Question 1

You have estimated spot rates of Treasuries as follows:

r1 = 5%,

r2 = 5.4%

r3 = 5.7%

r4 = 5.9%

r5 = 6%

Face Value of bond is 1000

a. What are the discount factors for each of each of the next five years (that is, the present value of $1 paid

in year t)?

b. Calculate the PV of the following bonds, assuming annual coupons:

i. 5% coupon rate, two-year bond

ii. 5% coupon rate, five-year bond

iii. 10% coupon rate, five-year bond

c. Explain intuitively why the yield-to-maturity on the 10% bond (iii) is less than that on the 5% bond (ii).

Hint: Think about yield to maturity as a weighted average (by cash flows) of the spot rates.

d. What should be the yield-to-maturity on a five-year zero-coupon bond?

e. Show that the correct yield-to-maturity on a five-year annuity (that makes annual payments of $1) is 5.75%.

f. Explain intuitively why the yield on the five-year bonds described in part(c) must lie between the yield on a

five-year zero-coupon bond in part(d) and a five-year annuity in part(e).