1. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-1 McGraw-Hill/Irwin Chapter Two Determinants of Interest Rates

2. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-2 McGraw-Hill/Irwin 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 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. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-3 McGraw-Hill/Irwin 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 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. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-4 McGraw-Hill/Irwin 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 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. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-5 McGraw-Hill/Irwin 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 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. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-6 McGraw-Hill/Irwin Present Value of a Cashflow 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 PVs decrease as interest rates increase 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 PVs decrease as interest rates increase

7. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-7 McGraw-Hill/Irwin Calculating the Present Value (PV) of a Cashflow PV = FV n (1/(1 + i/m)) nm = FV n (PVIF i/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 PV = FV n (1/(1 + i/m)) nm = FV n (PVIF i/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. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-8 McGraw-Hill/Irwin 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(PVIF i/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 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(PVIF i/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. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-9 McGraw-Hill/Irwin 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 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

10. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-10 McGraw-Hill/Irwin 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 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

11. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-11 McGraw-Hill/Irwin Relation between Interest Rates and Present and Future Values Present Value (PV) Interest Rate Future Value (FV) Interest Rate

12. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-12 McGraw-Hill/Irwin 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 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

13. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-13 McGraw-Hill/Irwin 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

14. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-14 McGraw-Hill/Irwin Supply of Loanable Funds Interest Rate Quantity of Loanable Funds Supplied and Demanded DemandSupply

15. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-15 McGraw-Hill/Irwin Funds Supplied and Demanded by Various Groups (in billions of dollars) Funds Supplied Funds Demanded Net 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 Funds Supplied Funds Demanded Net 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

16. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-16 McGraw-Hill/Irwin Determination of Equilibrium Interest Rates Interest Rate Quantity of Loanable Funds Supplied and Demanded D S I H i I L E Q

17. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-17 McGraw-Hill/Irwin Effect on Interest rates from a Shift in the Demand Curve for or Supply curve of Loanable Funds Increased supply of loanable funds Quantity of Funds Supplied Interest Rate DD SS SS* E E* Q* i* Q** i** Increased demand for loanable funds Quantity of Funds Demanded DD DD* SS E E* i* i** Q*Q**

18. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-18 McGraw-Hill/Irwin 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 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)

19. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-19 McGraw-Hill/Irwin Liquidity Risk –risk that a security can not be sold at a predictable price with low transaction cost on short notice Special Provisions –Taxability (Exempt = Lower rate paid) –Convertibility (Lower rate paid) –Callability (Higher rate paid) Time to Maturity Liquidity Risk –risk that a security can not be sold at a predictable price with low transaction cost on short notice Special Provisions –Taxability (Exempt = Lower rate paid) –Convertibility (Lower rate paid) –Callability (Higher rate paid) Time to Maturity

20. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-20 McGraw-Hill/Irwin 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% 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%

21. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-21 McGraw-Hill/Irwin 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 = i jt - i Tt Example: DRP Aaa = 7.55% - 6.35% = 1.20% DRP Bbb = 8.15% - 6.35% = 1.80% Both bonds are 30 year bonds. 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 = i jt - i Tt Example: DRP Aaa = 7.55% - 6.35% = 1.20% DRP Bbb = 8.15% - 6.35% = 1.80% Both bonds are 30 year bonds.

22. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-22 McGraw-Hill/Irwin 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 EXEMPT = i TAX * (1 - t s - t F ) i EXEMPT / (1 - t s - t F ) = i TAX Where: i TAX = Taxable equivalent rate i EXEMPT = Interest rate on a municipal bond t s = State plus local tax rate t F = Federal tax rate 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 EXEMPT = i TAX * (1 - t s - t F ) i EXEMPT / (1 - t s - t F ) = i TAX Where: i TAX = Taxable equivalent rate i EXEMPT = Interest rate on a municipal bond t s = State plus local tax rate t F = Federal tax rate

23. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-23 McGraw-Hill/Irwin Term to Maturity and Interest Rates: Yield Curve Yield to Maturity Time to Maturity (a) (b) (c) (a) Upward sloping (b) Inverted or downward sloping (c) Flat

24. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-24 McGraw-Hill/Irwin 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 –an extension of the unbiased expectations theory, namely, 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 to move outside of that preferred maturity 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 –an extension of the unbiased expectations theory, namely, 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 to move outside of that preferred maturity

25. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-25 McGraw-Hill/Irwin Chapter Three Interest Rates and Security Valuation

26. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-26 McGraw-Hill/Irwin Various Interest Rate Measures Coupon rate Required Rate of Return Expected rate of return Realized Rate of Return Coupon rate Required Rate of Return Expected rate of return Realized Rate of Return

27. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-27 McGraw-Hill/Irwin Bond Valuation The valuation of a bond instrument employs time value of money concepts –Reflects present value of all cash flows promised or projected, discounted at the required rate of return (rrr) –Expected rate of return (Err) is the interest rate that equates the current market price to the present value of all promised cash flows received over the life of the bond –Realized rate of return (rr) on a bond is the actual return earned on a bond investment that has already taken place The valuation of a bond instrument employs time value of money concepts –Reflects present value of all cash flows promised or projected, discounted at the required rate of return (rrr) –Expected rate of return (Err) is the interest rate that equates the current market price to the present value of all promised cash flows received over the life of the bond –Realized rate of return (rr) on a bond is the actual return earned on a bond investment that has already taken place

28. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-28 McGraw-Hill/Irwin Bond Valuation Formula V b = INT/2 + INT/2 +... + INT/2 __ (1 + i d /2) 1 (1 + i d /2) 2 (1 + i d /2) 2N + M_ _ _ (1 + i d /2) 2N Where: V b = Present value of the bond M = Par or face value of the bond INT = Annual interest (or coupon) payment per year on the bond; equals the par value of the bond times the (percentage) coupon rate N = Number years until the bond matures i d = Interest rate used to discount cash flows on the bond V b = INT/2 + INT/2 +... + INT/2 __ (1 + i d /2) 1 (1 + i d /2) 2 (1 + i d /2) 2N + M_ _ _ (1 + i d /2) 2N Where: V b = Present value of the bond M = Par or face value of the bond INT = Annual interest (or coupon) payment per year on the bond; equals the par value of the bond times the (percentage) coupon rate N = Number years until the bond matures i d = Interest rate used to discount cash flows on the bond

29. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-29 McGraw-Hill/Irwin Bond Valuation Example V b = 1,000(.1) (PVIFA 8%/2, 12(2) ) + 1,000(PVIF 8%/2, 12(2) ) 2 Where: V b = $1,152.47 (solution) M = $1,000 INT = $100 per year (10% of $1,000) N = 12 years i d = 8% (rrr) PVIF = Present value interest factor of a lump sum payment PVIFA = present value interest factor of an annuity stream V b = 1,000(.1) (PVIFA 8%/2, 12(2) ) + 1,000(PVIF 8%/2, 12(2) ) 2 Where: V b = $1,152.47 (solution) M = $1,000 INT = $100 per year (10% of $1,000) N = 12 years i d = 8% (rrr) PVIF = Present value interest factor of a lump sum payment PVIFA = present value interest factor of an annuity stream

30. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-30 McGraw-Hill/Irwin A Better Example of Finding the Price of a Bond 1 CF t Time(yrs) CF t (1 + 4%) 2t (1 + 4%) 2t 1 CF t Time(yrs) CF t (1 + 4%) 2t (1 + 4%) 2t.5 1 1.5 2 2.5 3 3.5 4 50 1,050 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 48.08 46.23 44.45 42.74 41.10 39.52 38.00 767.22 Coupon/Principal Payments $1067.34 10% Coupon Bond, 8% Discount Rate, 4 Years to Maturity What’s the current price? PV factor PV of the Cashflow

31. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-31 McGraw-Hill/Irwin Description of a Premium, Discount, and Par Bond Premium bond—when the coupon rate, INT, is greater then the required rate of return, rrr, the fair present value of the bond (V b ) is greater than its face value (M) Discount bond— when INT<rrr, then V b <M Par bond— when INT=rrr, then V b =M Premium bond—when the coupon rate, INT, is greater then the required rate of return, rrr, the fair present value of the bond (V b ) is greater than its face value (M) Discount bond— when INT<rrr, then V b <M Par bond— when INT=rrr, then V b =M

32. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-32 McGraw-Hill/Irwin Yield to Maturity The return or yield the bond holder will earn on the bond if he or she buys it at its current market price, receives all coupon and principal payments as promised, and holds the bond until maturity V b = INT (PVIFA ytm/m, Nm ) + M(PVIF ytm/m,Nm ) m The return or yield the bond holder will earn on the bond if he or she buys it at its current market price, receives all coupon and principal payments as promised, and holds the bond until maturity V b = INT (PVIFA ytm/m, Nm ) + M(PVIF ytm/m,Nm ) m

33. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-33 McGraw-Hill/Irwin Summary of Factors that Affect Security Prices and Price Volatility when Interest Rates Change Interest Rate Time Remaining to Maturity Coupon Rate Interest Rate Time Remaining to Maturity Coupon Rate

34. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-34 McGraw-Hill/Irwin Impact of Interest Rate Changes on Security Values Interest Rate Bond Value Interest Rate Bond Value 12% 10% 8% 874.501,0001,152.47

35. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-35 McGraw-Hill/Irwin Balance sheet of an FI before and after an Interest Rate Increase (a) Balance Sheet before the Interest Rate Increase Assets Bond (8% required rate of return) $1,152.47 Liabilities and Equity Bond (10% required rate of return) $1,000 Equity $152.47 (b) Balance Sheet after 2% increase in the Interest Rate Increase Assets $1,000 Bond (10% required rate of return) Liabilities and Equity Bond (12% required rate of return) Equity $874.50 $125.50

36. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-36 McGraw-Hill/Irwin Impact of Maturity on Security Values 12 Years to Maturity 16 Years to Maturity Required Rate of Return Fair Price* Price Change Percentage Price Change 8% $1,152.47 -$152.47 -13.23% 10% $1,000.00 -$125.50 -12.55% 12% $874.50 Fair Price* Price Change Percentage Price Change $1,178.74 -$178.74 -15.16% $1,000.00 -$140.84 -14.08% $859.16 *The bond pays 10% coupon interest compounded semiannually and has a face value of $1,000

37. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-37 McGraw-Hill/Irwin Impact of a Bond’s Maturity on its Interest Rate Sensitivity Absolute Value of Percent Change in a Bond’s Price for a Given Change in Interest Rates Absolute Value of Percent Change in a Bond’s Price for a Given Change in Interest Rates Time to Maturity

38. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-38 McGraw-Hill/Irwin Impact of a Bond’s Coupon Rate on Its Interest Rate Sensitivity Interest Rate Interest Rate Bond Value Low-Coupon Bond High-Coupon Bond

39. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-39 McGraw-Hill/Irwin Duration: A Measure of Interest Rate Sensitivity The weighted-average time to maturity on an investment N N  CF t  t  PV t  t t = 1 (1 + R) t t = 1 D = N = N  CF t  PV t t = 1 (1 + R) t t = 1 The weighted-average time to maturity on an investment N N  CF t  t  PV t  t t = 1 (1 + R) t t = 1 D = N = N  CF t  PV t t = 1 (1 + R) t t = 1

40. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-40 McGraw-Hill/Irwin Features of the Duration Measure Duration and Coupon Interest –the higher the coupon payment, the lower is a bond’s duration Duration and Yield to Maturity –duration increases as yield to maturity increases Duration and Maturity –Duration increases with the maturity of a bond but at a decreasing rate Duration and Coupon Interest –the higher the coupon payment, the lower is a bond’s duration Duration and Yield to Maturity –duration increases as yield to maturity increases Duration and Maturity –Duration increases with the maturity of a bond but at a decreasing rate

41. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-41 McGraw-Hill/Irwin Discrepancy Between Maturity and Duration on a Coupon Bond

42. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-42 McGraw-Hill/Irwin Example of Duration Calculation 1 CF t CF t X t Percent of Initial t CF t (1 + 4%) 2t (1 + 4%) 2t (1 + 4%) 2t Investment Recovered 1 CF t CF t X t Percent of Initial t CF t (1 + 4%) 2t (1 + 4%) 2t (1 + 4%) 2t Investment Recovered.5 1 1.5 2 2.5 3 3.5 4 50 1,050 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 48.08 46.23 44.45 42.74 41.10 39.52 38.00 767.22 24.04 46.23 66.67 85.48 102.75 118.56 133.00 3,068.88 24.04/1,067.34 = 0.02 46.23/1,067.34 = 0.04 66.67/1,067.34 = 0.06 85.48/1,067.34 = 0.08 102.75/1,067.34 = 0.10 118.56/1,067.34 = 0.11 133.00/1,067.34 = 0.13 3,068.88/1,067.34 = 2.88 Duration = 3,645.61 1,067.34 = 3.42 years PV factor PV of Cashflow Time Weighted PV of Cashflow $1067.34 3.42 10% Coupon Bond, 8% Discount Rate, 4 Years to Maturity

43. ©2007, The McGraw-Hill Companies, All Rights Reserved 2-43 McGraw-Hill/Irwin Economic Meaning of Duration Measure of the average life of a bond Measure of a bond’s interest rate sensitivity (elasticity) Measure of the average life of a bond Measure of a bond’s interest rate sensitivity (elasticity)