would not have the option of holding it until it matured. Hence, the yield to maturity would not be earned. • If the current interest rates are well below an outstanding bond ’ s coupon rate, then a callable bond is likely to be called, and investors will estimate its expected rate of return as the yield to call (YTC) rather than as the yield to maturity. The YTC is calculated by solving the following formula, ( ) ( ) N d t d r 1 Price Call N 1 t r 1 INT b v + = + + = ∑
5 9 A Summary Bond Selling at . . .Satisfies This Condition Discount Coupon Rate < Current Yield < YTM Premium Coupon Rate > Current Yield > YTM Par Value Coupon Rate = Current Yield = YTM 10 Bond Price versus Required Yield • There is an inverse relationship between bond price and required yield. This is because the price of the bond is the present value of the cash flows. As the required yield increases, the present value of the cash flows decreases; hence the price decreases. • When the required yield decrease, the present value of the cash flows increases and therefore the price of the bond rises.
6 11 Time Path of a Bond Time Price At Maturity Par Value Bond traded at discount Bond traded at premium Price of bond at maturity is equal to the clean price. If investor were to buy the bond at maturity, he would be entitled to par value and there is no more coupon payment. However, the bond investor bought the bond 6 month prior to maturity will receive coupon and par value. 12 Relationship between Bond Price & Required Yield Required Yield Price
8 15 Term Structure of Interest Rates (Yield Curve) • The relationship between a security yield-to-maturity and its term to maturity is known to as the maturity structure or term structure of interest rates. It is also referred to as the yield curve.
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