## Christmas Assignment Case Solution

Furthermore, the price of a 3 year Semi-annual coupon bond has been calculated with annual coupon rate 3% and face value amounting to $100 in which it was determined that the bond value after maturity would amount to 109.27 as represented in the exhibit below. However, the future value of the bond was calculated by multiplying the face value of the bond by the return factor of the coupon rate using the formula represented as (1+ coupon rate) ^No. of years.

Calculation |
Years |

Bond term | 3 |

Annual coupon rate | 3% |

face value | $100 |

Future Value at maturity |
109.2727 |

Forwards Rates

Assuming that the answer in (a) was calculated on quarter compounding par yield basis, the three monthly discount rates were calculated with the assumption that the discount factor is 10%. Furthermore, by using the formula represented as, (1+discount rate) ^ t, where t, is equal to 0, 0.25, 0.50 to 9.75, would enable to determine the discounts rate, with respect to the bond terms on a 3 monthly basis. The exhibit above represents the discount rate calculated through the use of above mentioned formula.Â The forward rate had been calculated for 1, 2 and 3 years, however with the help of it their monthly forwards had also been determined with respect to part (e). On the other hand, for part (d) the formula represented as **[(1+R) ^{t+3}/(1+R)^{t}]^(1/3)-1Â **has been used to calculate the forward rates for three year term and with it, their monthly forward rates by dividing the figure achieved through the formula above, by 4, which is the amount of periods available in a year. The calculation could be evaluated and assessed in the excel exhibits.

Quarterly |
t |
Discount factor |

Dec-16 | 0.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1.00 |

Mar-17 | 0.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.98 |

Jun-17 | 0.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.95 |

Sep-17 | 0.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.93 |

Dec-17 | 1.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.91 |

Mar-18 | 1.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.89 |

Jun-18 | 1.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.87 |

Sep-18 | 1.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.85 |

Dec-18 | 2.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.83 |

Mar-19 | 2.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.81 |

Jun-19 | 2.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.79 |

Sep-19 | 2.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.77 |

Dec-19 | 3.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.75 |

Mar-20 | 3.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.73 |

Jun-20 | 3.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.72 |

Sep-20 | 3.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.70 |

Dec-20 | 4.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.68 |

Mar-21 | 4.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.67 |

Jun-21 | 4.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.65 |

Sep-21 | 4.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.64 |

Dec-21 | 5.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.62 |

Mar-22 | 5.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.61 |

Jun-22 | 5.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.59 |

Sep-22 | 5.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.58 |

Dec-22 | 6.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.56 |

Mar-23 | 6.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.55 |

Jun-23 | 6.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.54 |

Sep-23 | 6.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.53 |

Dec-23 | 7.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.51 |

Mar-24 | 7.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.50 |

Jun-24 | 7.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.49 |

Sep-24 | 7.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.48 |

Dec-24 | 8.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.47 |

Mar-25 | 8.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.46 |

Jun-25 | 8.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.44 |

Sep-25 | 8.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.43 |

Dec-25 | 9.00 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.42 |

Mar-26 | 9.25 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.41 |

Jun-26 | 9.50 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.40 |

Sep-26 | 9.75 | Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.39 |

**Graphical Representation**

The primary factors responsible for the line not coinciding could be the fact that with respect to part (d) the forwards rates are calculated using discount rates, which was calculated based on an assumption using the discount rate and time value of money concept. Similarly, with respect to part (e) the forwards rates were calculated based on the actual rates provided in the case, amounting to 0.508, which a constant flow of actual rates over the term periods. However, it can be assessed that the discount factor initial values are significantly higher than the actual rate given in the case. Therefore, it allowed the forward rates calculated under part (d) to be lower initially, which shows higher forward rates as compared to the forwards rates calculated under part (e). Moreover, it can be evaluated from the graph below, the forwards rate calculated under part (d), depicts a downward trend. Whereas, the forwards rate calculated under part (e) depicts a relatively constant trend…………………….

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