Q-10-281

Expert-verifiedFound in: Page 330

Book edition
9th

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

Pages
748 pages

ISBN
9780078034695

**Question: A two-year bond with par value $1,000 making annual coupon payments of $100 is priced at $1,000. What is the yield to maturity of the bond? What will be the realized compound yield to maturity if the one-year interest rate next year turns out to be: **

**( a ) 8%,**

**( b ) 10%, **

**( c ) 12%?**

**Answer**

a. 9.91%

b. 10.00%

c. 10.09%

The bond is selling at par value.

Its yield to maturity equals the coupon rate, 10%.

If the first-year coupon is reinvested at an interest rate of r percent, then total proceeds at the end (1 + r) + 1100].

Therefore, realized compound yield to maturity of the second year will be a function of r as given below:

r | Total proceeds | Realized YTM = √Proceeds / 1000 -1 |

8% | $1208 | √1208/1000 - 1 = 0.0991 = 9.91 % |

10% | $ 1210 | √1210/1000 - 1 = 0.1000 = 10.00 % |

12% | $ 1212 | √1212/1000 - 1 = 0.1009 = 10.09 % |

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