The yield to maturity on 1-year zero-coupon bonds is currently 7.5%; the YTM on 2-year zeros is 8.5%. The Treasury plans to issue a 2-year maturity coupon bond, paying coupons once per year with a coupon rate of 10%. The face value of the bond is $100.

a. At what price will the bond sell?

b. What will the yield to maturity on the bond be?

c. If the expectations theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year?

d. Recalculate your answer to (c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1.5%.

The price of the bond = Coupon payment for year 1 / (1+ YTM on 1-year zero-coupon bonds) + (Coupon payment for year 2 + maturity Value) / (1+ YTM on 2-year zero-coupon bonds) ^2

= $10/ (1+7.5%) + ($10 + $100)/ (1+8.5%) ^2

=$9.30 +$93.44

=$102.74

b. What will the yield to maturity on the bond be?

Solution:

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C/ (1+YTM) + (M+C) / (1+YTM) ^2

Where,

P0 = the current market price of bond =$102.74

C = coupon payment = 10% of $100 = $10

YTM = interest rate, or yield to maturity =?

M = value at maturity, or par value = $ 100

Now we have,

$102.74 = $10/ (1+YTM) + $110 / (1+YTM) ^2

YTM = 2.73%

(c) If the expectations theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year?

Solution

Under expectation theory

ft = E(rt )

Therefore (1+ ft) = (1.085) ^ 2 / 1.075 = 1.0951

Or ft = E(rt )= 1.0951 -1 = 0.0951 or 9.51%

By using this theory the bond price on year,

P = $110/1.0951 = $100.44

(d) Recalculate your answer to (c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1.5%.

Solution

If the liquidity premium is 1.5%,

Then ft = E (rt) + L

Where L is liquidity premium = 1.5%

Therefore,

E(rt) = ft - L = 9.51% - 1.5% = 8.01%

And price of the bond

P = $110/1.0801 = $101.84