Question

Suppose that our one-year 10% coupon bond was originally issued as a 20-year-maturity bond 19 years ago. At that time, the yield curve as flat at 10% per year. Now the bond has one year remaining before it matures, and the interest rate on one-year bonds is 5% per year.

Although the 10% coupon bond was issued at par ($1000), its market price will now be $1047.62.

How does the market price come out to be $1047.62 ????

Answer 1

The current market price of the bond is equal to the sum of present value of the bond's future cash flows.The future cash flows of the bond are the par value of $1000 (as the bond matures next year and par value is received back upon maturity) and the annual coupon payment of $100 (10% of the par value of $1000).

Therefore, Total Future Cash Flow Received (after one year or upon maturity or 20 years after bond issue) = Par Value + Annual Coupon Payment = 1000 + 100 = $ 1100

This Future Cash Flow needs to be discounted for one year (as market price of the bond needs to be determined today which is a period of one year) at the current existing yield of 5% and not the yield prevalent at the time of bond issued (which was 10%).

Therefore, if current Market Value is P, then

P = 1100 / (1.05) = $ 1047.62