Question

An analyst is evaluating two bonds, Bond Q and Bond P. The
effective maturity of both bonds is 4 years. The face value of both
bonds is $1000 and the yield to maturity for the bonds is 8%. Bond
Q is a zero coupon bond whereas Bond P pays a 10% annual coupon.

a) Assuming that the yield to maturity of each bond remains at 8%
over the next 4 years, calculate the price of both bonds for every
year i.e. price at n=4, price at n=3, price at n=2. Price at n= 1,
and price at n=0.

b) Plot the time path of prices for each bond (on same
scale/graph).

Answer #1

Price of bond P at time t = PV of all coupons left at time t+ PV of Face Value at time t

Bond P | ||||||

Time | Cash flow | PV @ time 0 | PV at time 1 | PV at time 2 | PV at time 3 | Price |

0 | 1066.2 | |||||

1 | 100 | 92.6 | 1051.5 | |||

2 | 100 | 85.7 | 92.6 | 1035.7 | ||

3 | 100 | 79.4 | 85.7 | 92.6 | 1018.5 | |

4 | 1100 | 808.5 | 873.2 | 943.1 | 1018.5 | 1000 |

Price of Zero-coupon bond at time t = PV of the face value at time t

Bond Q | |

Time | Price |

0 | 854.8 |

1 | 889.0 |

2 | 924.6 |

3 | 961.5 |

4 | 1000 |

Graph

We have time on the x-axis and price on the y-axis

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