Question

 

1. Compute the duration (D) for a coupon bond with the following features:

      ● face value            $ 100

      ● coupon                  10%

      ● yield                        8%

      ● maturity              3 years

      ● semi-annual

a.) Compute the Mac.D for Problem 1 by means of the formula.

b.) Compute the corresponding Mod.D.

c.) If the market interest rate (yield) goes up by 20 basis points to 8.2%, determine

      the approximate fair market price of this bond.

Answer 1

Price of bonds(p) computed using YTM formula;

YTM = C+(F-P)/T

(F+P)/2

Where,

                Y              =             Yield to maturity of bond =             8.20%

                C             =             Coupon rate of bond                  =             10.00%

                T              =             Maturity period of bond =             3 years

                F              =             Face value of Bond                 =             $100.00

                P             =             Price of Bond                           =             ?

Substite the values in above formula;

=> YTM * (F+P)/2                   =             C + (F-P)/T

=> 0.082 * (100 + P) /2 =             100*10% + (100-P)/3

=> 0.041*(100+P)                   =             10 + (100 – P)/3

=> 4.1 + 0.041P                     =             (30 + 100 – P)/3

=> (4.1 + 0.041P)*3   =             130 – P

=> 12.30 + 0.123P                  =             130 – P

=> P + 0.123P                       =             130 – 12.30

=> 1.123P                             =             117.70

=> P                                     =             117.70/1.123

=> P                                     =             104.81

Therefore, the price of bond is $104.81