Question

Problem 5: Bond A pays 12% coupon annually, has a par value of $1,000 and will mature in 3 years. Using a 10% discount rate (Yield-to-Maturity), what is the value of the bond?

Problem 6: Using your information on Bond A above, calculate the (Macaulay) duration of the bond.

Problem 7: What is the (Macaulay) duration of a bond with the following characteristics: N = 5, PMT = 90, FV = 1000, I/Y = 12%?

Problem 8: What is the duration of a bond with the following characteristics: N = 5, PMT = 10, FV = 1000, I/Y = 12%?

Problem 9: The modified duration of a bond is 9.27 Years. What is the approximate change in the value of the bond if interest rates drop by 3 percentage points (3%)?

Problem 10: A bond portfolio has a (Macaulay) duration of 7.23 years. Using a yield-to-maturity of 18%, what is the approximate change in the value of the bond portfolio if interest rates increase by 5%?

Answer 1

Problem 5

This is a simple question. The value is the present value of all future cash flows.

In this case u make a cashflow chart at Future Value (120,120.1120) and discount it at 10%.

Hence the value is 1049.737$

Problem 6

Duration (or Macaulay Duration) is a measure of the sensitivity of a Bond;s Market Value to the interest rates.

It is calculated by dividing the Present Value of the Future Cash Flows (Weighted with time to receive) by the Current Market Value.

As Current Market Value is not given in any of the problems I'm assuming a prefect market condition and Current Market Value is the same as the Value of the bond with 10% required rate of return.

[But I will also provide an answer in the bracket with the face value, which is just discounting with 12%, or the same as dividing with 1000$]

In this case, as above ,the cash flows are 120,120,1120 and when weighted with the time to receive (1,2,3) they are

120,240,3360 and should be discounted at 10% to give a sum of 2831.86$ and divided by 1049.74$

Duration = 2.6977 years [or 2.6901 years]

Problem 7

The same as above, the value of the bond is $891.86 and PV of Weighted Discounted Cashflows is $3737.30

As Current Market Value is not given in any of the problems I'm assuming a prefect market condition and Current Market Value is the same as the Value of the bond with 12% required rate of return.

[But I will also provide an answer in the bracket with the face value, which is just discounting with 9%, or the same as dividing with 1000$]

Duration = 4.19 Years [4.24 Years]

Problem 8

The same as above, the value of the bond is $603.48 and PV of Weighted Discounted Cashflows is $2937.15

As Current Market Value is not given in any of the problems I'm assuming a prefect market condition and Current Market Value is the same as the Value of the bond with 12% required rate of return.

[But I will also provide an answer in the bracket with the face value, which is just discounting with 1%, or the same as dividing with 1000$]

Duration = 4.86 Years [4.90 Years]

[I think the pmt is 100 not 10, if it is the answer is 4.14 Years]

Problem 9

Modified duration is the change in the value of a bond for a 100 basis point (1%) change in the interest rates.

It is Macaulay Duration divided by (1 + YTM/n).

So if 9.27 is modified duration then value change in bond for 1% increase in rate is -(1%*9.27*100%)= -9.27%

As Interest rate drops 3% Change in Value of Bond is -(-3%*9.27*100%) = + 27.81%

Problem 10

So, for this problem we need to find Modified Duration= (Macaulay Duration)/(1+(TYM/n))

"n" is time period of the YTM being considered, in this case is 1

"YTM" is Yield to Maturity is 18%

Modified Duration = 7.23/(1 +(18%/1)) = 7.23/(1+0.18) = 6.127 years

And for increase in interest rates by 5%, the change in value of Bond = -(5 * 6.127 * 100%) = -30.635%