Question

Suppose a? ten-year, $ 1000 bond with an 8.1 % coupon rate and semiannual coupons is trading for $ 1034.99. a. What is the? bond's yield to maturity? (expressed as an APR with semiannual? compounding)? b. If the? bond's yield to maturity changes to 9.5 % ?APR, what will be the? bond's price? (Round to two decimal? places.)

Answer 1

a)Calculation of Yield to maturity
Interest as it is semi annual(1000*0.081/2)	40.5
Face value	$1000
BOnd price	$1034.99
Years to maturity( as semi annual so 10*2)	20
Yield to maturity=	Interest+ (Face value-bond price)/years to maturity
	(face value + bond price)/2
	40.5+(1000-1034.99)/20
	(1000+1034.99)/2
	3.81%
Yield to maturity for half year is 3.81% Yield to maturity for full year is 7.62% b)Statement showing price of bond: ( In case of semi annual bond, yield= 9.5/2=4.75%, Coupon rate=8.1/2=4.05%, Years=20 Particulars Time PVf @4.75% Amount PV Cash Flows (Interest)                          1.00                   0.9547          40.50                 38.66 Cash Flows (Interest)                          2.00                   0.9114          40.50                 36.91 Cash Flows (Interest)                          3.00                   0.8700          40.50                 35.24 Cash Flows (Interest)                          4.00                   0.8306          40.50                 26.73 Cash Flows (Interest)                          5.00                   0.7929          40.50                 32.11 Cash Flows (Interest)                          6.00                   0.7570          40.50                 30.66 Cash Flows (Interest)                          7.00                   0.7226          40.50                 29.27 Cash Flows (Interest)                          8.00                   0.6899          40.50                 27.94 Cash Flows (Interest)                          9.00                   0.6586          40.50                 26.67 Cash Flows (Interest)                        10.00                   0.6287          40.50                 25.46 Cash Flows (Interest)                        11.00                   0.6002          40.50                 24.31 Cash Flows (Interest)                        12.00                   0.5730          40.50                 23.21 Cash Flows (Interest)                        13.00                   0.5470          40.50                 22.15 Cash Flows (Interest)                        14.00                   0.5222          40.50                 21.15 Cash Flows (Interest)                        15.00                   0.4985          40.50                 20.19 Cash Flows (Interest)                        16.00                   0.4759          40.50                 19.27 Cash Flows (Interest)                        17.00                   0.4543          40.50                 18.40 Cash Flows (Interest)                        18.00                   0.4337          40.50                 17.57 Cash Flows (Interest)                        19.00                   0.4141          40.50                 16.77 Cash Flows (Interest)                        20.00                   0.3953          40.50                 16.01 Cash flows (Maturity Amount)                        20.00                   0.3953    1,000.00               395.30 Fair Price               903.98 Price of Bond is $903.98