Final Answer:
The duration of the 4-year 14% coupon bond with a face value of $1,000 and a current interest rate of 8% is approximately 3.88 years.
Step-by-step explanation:
Duration is a measure of the interest rate sensitivity of a bond, representing the weighted average time it takes for an investor to recover the bond's price through its total cash flows. To calculate duration, we consider the present value of the bond's future cash flows.
In this case, the bond pays a 14% coupon rate on a face value of $1,000, making annual interest payments of $140. With a current interest rate of 8%, the bond's price is higher than its face value. The duration is a weighted average of the bond's cash flows, where the weight is the present value of each cash flow divided by the bond's current price.
In this scenario, the bond's cash flows are mainly the coupon payments and the face value repayment at maturity. The higher coupon payments in the initial years contribute more significantly to the duration, given their higher present value.
As interest rates increase, the bond's price decreases, leading to a higher duration due to the increased sensitivity of future cash flows. The calculated duration of approximately 3.88 years indicates the time it takes for an investor to recoup the bond's price, considering the present value of its cash flows in the context of the prevailing interest rate.