ABC Corporation has 4-year, 5% annual coupon bonds outstanding. Given a 6.5% yield to maturity, determine the duration of these bonds.

Question

Quizplus · Accepted Answer

To calculate the duration of a bond, we use the formula:

Duration = (1 + (1 / y)) * ((PV of all future cash flows) - (Face value / (1 + y)^n)) / (PV of bond * y)

where y represents the yield to maturity, n represents the number of periods, and PV represents the present value.

First, we need to calculate the present value of the bond, which is the sum of the present values of all the coupon payments and the face value:

PV of bond = (50 / (1 + 0.065)^1) + (50 / (1 + 0.065)^2) + (50 / (1 + 0.065)^3) + (1,000 / (1 + 0.065)^4) 
PV of bond = 1,754.25

Next, we need to calculate the present value of all the future cash flows weighted by their time until payment. We can break this down into two parts: the present value of the coupon payments and the present value of the face value:

PV of coupon payments = (1 / (1 + 0.065)^1) * 50 + (2 / (1 + 0.065)^2) * 50 + (3 / (1 + 0.065)^3) * 50 
PV of coupon payments = 132.91

PV of face value = (4 / (1 + 0.065)^4) * 1,000 
PV of face value = 743.80

So the present value of all future cash flows is:

PV of all future cash flows = PV of coupon payments + PV of face value
PV of all future cash flows = 876.71

Now we can plug in all the values into the duration formula:

Duration = (1 + (1 / 0.065)) * ((876.71) - (1,000 / (1 + 0.065)^4)) / (1,754.25 * 0.065) 
Duration = 2.90

Therefore, the duration of the bond is 2.90 years, which corresponds to answer choice C.

ABC Corporation Has 4-Year, 5% Annual Coupon Bonds Outstanding