Final answer:
The duration of 2-year bonds paying a 6% annual coupon and selling at par would typically be calculated considering the time and present value of the bond's cash flows. When the discount rate equals the coupon rate, the bond's price is at par, and when the discount rate increases, the bond price decreases due to a lower present value of expected cash flows.
Step-by-step explanation:
The question is about determining the duration of mid-term debt that consists of 2-year bonds with a 6% annual coupon rate and selling at par. This involves understanding the concept of bond duration, which measures the sensitivity of a bond's price to interest rate changes and indicates the weighted average time it takes to receive the bond's cash flows.
To calculate the present value of the bond when the discount rate is equal to the coupon rate (for example, 8% as mentioned in the SEO reference), you would discount the bond's future cash flows—that is, the annual interest payments and the principal repayment—back to their present value using the same rate. If interest rates rise, like going from 8% to 11%, the bond's price would decrease. This is because the present value of future cash flows is lower when discounted at a higher rate.
The bond's present value when the discount rate equals the coupon rate (8% in the example, though we're asked about 6%) is as follows:
- Year 1 Interest: PV = $240 / (1 + 0.08) = $222.22
- Year 2 Interest + Principal: PV = ($240 + $3,000) / (1 + 0.08)^2 = $2,777.78
- Total present value: $222.22 + $2,777.78 = $3,000.00
If the discount rate rises to 11%, then:
- Year 1 Interest: PV = $240 / (1 + 0.11) = $216.22
- Year 2 Interest + Principal: PV = ($240 + $3,000) / (1 + 0.11)^2 = $2,630.58
- Total present value: $216.22 + $2,630.58 = $2,846.80
Note that the bond sells at a discount compared to its face value because the discount rate is now higher than the coupon rate, reflecting the increased yield required by investors in the market.