Question

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A bond pays annual interest. Its coupon rate is 3%. Its value at maturity is $1,000....

A bond pays annual interest. Its coupon rate is 3%. Its value at maturity is $1,000. It matures in 4 years. Its yield to maturity is currently 9%. The duration of this bond is ________ years.

A) 3.34 B) 3.22 C) 3.81 D) 4.54

Expert Solution

Face value of the bond = $1000

Time to maturity = 4 year

YTM = 9%

Annual coupon rate = 3%

The bond pays Annual coupons.

Annual coupons = Annual coupon rate*Face value = (3%)*1000 = 30

The Cashflows for this bond is:

C1 = 30, C2 = 30, C3 = 30, C4 = 1030

We will first calculate the present value of all the cashflow as shown below

Present value of C1 = PV1 = C1/(1+YTM)1 = 30/(1+9%)1 = 27.5229357798165

Present value of C2 = PV2 = C2/(1+YTM)2 = 30/(1+9%)2 = 25.2503997979968

Present value of C3 = PV3 = C3/(1+YTM)3 = 30/(1+9%)3 = 23.1655044018319

Present value of C4 = PV4 = C4/(1+YTM)4 = 1030/(1+9%)4 = 729.677967397152

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 = 27.5229357798165+25.2503997979968+23.1655044018319+729.677967397152 = 805.616807376797

Maculay Duration is calculated using the formula:

Maculay Duration = [(1*27.5229357798165)+(2*25.2503997979968)+(3*23.1655044018319)+(4*729.677967397152)]/805.616807376797 = 3066.23211816991/805.616807376797 = 3.80606771121621

Duration = 3.81 years (Rounded to two decimals)

Answer -> 3.81 (Option C)

jeff jeffy answered 1 year ago

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