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- 1. 3- McGraw-Hill/Irwin Chapter Three Interest Rates and Security Valuation
- 2. Various Interest Rate Measures <ul><li>Coupon rate </li></ul><ul><ul><li>periodic cash flow a bond issuer contractually promises to pay a bond holder </li></ul></ul><ul><li>Required rate of return ( rrr ) </li></ul><ul><ul><li>rates used by individual market participants to calculate fair present values ( PV ) </li></ul></ul><ul><li>Expected rate of return ( Err ) </li></ul><ul><ul><li>rates participants would earn by buying securities at current market prices ( P ) </li></ul></ul><ul><li>Realized rate of return ( rr ) </li></ul><ul><ul><li>rates actually earned on investments </li></ul></ul>3- McGraw-Hill/Irwin
- 3. Required Rate of Return <ul><li>The fair present value ( PV ) of a security is determined using the required rate of return ( rrr ) as the discount rate </li></ul><ul><li>CF 1 = cash flow in period t ( t = 1, …, n ) </li></ul><ul><li>~ = indicates the projected cash flow is uncertain </li></ul><ul><li>n = number of periods in the investment horizon </li></ul>3- McGraw-Hill/Irwin
- 4. Expected Rate of Return <ul><li>The current market price ( P ) of a security is determined using the expected rate of return ( Err ) as the discount rate </li></ul><ul><li>CF 1 = cash flow in period t ( t = 1, …, n ) </li></ul><ul><li>~ = indicates the projected cash flow is uncertain </li></ul><ul><li>n = number of periods in the investment horizon </li></ul>3- McGraw-Hill/Irwin
- 5. Realized Rate of Return <ul><li>The realized rate of return ( rr ) is the discount rate that just equates the actual purchase price ( ) to the present value of the realized cash flows ( RCF t ) t ( t = 1, …, n ) </li></ul>3- McGraw-Hill/Irwin
- 6. Bond Valuation <ul><li>The present value of a bond ( V b ) can be written as: </li></ul><ul><li>M = the par value of the bond </li></ul><ul><li>INT = the annual interest (or coupon) payment </li></ul><ul><li>T = the number of years until the bond matures </li></ul><ul><li>i = the annual interest rate (often called yield to maturity (ytm) ) </li></ul>3- McGraw-Hill/Irwin
- 7. Bond Valuation <ul><li>A premium bond has a coupon rate ( INT) greater then the required rate of return ( rrr ) and the fair present value of the bond ( V b ) is greater than the face value ( M ) </li></ul><ul><li>Discount bond: if INT < rrr , then V b < M </li></ul><ul><li>Par bond: if INT = rrr, then V b = M </li></ul>3- McGraw-Hill/Irwin
- 8. Equity Valuation <ul><li>The present value of a stock ( P t ) assuming zero growth in dividends can be written as: </li></ul><ul><li>D = dividend paid at end of every year </li></ul><ul><li>P t = the stock’s price at the end of year t </li></ul><ul><li>i s = the interest rate used to discount future cash flows </li></ul>3- McGraw-Hill/Irwin
- 9. Equity Valuation <ul><li>The present value of a stock ( P t ) assuming constant growth in dividends can be written as: </li></ul><ul><li>D 0 = current value of dividends </li></ul><ul><li>D t = value of dividends at time t = 1, 2, …, ∞ </li></ul><ul><li>g = the constant dividend growth rate </li></ul>3- McGraw-Hill/Irwin
- 10. Equity Valuation <ul><li>The return on a stock with zero dividend growth, if purchased at price P 0 , can be written as: </li></ul><ul><li>The return on a stock with constant dividend growth, if purchased at price P 0 , can be written as: </li></ul>3- McGraw-Hill/Irwin
- 11. Relation between Interest Rates and Bond Values 3- McGraw-Hill/Irwin Interest Rate Bond Value 12% 10% 8% 874.50 1,000 1,152.47
- 12. Impact of Maturity on Interest Rate Sensitivity 3- McGraw-Hill/Irwin Absolute Value of Percent Change in a Bond’s Price for a Given Change in Interest Rates Time to Maturity
- 13. Impact of Coupon Rates on Interest Rate Sensitivity 3- McGraw-Hill/Irwin Bond Value Interest Rate Low-Coupon Bond High-Coupon Bond
- 14. Duration <ul><li>Duration is the weighted-average time to maturity (measured in years) on a financial security </li></ul><ul><li>Duration measures the sensitivity (or elasticity) of a fixed-income security’s price to small interest rate changes </li></ul>3- McGraw-Hill/Irwin
- 15. Duration <ul><li>Duration ( D ) for a fixed-income security that pays interest annually can be written as: </li></ul><ul><li>t = 1 to T , the period in which a cash flow is received </li></ul><ul><li>T = the number of years to maturity </li></ul><ul><li>CF t = cash flow received at end of period t </li></ul><ul><li>R = yield to maturity or required rate of return </li></ul><ul><li>PV t = present value of cash flow received at end of period t </li></ul>3- McGraw-Hill/Irwin
- 16. Duration <ul><li>Duration ( D ) (measured in years) for a fixed-income security in general can be written as: </li></ul><ul><li>m = the number of times per year interest is paid </li></ul>3- McGraw-Hill/Irwin
- 17. Duration <ul><li>Duration and coupon interest </li></ul><ul><ul><li>the higher the coupon payment, the lower the bond’s duration </li></ul></ul><ul><li>Duration and yield to maturity </li></ul><ul><ul><li>the higher the yield to maturity, the lower the bond’s duration </li></ul></ul><ul><li>Duration and maturity </li></ul><ul><ul><li>duration increases with maturity at a decreasing rate </li></ul></ul>3- McGraw-Hill/Irwin
- 18. Duration and Modified Duration <ul><li>Given an interest rate change, the estimated percentage change in a (annual coupon paying) bond’s price is found by rearranging the duration formula: </li></ul><ul><li>MD = modified duration = D /(1 + R ) </li></ul>3- McGraw-Hill/Irwin
- 19. Figure 3-7 3- McGraw-Hill/Irwin
- 20. Convexity <ul><li>Convexity ( CX ) measures the change in slope of the price-yield curve around interest rate level R </li></ul><ul><li>Convexity incorporates the curvature of the price-yield curve into the estimated percentage price change of a bond given an interest rate change: </li></ul>3- McGraw-Hill/Irwin

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