Final answer:
To calculate the price of a one-year coupon bond, discount the semi-annual coupon payments and face value at the given YTM with semiannual compounding. The present value of these cash flows is the price of the bond, which can change with fluctuations in interest rates.
Step-by-step explanation:
The question asks us to calculate the price of a one-year coupon bond with a face value of $1000, a coupon rate of 6.8%, and semi-annual payments considering the current yield to maturity (YTM) for similar Treasury STRIPS. Yield to maturity (YTM) is the rate of return on a bond if held to maturity, accounting for interest payments and the difference between the bond's current market price and its face value.
To find the price of the bond, we need to discount the expected cash flows - the coupon payments and the face value - back to the present using the YTM as the discount rate. The bond makes two coupon payments of $34 each (6.8% of $1000 divided by 2) and pays the face value of $1000 at maturity. The YTM for the one-year horizon is 7.1%, with semiannual compounding which translates to a semiannual rate of 7.1% / 2 = 3.55%. The price of the bond is the present value of these cash flows.
The present value of the first coupon payment is $34 / (1 + 0.0355)^1, and the present value of the second coupon payment plus face value is ($34 + $1000) / (1 + 0.0355)^2. Summing these will give us the price of the bond:
First coupon payment's present value: $34 / 1.0355 = $32.85
Second coupon payment and face value's present value: ($34 + $1000) / 1.0355^2 = $997.61
Price of the bond = $32.85 + $997.61 = $1030.46
The calculation assumes that the yield to maturity remains the same over the next year and that the coupons can be reinvested at the same rate. The price of a bond will be lower than face value when interest rates rise since newer bonds will offer higher returns. Conversely, if interest rates fall, existing bonds with higher coupon rates become more valuable and can be sold for more than their face value.