The yield to maturity on one-year zero-coupon bonds is ...
The yield to maturity on one-year zero-coupon bonds is currently 5 percent;
the YTM on two-year zeroes is 6 percent. The federal government plans to issue a
two-year maturity coupon bond, paying coupons once per year with a coupon rate of
9 percent. The face value of the bond is $1000.
a. At what price will the bond sell?
P = [(90/1.05) + (1090/1.062)
= $1,055.81
b. What will be the yield to maturity on the bond?
5.96% (Please see the attached excel sheet for calculations)
c. If the expectations theory is correct, what is the market expectation of the
price that the bond will sell for next year?
The forward rate for next year is 9%
1 + f2 = [1.062/1.05] = 1.0701, which implies f2 = 7.01%. Therefore, using an expected rate for next year of r2 = 9%, we can find that the forecast bond price is
P = (1,071/1.09) = $981.74
d. Recalculate your answer to (c) if you believe in the liquidity preference theory
and you believe that the liquidity premium is 2 percent.
If the liquidity premium is 2%, then the forecast interest rate is:
E[r2] = f2 – liquidity premium = 9% - 2% = 7%, and you forecast the bond to sell at:
(1,090/1.07) = $1,018.69
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