Question

You buy an 8 percent coupon, 10-year maturity bond when its
yield to maturity is 9 percent. One year later, the yield to
maturity is 10 percent. Assume the face value of the bond is
$1,000.

(a) What is the price of the bond today?

(b) What is the price of the bond one year later?

(c) What is your rate of return over the one-year holding
period?

Answer #1

Value of the bond is Present value of future cash inflows. So, the value of the bond is calculated by discounting the future cash inflows.

(**a) Price of the bond today:**

Year |
Nature |
Amount |
[email protected]% |
Present value |

1-10 | Coupon | $ 80 | PVAF(9%,10)=6.4176 | $513.408 |

10 | Redemption | $1000 | PVF(9%,10) =0.4224 | $422.4 |

Value of the Bond today |
$935.808 |

(**b) Price of the bond 1 year later:**

Year |
Nature |
Amount |
[email protected]% |
Present value |

1-9 | Coupon | $ 80 | PVAF(10%,9)=5.7590 | $460.72 |

9 | Redemption | $1000 | PVF(10%,9) =0.4241 | $424.1 |

Value of the Bond after 1 yr |
$884.82 |

(**c) Rate of
return over 1 yr holding period:**

Rate of return = coupon received + (Sale price - purchase price) / Bond purchase price

= ($80 + ($884.82 - $935.808)) /$935.808

= ($80 - $50.98) / $935.808

= $29.02 / $935.808

**=0.03101 (or) 3.101%**

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