3330 PS3 sol - Cornell University Fall 2010 Economics 3330:...

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Cornell University Fall 2010 Economics 3330: Problem Set 3 Solutions 1. Coupon Renegotiation (Question 20 of Chapter 14 of the text, modified) A 10-year bond of a firm in severe financial distress has an annual coupon of $80 and sells for $500. The firm is currently renegotiating the debt, and it appears that the lenders will allow the firm to reduce coupon payments on the bond and on the principal to one-half the originally contracted amount. The firm can handle these lower payments. What is the stated and expected yield to maturity of the bond? The stated yield to maturity, based on promised payments, equals 19.9%. The expected yield to maturity is 8%. These are obtained through standard YTM calculations, with expected payments substituted for promised payments in the latter. 2. Rates (Question 12 of Chapter 15 of text) Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2- year zero sells at $84.99. You are considering the purchase of a 2-year maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 12% per year. a. What is the yield to maturity of the 2-year zero? The 2-year coupon bond? The one-year zero-coupon bond has a yield to maturity of 6%, as shown below: 1 y 1 100 $ 34 . 94 $ y 1 = 0.06000 = 6.000% The yield on the two-year zero is 8.472%, as shown below: 2 2 ) y 1 ( 100 $ 99 . 84 $ y 2 = 0.08472 = 8.472% The price of the coupon bond is: 51 . 106 $ ) 08472 . 1 ( 112 $ 06 . 1 12 $ 2 Therefore: yield to maturity for the coupon bond = 8.333% b. What is the forward rate for the second year? % 00 . 11 1100 . 0 1 06 . 1 ) 08472 . 1 ( 1 y 1 ) y 1 ( f 2 1 2 2 2 c. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year? Expected price 90 . 100 $ 11 . 1 112 $
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Expected holding period return = % 00 . 6 0600 . 0 51 . 106 $ ) 51 . 106 $ 90 . 100 ($ 12 $ This holding period return is the same as the return on the one-year zero. d. Will the expected rate of return be higher or lower than the forward rate if you accept the liquidity preference hypothesis? If there is a liquidity premium, then: E(r 2 ) < f 2 E(Price) = 90 . 100 $ ) r ( E 1 112 $ 2 E(HPR) > 6% 3. Immunization You will be paying $50,000 a year in tuition expenses at the end of each of the next two years. Bonds currently yield 2%.
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This note was uploaded on 04/06/2011 for the course ECON 314 taught by Professor Bar during the Fall '08 term at Cornell University (Engineering School).

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3330 PS3 sol - Cornell University Fall 2010 Economics 3330:...

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