857.3 $12,849.2 $18,002.1 Business - nonfinancial 9,892.5 28,229.9 -18,337.4 Business - financial 29,508.9 39,484.7 -9,975.8 Government units 10,072.9 4,873.7 5,199.2 Foreign participants 8,193.8 3,081.9 5,111.9

  22. Determination of Equilibrium Interest Rates D S Interest Rate I H i E I L Q Quantity of Loanable Funds Supplied and Demanded

  23. 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

  24. 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)

  25. 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 • Term to Maturity

  26. 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%

  27. 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 = 6.61% - 5.48% = 1.13% DRPBaa = 7.92% - 5.48% = 2.44%

  28. 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

  29. 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

  30. 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

  31. 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

More Related