Question

Suppose a ten-year, $1,000 bond with an 8.1% coupon rate and semiannual coupon is trading for $1,035.36

Question

A. What is the bond's yield to maturity (expressed as an APR with semiannual compounding)? (round to 2 decimal places)

B. If the bond's yield to maturity changes to 9.9% APR, what will be the bond's price? (round to 2 decimal places)

Answer 1

a)

Yield to Maturity = [Coupon+{(Redemption Price-Issue Price)/Term}]/[(Redemption Price+Issue Price)/2]

Coupon = Par Value*Coupon Rate = 1000*8.1% = $81

Redemption Price (assumed, redeeming at par) = $1000

= [81+{(1000-1035.36)/10}]/[(1000+1035.36)/2]

= 77.464/1017.68

= 0.07611 = 7.61%

b)

Period	Cash Flow	Discounting Factor [1/(1.099^year)]	PV of Cash Flows (cash flows*discounting factor)
1	81	0.909918107	73.7033667
2	81	0.827950962	67.06402793
3	81	0.753367572	61.02277337
4	81	0.685502796	55.52572645
5	81	0.623751406	50.52386392
6	81	0.567562699	45.97257864
7	81	0.516435577	41.83128174
8	81	0.469914083	38.06304071
9	81	0.427583333	34.63424997
10	81	0.389065817	31.51433118
10	1000	0.389065817	389.065817
		Price of the Bond = Sum of PVs	888.9210576 = $888.92