Question

In: Finance

Find the duration of a 6.0% coupon bond making annual coupon payments if it has four...

Find the duration of a 6.0% coupon bond making annual coupon payments if it has four years to maturity and a yield to maturity of 5.0%. (assuming a face value of $1,000)

A.

4.54 Years

B.

4.00 Years

C.

3.82 Years

D.

5.00 Years

E.

3.68 Years

F.

4.48 Years

Solutions

Expert Solution

Face Value of the bond = $1000

Annual coupon rate = 6%

Annual coupon payment = Annual coupon rate*Face Value = 6%*1000 = 60

YTM = 5%

The cashflow for the bond is:

C1 = 60, C2 = 60, C3 = 60, C4 = 1060

Year Cashflow
1 60
2 60
3 60
4 1,060

Present value of C1 = PV1 = C1/(1+YTM)1 = 60/(1+5%)1 = 57.1428571428571

Present value of C2 = PV2 = C2/(1+YTM)2 = 60/(1+5%)2 = 54.421768707483

Present value of C3 = PV3 = C3/(1+YTM)3 = 60/(1+5%)3 = 51.8302559118886

Present value of C4 = PV4 = C4/(1+YTM)4 = 1060/(1+5%)4 = 872.064623279395

We know that price of the bond is the sum of the present value of all the cash flows

Price of the Bond = P = PV1 + PV2 + PV3 + PV4 = 57.1428571428571 + 54.421768707483 + 51.8302559118886 + 872.064623279395 = 1035.45950504162

Now, Duration is calculated using the formula:

Duration = [(1*57.1428571428571)+(2*54.421768707483)+(3*51.8302559118886)+(4*872.064623279395)]/1035.45950504162 = 3809.73565541107/1035.45950504162 = 3.67927054304062 ~ 3.68 years(Rounded to two decimals)

Answer -> 3.68 years (Option E)


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