Question

Insook, Inc., and Hankyu Corp. both have 7 percent coupon bonds outstanding, with semi-annual interest payments, and both are prices at par value. The Insook, Inc. bond has 2 years to maturity, whereas the Hankyu Corp. bond has 5 years to maturity.

a. If the interest rates suddenly rise by 2 percent, what is the price of Insook, and Hankyu’s bonds respectively?

b. What is the Macaulay duration of Insook, and Hankyu’s bonds respectively if the interest rates increase by 2%?

c.Which bond (Insook or Hankyu) is exposed to higher interest rate risk? Why?

d) What are factors affecting interest rate risk?

Which bond (Insook or Hankyu) is exposed to higher interest rate risk? Why?

Answer #1

**Solution**

Since both the bonds are trading at par value, YTM = interest rate = 7%

Now YTM is increased by **2% , and hence new YTM =
9%**

Since interest is paid semi annual , YTM = 9%/2 = 4.5%

Statement showing Price and Macaulay duration of Insook, Inc

No of payments | Interest payments | Redemption value | Total cash flow | PVIF @ 4.5% | PV of cash flow | Weightage of PV of cash flow | Macaulay duration |

1 | 35 | 35 | 0.9569 | 33.49 | 0.0347 | 0.03 | |

2 | 35 | 35 | 0.9157 | 32.05 | 0.0332 | 0.07 | |

3 | 35 | 35 | 0.8763 | 30.67 | 0.0318 | 0.10 | |

4 | 35 | 1000 | 1035 | 0.8386 | 867.91 | 0.9002 | 3.60 |

964.12 |
3.80 |

Price of bond is nothing but present value of future cash flow

Thus price of Insook, Inc = $**964.12**

Macaulay duration = 3.80/2 = **1.9** years

Statement showing Price and Macaulay duration of Hankyu Corp.

No of payments | Interest payments | Redemption value | Total cash flow | PVIF @ 4.5% | PV of cash flow | Weightage of PV of cash flow | Macaulay duration |

A | B | C =A x B | |||||

1 | 35 | 35 | 0.9569 | 33.49 | 0.0364 | 0.04 | |

2 | 35 | 35 | 0.9157 | 32.05 | 0.0348 | 0.07 | |

3 | 35 | 35 | 0.8763 | 30.67 | 0.0333 | 0.10 | |

4 | 35 | 35 | 0.8386 | 29.35 | 0.0319 | 0.13 | |

5 | 35 | 35 | 0.8025 | 28.09 | 0.0305 | 0.15 | |

6 | 35 | 35 | 0.7679 | 26.88 | 0.0292 | 0.18 | |

7 | 35 | 35 | 0.7348 | 25.72 | 0.0279 | 0.20 | |

8 | 35 | 35 | 0.7032 | 24.61 | 0.0267 | 0.21 | |

9 | 35 | 35 | 0.6729 | 23.55 | 0.0256 | 0.23 | |

10 | 35 | 1000 | 1035 | 0.6439 | 666.47 | 0.7237 | 7.24 |

920.87 |
8.54 |

Price of bond is nothing but present value of future cash flow

Thus price of Hankyu Corp. = $**920.87**

Macaulay duration = 8.54/2 = **4.27** years

Thus

a) If interest rate rises by 2% then

Price of Insook, Inc = $**964.12**

Price of Hankyu Corp. = $**920.87**

b) If interest rate rises by 2% then

Macaulay duration Insook, Inc = **1.9** years

Macaulay duration Hankyu Corp = **4.27** years

c) **Hankyu
Corp's bond is exposed to higher interest rate risk**
because it has larger duration, greater the duration more price is
sensitive to interest rate change

d) Factors affecting interest rate risk are **duration of
bond , coupon rate of bond, credit risk of the company issuing the
bonds** etc

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