Seminar Exercises – Session 4
Session 4: Interest Rates and Bond Valuation
Read: Chapter 8: Valuing Bonds
1. You have estimated spot rates as follows:
Year
Spot Rate
1
5.00%
2
5.40%
3
5.70%
4
5.90%
5
6.00%
a. What are the discount factors for each date (that is, the present value of $1 paid in year
t)?
b. What are the forward rates for each period?
c. Calculate the PVs of the following government bonds. Assume annual compounding.
i. 5 percent coupon, two-year maturity.
ii. 5 percent coupon, five-year maturity.
iii. 10 percent coupon, five-year maturity.
2. Look at the material in the Question 1. Answer the following questions.
a. Explain intuitively why the yield to maturity on the 10 percent bond is less than that on
the 5 percent bond.
b. What should be the yield to maturity on a five-year zero coupon bond?
c. Show that the correct yield to maturity on a five-year annuity is 5.75 percent.
d. Explain intuitively why the yield on the five-year government bond described in part (c)
must lie between the yield on a five-year zero-coupon bond and a five-year annuity.
3. Look at the spot interest rates shown in the Question 1. Suppose that someone told you
that the six-year spot interest rate was 4.80 percent. Why would you not believe him? How
could you make money if he was right? What is the minimum sensible value for the six-
year spot rate?
4. A 6-year government bond makes annual coupon payments of 5 percent and offers a yield
of 3 percent annually compounded. Suppose that one year later the bond still yields 3
percent. What return has the bondholder earned over the 12-month period? Now suppose
instead that the bond yield is 2 percent at the end of the year. What return has the
bondholder earned in this case?
5. A 6 percent six-year bond yields 12 percent and a 10 percent six-year bond yields 8
percent. Calculate the six-year spot rate. (Assume annual coupon payments.)
