323.11
11.You look in the paper and see that an 8% coupon bond with
annual coupons, a par value of $1000, and 3 years to maturity is
selling for $1053.46. Why is that price correct? It can only be
correct if everyone agrees that they are just indifferent between
buying the bond and re-creating the cash flows on their own. That
is, if current market interest rates are 6% and the next coupon
is due in one year, how could you use $1053.46 to exactly
replicate the cash flows from the bond? Assume you have access to
an investment instrument (like a bank account) that returns 6%
per year. Explain how you would do this (you don't actually have
to work through the numbers--just tell me in words how you would
take $1053.46 and re-create the cash flows from the bond). (4)
In class, we went through an example of how we would create an annuity using the PV of the annuity (see your notes in the annuity topic). This is the same thing. You would take the $1053.46 and invest it in your 6% investment instrument. After one-year, you would withdraw $80 to pay the first coupon, leaving the remaining balance to continue earning interest. You would do the same after 2 years. Finally, at the end of 3 years there should be exactly $1080 left in the account, which you would withdraw to pay the 6 coupon plus the principal of the bond.