A Bond with a face value of CCU 100 is currently trading at CCU 103, coupon rate 8% to be paid annually. The bond has a yield to maturity of 7% p.a. and has three more years coupon payments to maturity. What is the duration of the bond? 2.887 2.776 2.631
Question
A Bond with a face value of CCU 100 is currently trading at CCU 103, coupon rate 8% to be paid annually. The bond has a yield to maturity of 7% p.a. and has three more years coupon payments to maturity. What is the duration of the bond? 2.887 2.776 2.631
Solution 1
To calculate the duration of the bond, we need to calculate the present value of the cash flows and the time they are received. The formula for the duration is:
Duration = (C / (1 + r)) * 1 + (C / (1 + r)^2) * 2 + (C / (1 + r)^3) * 3 + ((C + FV) / (1 + r)^3) * 3
Where: C = Annual coupon payment r = Yield to maturity FV = Face value of the bond
Given: C = 8% of CCU 100 = CCU 8 r = 7% or 0.07 FV = CCU 100
Substituting the values into the formula:
Duration = (8 / (1 + 0.07)) * 1 + (8 / (1 + 0.07)^2) * 2 + (8 / (1 + 0.07)^3) * 3 + ((8 + 100) / (1 + 0.07)^3) * 3
After calculating the above expression, you will get the duration of the bond. The closest option to the calculated value will be the answer.
Solution 2
To calculate the duration of the bond, we need to calculate the present value of the cash flows and the time they are received. The formula for the duration is:
Duration = (C / (1 + r)) * 1 + (C / (1 + r)^2) * 2 + (C / (1 + r)^3) * 3 + (M / (1 + r)^3) * 3
Where: C = annual coupon payment = 8% of CCU 100 = CCU 8 r = yield to maturity = 7% M = maturity value = CCU 100
Substituting the values into the formula:
Duration = (8 / (1 + 0.07)) * 1 + (8 / (1 + 0.07)^2) * 2 + (8 / (1 + 0.07)^3) * 3 + (100 / (1 + 0.07)^3) * 3
Calculating the above expression will give us the duration of the bond.
Please note that the duration is a measure of the sensitivity of the price of the bond to changes in interest rates. It is not a measure of the time to maturity. The options provided (2.887, 2.776, 2.631) seem to be potential results of the calculation, but without doing the actual calculation, it's not possible to confirm which one is correct.
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