Present_Value,_with_Answers

Present_Value_with_ - Present Value Financial Economics Bruce C Dieffenbach Question 1 When the price of a bond equals the maturity value then the

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Present Value Financial Economics Bruce C. Dieffenbach Question 1 When the price of a bond equals the maturity value, then the yield to maturity equals the current yield. Show this property for a two-year bond. The bond price P equals the present value of the coupon payments C and the maturity value 1000: P = C 1 + R + C + 1000 ( 1 + R ) 2 . When P = 1000, show R = C / 1000. (Hint: Substitute R = C / 1000 into the right-hand side, and show that C cancels out, to give a value of 1000.) Answer 1 Evaluate the present value by substituting R = C / 1000: PV = C 1 + R + C + 1000 ( 1 + R ) 2 = C 1 + C / 1000 + C + 1000 ( 1 + C / 1000 ) 2 = 1000 C 1000 + C + 1000 2 ( 1000 + C ) ( 1000 + C ) 2 = 1000 , as desired. Alternatively, one could solve 1000 = C 1 + R + C + 1000 ( 1 + R ) 2 for R , using the quadratic formula. Question 2 Consider the following, quoted from an article in the Wall Street Journal : Disney Amazes Investors With Sale of 100-Year Bonds The corporate race to lock in low credit costs hit a fever pitch as Walt Dis- ney Co. began marketing the first sale of 100-year bonds by any borrower since 1954. Bond traders were stunned to hear that the entertainment concern is expecting to sell $150 million of 100-year bonds at a yield of only about 7.5%, barely . .. above 30-year U. S. Treasury bonds. “It’s crazy,” said William Gross. “Look at the path of Coney Island over the last 50 years and see what happens to amusement parks.” Investors buy- ing a 100-year Disney issue will need to have a “lot of confidence in the longevity of Mickey Mouse,” said John Lonski. Do you agree with the reaction of these two men? Discuss the validity of their comments, from the viewpoint of present value. Can one justify buying the bonds only if Mickey will still be popular in 100 years? Answer 2
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This note was uploaded on 04/20/2008 for the course ECO 466y taught by Professor Dieffenbach during the Spring '08 term at SUNY Albany.

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