Question

The yield to maturity on 1-year zero-coupon bonds is currently 5%; the YTM on 2 -year zeros is 6%. The Treasury plans to issue a 2 -year maturity coupon bond, paying coupons once per year with a coupon rate of 7.5\%. 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 part (c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1%

Answer 1

To calculate the price at which the bond will sell, find the present value of the future cash flows. The yield to maturity (YTM) on the bond can be calculated using the present value of the cash flows and the current price. The market expectation of the price that the bond will sell for next year depends on the expectations theory of the yield curve or the liquidity preference theory with the liquidity premium.

Step-by-step explanation:

To calculate the price at which the bond will sell, we need to determine the present value of the future cash flows. The bond will pay coupons once per year for 2 years at a coupon rate of 7.5%. The face value is $100, so the coupon payments will be $7.50 per year. Using the yield to maturity (YTM) of 6%, we can discount these cash flows back to their present value. The price of the bond can be calculated as follows:

Year 1: Coupon payment = $7.50, Present value = $7.50 / (1 + 0.06) = $7.07

Year 2: Coupon payment = $7.50, Present value = $7.50 / (1 + 0.06)2 = $6.69

At the end of Year 2, the bond will also repay the face value of $100. The present value of the face value is $100 / (1 + 0.06)2 = $89.02

Adding up these present values, we get $7.07 + $6.69 + $89.02 = $102.78. Therefore, the bond will sell for a price of $102.78.

To calculate the yield to maturity (YTM) on the bond, we can use the present value of the future cash flows and the current price of the bond. The YTM is the discount rate that equates the present value of the cash flows to the current price. The YTM can be calculated using trial and error or using financial formulas. In this case, the YTM is approximately 5.83%.

According to the expectations theory of the yield curve, the market expectation of the price that the bond will sell for next year is equal to the price of the 1-year zero-coupon bond. Since the YTM on the 1-year zero-coupon bond is 5%, the market expectation of the price that the bond will sell for next year is calculated as follows:

Price = Face value / (1 + YTM) = $100 / (1 + 0.05) = $95.24

If you believe in the liquidity preference theory and the liquidity premium is 1%, then the market expectation of the price that the bond will sell for next year would be calculated as follows:

Price = Face value / (1 + YTM + liquidity premium) = $100 / (1 + 0.05 + 0.01) = $92.59