Final answer:
To determine the price of the T-note, the cash flows must be discounted using the prices of corresponding zero-coupon bonds as discount factors. Adding the present values of these cash flows will give us the price of the 3-year T-note. Changes in market interest rates affect bond prices due to the inverse relationship between interest rates and the present value of future cash flows.
Step-by-step explanation:
The question pertains to the calculation of the price of a 3-year Treasury note (T-note) that pays annual coupons and has a given face value, considering current market prices of zero-coupon bonds. To find the price of the T-note, each of the cash flows (coupons and face value) must be discounted to the present value using the respective zero-coupon bond prices as discount factors since these prices represent the present value of $1 payable in 1, 2, and 3 years under the current market conditions.
The annual coupon payment is 10% of the $1,000 face value, which means the investor receives $100 annually. To calculate the present value of the T-note, the cash flows are: $100 in one year, $100 in two years, and $1,100 (final coupon plus face value) in three years. Using the prices of the zero bonds as discount factors:
- $100 discounted by the one-year zero bond price of 0.95
- $100 discounted by the two-year zero bond price of 0.90
- $1,100 discounted by the three-year zero bond price of 0.80
Adding these present values together gives the current price of the T-note. This method is similar to the calculations used for a simple two-year bond example provided for reference.
When discount rates or market interest rates change, the present value of future cash flows changes inversely. This phenomenon reflects why bond prices move inversely to interest rates. If the discount rate (or market yield) increases, the present value of future cash flows decreases, resulting in a lower bond price (present discounted value). Hence, bonds issued at lower interest rates than the market rate will be sold at a discount, whereas bonds issued at higher rates will be sold at a premium.