Question

Consider a business loan maturing in three years that has three remaining annual payments in one, two, and three years. The annual payments are all equal to $3 Million. While analyzing the loan, you are using a YTM equal to 10%.

Determine the duration of the loan and then, using this estimated duration and a duration analysis, predict the percentage change in the value of the loan after a 0.5 percentage point increase in the interest rate. You should assume that a one percentage point change in the rate is approximately equal to a one percent change in the rate.

Answer #1

Year | Cashflow(million) | PV @10 | PV | Proption of bond value | Propotion of Bond value *Time(yars) |

1 | 3 | 0.909 | 2.727 | 0.365544698 | 0.365544698 |

2 | 3 | 0.8264 | 2.4792 | 0.332327985 | 0.66465597 |

3 | 3 | 0.7513 | 2.2539 | 0.302127317 | 0.906381952 |

7.4601 |
1 |
1.93658262 |

Duration Years = | 1.936583 | ||

Volatility = | Duration / (1+YTM) | ||

1.936583/1.10 | |||

1.76053 |
|||

1.76 |

Value of loan if interest rate incfreases to .5 percentage point
thevalue of loan will decrease by .5*1.76 = **.88
%**

(excel) Consider a 8% coupon bond
making annual coupon payments with 4 years until maturity
and a yield to maturity of 10%.
What is the modified duration of this bond?
If the market yield increases by 75 basis points, what is the
actual percentage change in the bond’s
price? [Actual, not approximation]
Given that this bond’s convexity is 14.13, what price would you
predict using the duration-with-convexity
approximation for this bond at this new yield?
What is the percentage error?

Find the duration of a 8% coupon bond making annual
coupon payments if it has three years until maturity and a yield to
maturity of 7.8%. What is the duration if the yield to maturity is
11.8%? (Do not round intermediate calculations. Round your
answers to 4 decimal places.)
YTM
Duration
7.8% YTM
11.8% YTM

Find the duration of a 6% coupon bond making annual coupon
payments if it has three years until maturity and a yield to
maturity of 7.7%. What is the duration if the yield to maturity is
11.7%? (Do not round intermediate calculations. Round your answers
to 4 decimal places.)
YTM Duration 7.7% YTM 11.7% YTM

Find the duration of a 8% coupon bond making annual
coupon payments if it has three years until maturity and a yield to
maturity of 7.8%. What is the duration if the yield to maturity is
11.8%? (Do not round intermediate calculations. Round your
answers to 4 decimal places.)
YTM
Duration
7.8% YTM

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