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The yield to maturity on one-year zero-coupon bonds is currently 7 percent; the YTM on two-year...

The yield to maturity on one-year zero-coupon bonds is currently 7 percent; the YTM on two-year zeroes is 8 percent. The federal government plans to issue a two-year-maturity coupon bond, paying coupons once per year with a coupon rate of 9 percent. The face value of the bond is $100.

  1. At what price will the bond sell?
  2. What will be the yield to maturity on the bond?
  3. 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?
  4. If the liquidity preference theory is correct and you believe that the liquidity premium is 1 percent, what is the market expectation of the price that the bond will sell for next year?

Solutions

Expert Solution

Ans:- (a) It is given in the question that YTM for a one-year zero-coupon bond is 7% and for two years is 8%. The government plans to issue a two-year coupon bond with a coupon of 9% and the face value of the bond is $100.

(a) In this Part, we need to find the price at which bond sells which is nothing but the present value of all the future cash flows. Let us assume the price at bond will sell be P

Now the Price P at which the bond will sell will be given by $9/(1+0.07)^1 + $109/(1 +0.08)^2 = $101.86.

(b) In this part, we need to find the yield to maturity on the bond. we can find YTM by Rate function of excel easily.

we know the following values PV = 101.86, FV = 100, NPER = 2, PMT =9

=Rate(nper,pmt,pv,fv)

=Rate(2,9,-101.86,100)

=7.958% is the required YTM i.e Yield to Maturity of the Bond.

(c) In this part, we need to calculate the market expectation price of the bond that it will sell for the next year. To find the market expectation price first, we need to find the next year forward rate by zero-coupon yield curve by the following equation.

1 + F2 = (1.08)^2/(1.07)

1 + F2 = 1.09009.

F2 = 9.009% = 9.01%

Now the market expectation of the bond will be given by $109/1.09009 = $99.99.

(d) If the liquidity preference theory is correct and the liquidity premium is 1% then we need to find the market expectation price of the bond.

Forecast Interest rate is given by = F2 - liquidity premium = 9.01% - 1% = 8.01%.

Now the required market expectation price of the bond will be given by $109/1.0801 =$100.91.

  

jeff jeffy answered 2 hours ago
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