CHAPTER 7 B-127
23. The bond has 14 years to maturity, so the bond price equation is:
Using a spreadsheet, financial calculator, or trial and error we find:
This is the semiannual interest rate, so the YTM is:
The current yield is the annual coupon payment divided by the bond price, so:
24. a. The bond price is the present value of the cash flows from a bond. The YTM is the interest rate
used in valuing the cash flows from a bond.
b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium,
since it provides periodic income in the form of coupon payments in excess of that required by
investors on other similar bonds. If the coupon rate is lower than the required return on a bond,
the bond will sell at a discount since it provides insufficient coupon payments compared to that
required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the
YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the
YTM is equal to the coupon rate.
c. Current yield is defined as the annual coupon payment divided by the current bond price. For
premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less
than the YTM, and for bonds selling at par value, the current yield is equal to the YTM. In all
cases, the current yield plus the expected one-period capital gains yield of the bond must be
equal to the required return.
25. The price of a zero coupon bond is the PV of the par, so:
b. In one year, the bond will have 24 years to maturity, so the price will be: