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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 is reinvested Simple interest interest earned on an investment is is not reinvested

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

5 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) 22 ]] = \$1,000(1.12) 22 = \$1,254.40

6 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 to present using current market interest rate lump sum payment a single cash payment received at at the the end of of some investment horizon annuity a series of of equal cash payments received at at fixed intervals over the the investment horizon PVs decrease as as interest rates increase

7 Calculating Present Value (PV) of a Lump Sum PV = FV nm n (1/(1 + i/m)) nm = FV n (PVIF i/m,nm ) where: PV = present value FV = future value (lump sum) received in in n years i i = simple annual interest n = number of of years in in investment horizon m = number of of compounding periods in in a year PVIF = present value interest factor of of a lump sum

8 Calculation of Present Value (PV) of an Annuity nm nm PV = PMT (1/(1 + i/m)) t t = PMT(PVIFA i/m,nm ) t t = 1 where: PV = present value PMT = periodic annuity payment received during investment i i = simple annual interest n = number of of years in in investment horizon m = number of of compounding periods in in a year PVIFA = present value interest factor of of an annuity

9 Calculation of Present Value of an Annuity You are offered a security investment that pays \$10,000 on the last day of of every quarter for the next 6 years in in exchange for a fixed payment today. PV = PMT(PVIFA i/m,nm i/m,nm ) at at 8% interest - = \$10,000( ) = \$189, at at 12% interest - = \$10,000( ) = \$169, at at 16% interest - = \$10,000( ) = \$152,469.63

10 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

11 Future Values Equations FV of lump sum equation FV n = PV(1 + i/m) nm nm = PV(FVIF i/m, i/m, nm nm ) FV of annuity payment equation (nm-1) FV n = PMT (1 (1 + i/m) t t = PMT(FVIFA i/m, i/m, mn mn ) (t (t = 1) 1)

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

13 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 (1 +.08/4) 4-1 = 8.24% At 12% interest - EAR = (1 (1 +.12/4) 4-1 = 12.55%

14 Discount Yields Money market instruments (e.g., Treasury bills and commercial paper) that are bought and sold on a discount basis i dy dy = [(P tt - P o )/P f f ](360/h) Where: P f f = Face value P o o = Discount price of of security

15 Single Payment Yields Money market securities (e.g., jumbo CDs, fed funds) that pay interest only once during their lives: at maturity i bey bey = i spy spy (365/360)

16 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

17 Supply of Loanable Funds Interest Rate Demand Supply Quantity of Loanable Funds Supplied and Demanded

18 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

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

20 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 Interest Rate DD SS SS* DD DD* SS i* i** E E* i** i* E E* Q* Q** Quantity of Funds Supplied Q* Q** Quantity of Funds Demanded

21 Factors Affecting Nominal Interest Rates Inflation continual increase in in price of of goods/services Real Interest Rate nominal interest rate in in the absence of of inflation Default Risk risk that issuer will fail to to make promised payment (continued)

22 Liquidity Risk risk that a security can not be sold at at a predictable price with low transaction cost on short notice Special Provisions taxability convertibility callability Time to Maturity

23 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%

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 DRP j j = i jt jt - i Tt Tt Example: DRP Aaa Aaa = 7.55% % = 1.20% DRP Bbb Bbb = 8.15% % = 1.80%

25 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 ss - t F ) Where: i c i = c Interest rate rate on on a corporate bond ii m = Interest rate rate on on a municipal bond tt s = s State plus local tax tax rate rate tt F = Federal tax tax rate rate

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

27 Term Structure of Interest Rates Unbiased Expectations Theory at at a given point in in time, the yield curve reflects the market s current expectations of of future short-term rates Liquidity Premium Theory investors will only hold long-term maturities if if they are offered a premium to to compensate for future uncertainty in in a security s value Market Segmentation Theory investors have specific maturity preferences and will demand a higher maturity premium

28 Forecasting Interest Rates Forward rate is is an expected or implied rate on a security that is is to be originated at some point in the future using the unbiased expectations theory R (f 1/2 2 = [(1 + R 1 )(1 + (f 2 ))] 1/2-1 where ff 22 = expected one-year rate for for year 2, 2, or or the the implied forward one-year rate for for next year

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Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save \$300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years