4.
(Bond valuation) Pybus Inc. is considering issuing bonds that will mature in 23 years with an annual coupon rate of 9%. Their par value will be
$1,000, and the interest will be paid semiannually. Pybus is hoping to get an AA rating on its bonds and, if it does, the yield to maturity on similar
AA bonds is 9.5%. However, Pybus is not sure whether the new bonds will receive an AA rating. If they receive an A rating, the yield to maturity
on similar A bonds is 10.5%. What will be the price of these bonds if they receive either an A or AA rating? (Round to the nearest cent.)
Solution
Par Value of the Bond $1,000.00
Coupon Rate 9%
No of years 23
Yield
For AA Rating 9.50%
For A Rating 10.50%
Since the coupon payment is semiannual the no of payments should be doubled, coupon payment
and yield should be halved.
For AA Rating
N
46
I
4.75%
Coupon Payment

45
Bond Value
$953.59
$45/(1+4.75%)^1+$45/(1+4.75%)^2……+$45/(1+4.75%)^46+$1000/(1+4.75%)^46
For A Rating
n
46
i
5.25%
Coupon Payment
45
Bond Value
$ 870.72
$45/(1+5.25%)^1+$45/(1+5.25%)^2……+$45/(1+5.25%)^46+$1000/(1+5.25%)^46
For AA
Rating
N 46
I 4.75%
Coupon
Paymen
t
45
Bond
Value
$953.5
9
$45/(1+4.75%)^1+$45/(1+4.75%)^2……+$45/(1+4.75%)^46+$1000/(1+4.75
%)^46