Suppose a seven-year, $1,000 bond with an 8.1% coupon rate and semiannual coupon

Question

Suppose a seven-year, $1,000 bond with an 8.1% coupon rate and semiannual coupons is trading with a yield to maturity of 6.59%. a. Is this bond currently trading at a discount, at par, or at a premium? Explain. b. If the yield to maturity of the bond rises to 7.03% (APR with semiannual compounding), what price will the bond trade for? a. Is this bond currently trading at a discount, at par, or at a premium? Explain. (Select the best choice below.) O A. Because the yield to maturity is less than the coupon rate, the bond is trading at a premium. OB. Because the yield to maturity is greater than the coupon rate, the bond is trading at par. ° C. Because the yield to maturity is greater than the coupon rate, the bond is trading at a premium. OD. Because the yield to maturity is less than the coupon rate, the bond is trading at a discount. b. If the yield to maturity of the bond rises to 7.03% (APR with semiannual compounding), what price will the bond trade for? The new price of the bond is $. (Round to the nearest cent.)

Explanation / Answer

a. The bond is currently trading at Premium. Because the yield to maturity is less than coupon rate.

b. Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Current Market Price of Bonds = $1058.33 (441.83+616.50)

Note : Since the bond makes semiannual interest payments, total no. of period is 14 (7*2), cashflow per period is 40.50(1000*8.1%/2) and cashflows are discounted at 3.515% (7.03/2).

*PVAF = (1-(1+r)-n)/r = (1-1.03515-14) / .03515 = 10.9095

**PVF = 1 / (1+r)n = 1 / 1.0351514 = .6165

Year Cash flow PVAF/PVF@3.515% Present Value (Cashflow*PVAF/PVF) 1-14 40.5 10.9095* 441.83 14 1000 0.6165** 616.50

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