Valuing Bonds Bond Cash Flows, Prices, and Yields

Transcript:Valuing Bonds Bond Cash Flows, Prices, and Yields:
Valuing Bonds Bond Cash Flows, Prices, and Yields Bond Terminology Face Value Notional amount used to compute the interest payments Coupon Rate Determines the amount of each coupon payment, expressed as an annual percentage rate Coupon Payment Zero-Coupon Bonds Zero-Coupon Bond (Zero) Does not make coupon payments Always sells at a discount (a price lower than face value), so they are also called pure discount bonds Treasury Bills are U.S. government zero-coupon bonds with a maturity of up to one year. Zero-Coupon Bonds Suppose that a one-year, risk-free, zero-coupon bond with a $100,000 face value has an initial price of $96,618.36. The cash flows would be: Although the bond pays no “interest,” your compensation is the difference between the initial price and the face value. Zero-Coupon Bonds Yield to Maturity The discount rate that sets the present value of the promised bond payments equal to the current market price of the bond. Price of a Zero-Coupon bond Zero-Coupon Bonds Yield to Maturity For the one-year zero coupon bond: Thus, the YTM is 3.5%. Example Suppose the following three zero-coupon bonds are trading at the prices shown. What is the yield to maturity for each bond? Example The general formula is found by re-arranging the present value equation: The specific solutions are: Zero-Coupon Bonds Risk-Free Interest Rates A default-free zero-coupon bond that matures on date n provides a risk-free return over that time period equal to the yield to maturity. Thus, the Law of One Price guarantees that the risk-free interest rate equals the yield to maturity on such a bond. Risk-Free Interest Rate (risk free zero coupon yield or spot rate) with Maturity n The zero coupon yield curve is a plot of the spot rates for different maturities. Things will not be this simple when we consider coupon bonds. Coupon Bonds Yield to Maturity The YTM is the single discount rate that equates the present value of the bond’s remaining cash flows to its current price. Yield to Maturity of a Coupon Bond YTM – Example On 9/1/95, PG&E bonds with a maturity date of 3/01/25 and a coupon rate of 7.25% were selling for 92.847% of par, or $928.47 per $1,000 of face value. What is their YTM? Semiannual coupon payment = 0.0725*1000/2 = $36.25. Number of semiannual periods to maturity = 30*2 – 1 = 59. YTM - Example r/2 can only be found by trial and