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【正文】 ture. Callable Bonds versus Noncallable Bonds 2550751001251501752000 4 8 12 16 20Y i e l d t o m at u r i t y ( % )Bond price (% of par)N on c al l ab l e b on dC al l ab l e b on d Bond Refunding ?Replacing all or part of a bond issue is called refunding. ?Usually, the first step in a typical bond refunding is to call the entire issue of bonds at the call price. ?Bond refunding raises two questions: ? Should firms issue callable bonds? ? Given that callable bonds have been issued, when should the bonds be called? Should Firms Issue Callable Bonds ?Call provisions have value to the issuing firms. ? Most bonds have call provisions ? Call provisions give issuers the option to redeem the outstanding bonds at a price lower than the market price of the bonds. ?Should the firms always issue callable bonds? ?Rational investors will incorporate the effect of call provision into the valuation. ? They will demand higher coupon rates on callable bonds than on noncallable bonds. An Example ?Kraus Intercable Company intends to issue perpetual bonds of $1000 at a 10 percent interest rate. Annual coupons have been set at $100. There is an equal chance that by the end of the year interest rates will do one of the following: (1) Fall to 62/3 percent. If so, the bond price will increase to $1500. (2) Increase to 20 percent. If so, the bond price will fall to $500. ?Suppose investors are risk neutral. What are the prices for noncallable bonds and callable bonds respectively? Noncallable Bond (Example) Value of Noncallable bonds Firstyear coupon + Expected price at end of year 1 + r $100 + ( * $1500) + ( * $500) 1 + r = = $1000 Callable Bond (Example) ?Suppose the Kraus Intercable Company can also issue callable bonds with call premium of $ 100 (call price, $ 1100). The bond can be called only at the end of the first year. ?The incentives of the pany at the end of first year. ? When interest rate falls to 62/3 percent, the bond is worth $1500. The pany will call the bond at $1100. ? When interest rate rises to 20 percent, the bond is worth $500, the pany will not call the bond. Value of Callable Bond (Example) ?Rational investors know that they will get $1100 + $100 if interest falls, and $100/ + $100 if interest rises. ?If the firm issues callable bond, the value of callable bond is only $. ($1100 + $100) * + ($100/ +$100) * 1 + = $ Required Coupon Rate of Callable Bond ?If the pany still want to raise $1000 for each callable bond it issues, the investor will require a higher coupon rate C. ($1100 + C) * + (C/ +C) * 1 + = $1000 C = $ The Paradox ?To issue a bond of market value $1000, Kraus can either issue noncallable bond with coupon $100, or callable bond with coupon $ and call price $1100. ?Both Kraus and the investors are indifferent with the two alternatives. ?Why are callable bond issued in the real world? Potential Explanations for Callable Bond ?Superior Interest Rate Forecasting ? Corporate insiders may know more about the discount rate (default risk premium) for the bond issued than investors. ? Problems of this argument: – Rational investors can also expect this opportunistic behavior and require a even higher coupon rate. – Corporate
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