Assume par value of the coupon = | $1,000 | ||||||
Calculation of Annual Coupon Payments | |||||||
Par value of the bond issued is = | $1,000 | ||||||
Annual Coupon % | 7.00% | ||||||
Annual Coupon Amount | $70.00 | ||||||
Semi Annual Coupon Amount | $35.00 | ||||||
Caclulation of the duration of the Bonds IF the YTM is 7.6% YTM | |||||||
Market rate of interest or Yield to Maturity or Required Return = 7.6% | |||||||
Bonds interest is paid semi annualy means so discounting factor = 7.6 % /2= 3.8 % | |||||||
Caclulation of the duration of the Bond | |||||||
Period (A) | Cash Flow (B) | Period X Cash Flow (AXB= C) | PV of $ 1 at 3.8% (D) | Present Value of the Cash Flow (CXD) | |||
1 | $35.00 | $35 | 0.96339 | $33.72 | |||
2 | $35.00 | $70 | 0.92812 | $64.97 | |||
3 | $35.00 | $105 | 0.89414 | $93.89 | |||
4 | $35.00 | $140 | 0.86141 | $120.60 | |||
5 | $35.00 | $175 | 0.82988 | $145.23 | |||
6 | $35.00 | $210 | 0.79950 | $167.89 | |||
6 | $1,000 | $6,000 | 0.79950 | $4,796.97 | |||
$5,423.26 | |||||||
Duration = | $5,423.26 | ||||||
Divide By = | "/"By | ||||||
Par Value = | 1000 | ||||||
Duration = | 5.4233 | ||||||
Answer = Duration of the Bonds = 5.4233 | |||||||
Caclulation of the duration of the Bonds IF the YTM is 11.6% YTM | |||||||
Market rate of interest or Yield to Maturity or Required Return = 11.6% | |||||||
Bonds interest is paid semi annualy means so discounting factor = 11.6 % /2= 5.8 % | |||||||
Caclulation of the duration of the Bond | |||||||
Period (A) | Cash Flow (B) | Period X Cash Flow (AXB= C) | PV of $ 1 at 5.8% (D) | Present Value of the Cash Flow (CXD) | |||
1 | $35.00 | $35 | 0.94518 | $33.08 | |||
2 | $35.00 | $70 | 0.89336 | $62.54 | |||
3 | $35.00 | $105 | 0.84439 | $88.66 | |||
4 | $35.00 | $140 | 0.79810 | $111.73 | |||
5 | $35.00 | $175 | 0.75435 | $132.01 | |||
6 | $35.00 | $210 | 0.71299 | $149.73 | |||
6 | $1,000 | $6,000 | 0.71299 | $4,277.97 | |||
$4,855.72 | |||||||
Duration = | $4,855.72 | ||||||
Divide By = | "/"By | ||||||
Par Value = | $1,000 | ||||||
Duration = | 4.8557 |
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