Q-10-38I

Expert-verifiedFound in: Page 332

Book edition
9th

Author(s)
Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus

Pages
748 pages

ISBN
9780078034695

**Question: Assume you have a one-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 8% coupon rate and pays the $80 coupon once per year. The third has a 10% coupon rate and pays the $100 coupon once per year.**

**a. If all three bonds are now priced to yield 8% to maturity, what are their prices?**

**b. If you expect their yields to maturity to be 8% at the beginning of next year, what will their prices be then? What is your rate of return on each bond during the one-year holding period?**

Answer

a.

Zero | 8% coupon | 10% coupon | |

Current Prices (A) | $463 | $1000 | $1134.20 |

b.

Rate of return (Income / Current Prices) | 8.00% | 8.00% | 8.00% |

Maturity period = 10 Years

Zero coupons matures at $1000

Coupon income for all three is $0, $80 and $100

If the yield to maturity of three bonds is 8% at the beginning of the next year, it would be calculated using 9 years of maturity in place of 10 years.

Therefore,

Zero | 8% coupon | 10% coupon | |

Current Prices (A) | $463 | $1000 | $1134.20 |

Zero | 8% coupon | 10% coupon | |

Current Prices (A) PV= (0.8, 10, PMT, 1000) | $463 | $1000 | $1134.20 |

Price one year from now (B) PV= (0.8, 9, PMT, 1000) | $500.25 | $1000 | $1124.94 |

Price increase (B-A) | $37.06 | $0.00 | $-9.26 |

Coupon income (Given) | $0.00 | $80 | $100 |

Income (Price increase + Coupon Income) | $37.06 | $80 | $90.74 |

Rate of return (Income / Current Prices) | 8.00% | 8.00% | 8.00% |

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