Question

Bond valuation

You are considering a 15-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. If you require an "effective" annual interest rate (not a nominal rate) of 11.06%, how much should you be willing to pay for the bond? Do not round intermediate steps. Round your answer to the nearest cent.

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Answer 1

Par/Face value	1000
Annual Coupon rate	0.08
Annual coupon	80
semi-annual coupon	40
Present Value = Future value/[(1+(r/m))^mt]
the nominal rate or the yield to maturity has to be calculated using the effective interest rate that is 11.06%.
r is the interest rate that is 10.77%.
.1106 = ((1+i/2)^2) - 1
(1.1106)^(1/2) = (1+i/2)
1.05385 - 1 = (i/2)
I = 10.77%
t is the year
m is the compounding period that is 2
mt is the time period.
price of the bond = sum of present values of future cash flows
r/2	0.05385
mt	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
future cash flow	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	40	1040
present value	37.95607	36.01657	34.17619	32.42984	30.77273	29.20029	27.70821	26.29236	24.94886	23.67402	22.46432	21.31643	20.22719	19.19362	18.21285	17.28221	16.39911	15.56115	14.766	14.01148	13.29552	12.61614	11.97147	11.35975	10.77929	10.22848	9.705824	9.209872	8.739263	215.6102
sum of present values	796.1253
You should be willing to pay $796.1 for the bond.