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Homework answers / question archive / Use the following information for a bond to calculate: a) the Macaulay Duration of the bond and; b) the Modified Duration of the bond explaining the significance of modified duration • 5 year maturity • Coupon of 10% • 6% yield to maturity Note: For the modified duration you may assume a change in yield of 1%
Use the following information for a bond to calculate:
a) the Macaulay Duration of the bond and;
b) the Modified Duration of the bond explaining the significance of modified duration
• 5 year maturity
• Coupon of 10%
• 6% yield to maturity
Note: For the modified duration you may assume a change in yield of 1%
Lets say face value of the bond = 1,000$
Coupon = 10% on face value = 10% of 1000 = 100$
Yield to Matuirty (Present Value Factor) = 6%
Macaylay's Duration Formula
Present Value Factor = 1/(1+YTM)^ Number of years cash flow to be bought back
= Sigma of (Present Values * time) / Sum of all present values of the bond
Sigma is the summation of values
| Particulars | 1 | 2 | 3 | 4 | 5 | Summation of all Present vales of bond |
| Coupon | 100 | 100 | 100 | 100 | 100 | |
| Maturity Value of Bond | 1000 | |||||
| Cash Flows (A) | 100 | 100 | 100 | 100 | 1100 | |
| Present Value Factor @ 6% (B) | 0.943396 | 0.889996 | 0.839619 | 0.792094 | 0.747258 | |
| Present Values (A*B) | 94.33962 | 88.99964 | 83.96193 | 79.20937 | 821.984 | 1168.494551 |
| time | 1 | 2 | 3 | 4 | 5 | |
| Present Values * Time | 94.33962 | 177.9993 | 251.8858 | 316.8375 | 4109.92 | |
| Sigma of (Present Values * Time ) | 4950.982112 |
= 4950.9821/1168.4946
= 4.2371 years
Macaulay's Duration = 4.24 Years.
Modified Duration Indicates the percentage change in price due to percentage change in yield. It follows the concept of prices and interest rates move in opposite direction.It is an extension to Macaulay's Duration which helps investor to know price sensitivity towards interest rate.
Formula for Modified Duration = Macaulay's Duration/(1+YTM)
It determines the effect that a 1% change in YTM will have on Price of the bond
Modified Duration = 4.2371/(1+0.06) = 3.9973
This means for every one percent move in yield will bring change in price to 3.9973%
