Question

1. The following table summarizes prices of various default-free, zero-coupon bonds (expressed as a percentage of face value): Maturity (years) Price (per $100 face value) $95.51 9105 $86.38 $81.65 $76.51 (a) Compute the yield to maturity for each bond. (b) Plot the zero-coupon yield curve (for the first five years). (c) Is the yield curve upward sloping, downward sloping, or flat? 2. Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%. (a) What is the dollar amount of each coupon payment? (b) Is this bond currently trading at a discount, at par, or at a premium? Explain. (c) If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), what price will the bond trade for? 3. Afirm issued a new series of bonds on January 1, 1992. The bonds were sold at par ($1,000), have a 12 percent coupon, and mature in thirty years. Coupon payments are made semi-annually (on June 30 and December 31). (a) What was the yield to maturity of the bond on 1/1/92? (b) Calculate the price of the bond on 1/1/97, five years later, assuming that the level of interest rate has fallen to 10%. (c) If, on July 1, 2012, an investor expects the bonds to sell for $896.64. What is the expected yield to maturity on the bonds at that date? 4. A bond with two years remaining until maturity offers a 3% coupon rate with interest paid annually At a market discount rate of 4%, find the price of this bond per 100 of par value. 5. An investor who owns a bond with a 9% coupon rate that pays interest semiannually and matures three years is considering its sale. If the yield-to-maturity on the bond is 11%, find the price of the bond per 100 of par value.

Answer 1

The YTM y for a zero-coupon bond maturing n years from today is given by the equation

M=P*(1+y)ⁿ

where M is the maturity price and P is the market price of the bond

a) For 1 year bond

100 = 95.51 *(1+y)

=> y = 100/95.51 -1 =0.04701 =4.70%

For 2 year bond

100 = 91.05 *(1+y)²

=> y = (100/91.05)^0.5 -1 =0.047997 =4.80%

For 3 year bond

100 = 86.38 *(1+y)³

=> y = (100/86.38)^0.333 -1 =0.05002 =5.00%

For 4 year bond

100 = 81.65 *(1+y)⁴

=> y = (100/81.65)^0.25 -1 =0.051988 =5.20%

For 5 year bond

100 = 76.51 *(1+y)⁵

=> y = (100/76.51)^0.2 -1 =0.05501 =5.50%

b) Yield curve is the plot of Yield to Maturities against the Maturity periods as given below

Yield Curve 5.60000% 5.50000% 5.40000% 5.30000% 5.20000% 5.10000% Yield to maturity 5.00000% 4.90000% 4.80000% 4.70000% 4.60000% 3 4 5

c) As we can clearly see from the plot, this is an upward sloping yield curve where the interest rates are increasing for higher maturity periods.