A fixed coupon bond with 4 years until maturity has a coupon rate of 5% paid annually and is currently trading at a yield of 4% p.a. Compute the following:
Calculate the Price of the bond.
Answer this :Calculate the Duration and Modified Duration of the Bond
Price of bond is present value of coupon payment plus present value of face value | ||||||||
Duration | Sum of (present value of Cash flow*Year)/Price of bond | |||||||
Modified duration | Duration/(1+YTM/n) | |||||||
YTM | Yield to maturity | |||||||
n | number of coupon payment per year | |||||||
Assuming face value of bond is $1000 | ||||||||
Calculation of price of bond and duration | ||||||||
Year | Cash flow | Discount factor @ 4% | Present value | Present value*year | ||||
1 | 50 | 0.961538462 | 1/(1.04^1) | $48.08 | $48.08 | |||
2 | 50 | 0.924556213 | 1/(1.04^2) | $46.23 | $92.46 | |||
3 | 50 | 0.888996359 | 1/(1.04^3) | $44.45 | $133.35 | |||
4 | 1050 | 0.854804191 | 1/(1.04^4) | $897.54 | $3,590.18 | |||
$1,036.30 | $3,864.06 | |||||||
Coupon amount | 1000*5% | |||||||
Duration | 3864.06/1036.30 | |||||||
Duration | 3.73 | |||||||
Thus, price of bond is $1,036.30 | ||||||||
Duration is 3.73 | ||||||||
Modified duration | 3.73/(1+(0.04/1)) | |||||||
Modified duration | 3.73/1.04 | |||||||
Modified duration | 3.59 | |||||||
A fixed coupon bond with 4 years until maturity has a coupon rate of 5% paid...
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