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Understanding Interest Rates and Security Valuation

Learn about various interest rate measures, required rate of return, expected rate of return, and bond and equity valuation concepts. Discover the impact of coupon rates, maturity, and duration on bond values.

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Understanding Interest Rates and Security Valuation

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  1. Chapter Three Interest Rates and Security Valuation McGraw-Hill/Irwin

  2. Various Interest Rate Measures • Coupon rate • periodic cash flow a bond issuer contractually promises to pay a bond holder • Required rate of return (rrr) • rates used by individual market participants to calculate fair present values (PV) • Expected rate of return (Err) • rates participants would earn by buying securities at current market prices(P) • Realized rate of return (rr) • rates actually earned on investments McGraw-Hill/Irwin

  3. Required Rate of Return • The fair present value (PV) of a security is determined using the required rate of return (rrr) as the discount rate CF1= cash flow in period t(t= 1, …, n) ~ = indicates the projected cash flow is uncertain n= number of periods in the investment horizon McGraw-Hill/Irwin

  4. Expected Rate of Return • The current market price (P) of a security is determined using the expected rate of return (Err) as the discount rate CF1 = cash flow in period t (t= 1, …, n) ~ = indicates the projected cash flow is uncertain n= number of periods in the investment horizon McGraw-Hill/Irwin

  5. Realized Rate of Return • 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 (RCFt) t (t = 1, …, n) McGraw-Hill/Irwin

  6. Bond Valuation • The present value of a bond (Vb) can be written as: M = the par value of the bond INT = the annual interest (or coupon) payment T = the number of years until the bond matures i = the annual interest rate (often called yield to maturity (ytm)) McGraw-Hill/Irwin

  7. Bond Valuation • A premium bond has a coupon rate (INT) greater then the required rate of return (rrr) and the fair present value of the bond (Vb) is greater than the face value (M) • Discount bond: if INT < rrr, then Vb< M • Par bond: if INT = rrr, then Vb= M McGraw-Hill/Irwin

  8. Equity Valuation • The present value of a stock (Pt) assuming zero growth in dividends can be written as: D = dividend paid at end of every year Pt = the stock’s price at the end of year t is = the interest rate used to discount future cash flows McGraw-Hill/Irwin

  9. Equity Valuation • The present value of a stock (Pt) assuming constant growth in dividends can be written as: D0 = current value of dividends Dt = value of dividends at time t = 1, 2, …, ∞ g = the constant dividend growth rate McGraw-Hill/Irwin

  10. Equity Valuation • The return on a stock with zero dividend growth, if purchased at price P0, can be written as: • The return on a stock with constant dividend growth, if purchased at price P0, can be written as: McGraw-Hill/Irwin

  11. Relation between InterestRates and Bond Values Interest Rate Bond Value 12% 10% 8% 874.50 1,000 1,152.47 McGraw-Hill/Irwin

  12. Impact of Maturity onInterest Rate Sensitivity Absolute Value of Percent Change in a Bond’s Price for a Given Change in Interest Rates Time to Maturity McGraw-Hill/Irwin

  13. Impact of Coupon Rates onInterest Rate Sensitivity Bond Value High-Coupon Bond Low-Coupon Bond Interest Rate McGraw-Hill/Irwin

  14. Duration • Duration is the weighted-average time to maturity (measured in years) on a financial security • Duration measures the sensitivity (or elasticity) of a fixed-income security’s price to small interest rate changes McGraw-Hill/Irwin

  15. Duration • Duration(D) for a fixed-income security that pays interest annually can be written as: t = 1 to T, the period in which a cash flow is received T = the number of years to maturity CFt = cash flow received at end of period t R = yield to maturity or required rate of return PVt= present value of cash flow received at end of period t McGraw-Hill/Irwin

  16. Duration • Duration(D) (measured in years) for a fixed-income security in general can be written as: m= the number of times per year interest is paid McGraw-Hill/Irwin

  17. Duration • Duration and coupon interest • the higher the coupon payment, the lower the bond’s duration • Duration and yield to maturity • the higher the yield to maturity, the lower the bond’s duration • Duration and maturity • duration increases with maturity at a decreasing rate McGraw-Hill/Irwin

  18. Duration and Modified Duration • Given an interest rate change, the estimated percentage change in a (annual coupon paying) bond’s price is found by rearranging the duration formula: MD = modified duration = D/(1 + R) McGraw-Hill/Irwin

  19. Figure 3-7 McGraw-Hill/Irwin

  20. Convexity • Convexity(CX) measures the change in slope of the price-yield curve around interest rate level R • Convexity incorporates the curvature of the price-yield curve into the estimated percentage price change of a bond given an interest rate change: McGraw-Hill/Irwin

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