Question

Problem 15-11 The yield to maturity on 1-year zero-coupon bonds is currently 8.5%; the YTM on 2-year zeros is 9.5%. The Treasury plans to issue a 2-year maturity coupon bond, paying coupons once per year with a coupon rate of 11%. The face value of the bond is $100. a. At what price will the bond sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What will the yield to maturity on the bond be? (Do not round intermediate calculations. Round your answer to 3 decimal places.) 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? (Do not round intermediate calculations. Round your answer to 2 decimal places.) d. Recalculate your answer to (c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1.5%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a. At what price will the bond sell?

• $102.71

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

• 0.0952 or 9.52%

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?

• $101.37

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

• $102.78

Step-by-step explanation:

current YTM for zero coupon bonds = 8.5% for 1 year bonds and 9.5% on 2 year bonds

The Treasury plans to issue a 2-year maturity coupon bond, paying coupons once per year with a coupon rate of 11%. The face value of the bond is $100.

bond price = PV of maturity value + PV coupons

• $100 / (1 + 9.5%)² = $83.40
• [$11 / (1 + 8.5%)] + [$11 / (1 + 9.5%)²] = $10.14 + $9.17 = $19.31
• issue price = $83.40 + $19.40 = $102.71

YTM = [C + (FV - PV)/n] / [(FV + PV)/2] = [11 + (100 - 102.71)/2] / [(100 + 102.71)/2] = 0.0952 or 9.52%

next year's price:

• $100 / (1 + 9.5%) = $91.32
• $11 / (1 + 9.5%) = $10.05
• total = 101.37

next year's price if you believe in liquidity preference theory (1.5%):

• $100 / (1 + 9.5% - 1.5%) = $92.59
• $11 / (1 + 9.5% - 1.5%) = $10.19
• total = $102.78