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Answer:
You should be willing to pay $984.93 for Bond X
Explanation:
The price of a bond is equivalent to the present value of all the cash flows that are likely to accrue to an investor once the bond is bought. These cash-flows are the periodic coupon payments that are to be paid annually and the proceeds from the sale of the bond at the end of year 5.
During the 5 years, there are 5 equal periodic coupon payments that will be made. Given a par value equal to $1,000 and a coupon rate equal to 11% the annual coupon paid will be = $110. This stream of cash-flows is an ordinary annuity.
The PV of the cash-flows = PV of the coupon payments + PV of the value of the bond at the end of year 5
Assuming that at the end of year 5 the yield to maturity on a 15-year bond with similar risk will be 10.5%, the price of the bond will be equal to :
110*PV Annuity Factor for 15 periods at 10.5%+ $1,000* PV Interest factor with i=10.5% and n =15
= =$1,036.969123
therefore, the value of the bond today equals
110*PV Annuity Factor for 5 periods at 12%+ $1,036.969123* PV Interest factor with i=12% and n =5
= =$984.93