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Bond Math

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Submitted By serrano2205
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3. In February 1995, Copiers, Inc. Issued one-year zero-coupon bonds with a face value of $1000. The bonds sold for $910 a piece and were rated AA by Standard & Poors. Buyers of the bonds were promised a single $1000 payment at the end of one year. At the time the bonds were issued, one-year Treasury securities were yielding 6.6%. Assume that the market risk premium was 7.2%.
A. What was the yield-to-maturity at the time if issuance of the Copiers, Inc, bond?
One-Year Zero Coupon Rate, with an AA rating.
Face Value = $ 1,000.00
Bond Issued at = $ 910.00
Years to Maturity = 1 year
Treasury Securities Interest Rate = 6.6 %
Market Risk Premium = 7.20 % If Present Value = Future Value / ( 1 + r )t | t = (Future Value / Present Value ) 1/ t – 1 | t = (1000 / 910 )1 - 1 | t = 1.0989 – 1 | t = 9.89 % Yield to Maturity | |

B. Using the table below, calculate the expected return on the Copiers, Inc. Bond when it was issued. Rating | AAA | | AA | | A | | BBB | Beta | 0.19 | | 0.20 | | 0.21 | | 0.22 | Source: Fama, Gene and Ken French, 1993, "Common Risk Factors in the Returns on Bonds and Stocks", on Bonds and Stocks, “Journal of Financial Economics, 33, 3-56, Table 4 |

Expected Return Rate = (Risk Free Return) + (Beta) * (Expected Market Return – Risk Free Return) Risk Free Return: Treasury Interest Rate = 6.6 % Expected Market Return: Return of market as a whole Considering that: Market Risk Premium = Expected Market Return – Risk Free Return = 7.2 % If Market Risk Premium = 7.2 %, and Risk Free Return = 6.6 % Expected Market Return = Risk Free Return + Market Risk Premium Expected Market Return = 6.6 % + 7.2 % = 13.8%

For each one of the Betas above, Expected Return Rate is: Expected Return Rate = 6.6 % + Beta * ( 13.8 % - 6.6 %), for a Beta value of … Expected Return Rate is as follows: Rating | Beta |

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