Question

Suppose a​ seven-year, $1,000 bond with a 8.03 % coupon rate and semiannual coupons is trading with a yield to maturity of 6.57%.

a. Is this bond currently trading at a​ discount, at​ par, or at a​ premuim? Explain.

b. If the yield to maturity of the bond rises to 7.26 % (APR with semiannual​ compounding), at what price will the bond​ trade?

Answer 1

a)When coupon rate is more than the Yield to maturity then it means bond is selling at a premium. Here coupon rate that is 8.03% is more then yield to maturity that is 6.57% so the bond is currently trading at a premium, b) Calculation of price of bond: ( In case of semi annual bond, yield= 7.26/2=3.63%, Coupon rate=8.03/2=4.015%, Years=14 Particulars Time PVf @3.63% Amount PV Cash Flows (Interest)                          1.00                   0.9650          40.15                 38.74 Cash Flows (Interest)                          2.00                   0.9312          40.15                 37.39 Cash Flows (Interest)                          3.00                   0.8986          40.15                 36.08 Cash Flows (Interest)                          4.00                   0.8671          40.15                 26.73 Cash Flows (Interest)                          5.00                   0.8367          40.15                 33.59 Cash Flows (Interest)                          6.00                   0.8074          40.15                 32.42 Cash Flows (Interest)                          7.00                   0.7791          40.15                 31.28 Cash Flows (Interest)                          8.00                   0.7518          40.15                 30.19 Cash Flows (Interest)                          9.00                   0.7255          40.15                 29.13 Cash Flows (Interest)                        10.00                   0.7001          40.15                 28.11 Cash Flows (Interest)                        11.00                   0.6756          40.15                 27.12 Cash Flows (Interest)                        12.00                   0.6519          40.15                 26.17 Cash Flows (Interest)                        13.00                   0.6291          40.15                 25.26 Cash Flows (Interest)                        14.00                   0.6070          40.15                 24.37 Cash flows (Maturity Amount)                        14.00                   0.6070    1,000.00               607.00 Fair Price           1,033.58 Price of bond is $1033.58