a. Several years ago, Castles in the Sand Inc. issued bonds at face
value of $1,000 at a yield to maturity of 7.4%. Now, with 8 years left
until the maturity of the bonds, the company has run into hard times
and the yield to maturity on the bonds has increased to 12%. What
is the price of the bond now? (Assume semiannual coupon
payments.) (Do not round intermediate calculations. Round
your answer to 2 decimal places.)
b. Suppose that investors believe that Castles can make good on
the promised coupon payments but that the company will go
bankrupt when the bond matures and the principal comes due. The
expectation is that investors will receive only 82% of face value at
maturity. If they buy the bond today, what yield to maturity do they
expect to receive? (Do not round intermediate calculations.
Enter your answer as a percent rounded to 2 decimal
places.)
: 09_16_2017_QC_CS-100495, 09_20_2017_QC_CS-100607
Explanation
Some values below may show as rounded for display purposes, though unrounded
numbers should be used for actual calculations.
Since the bonds were issued at par, the coupon rate had to match the yield to maturity
at the time of issuance. Thus, the coupon rate is 7.4%.
a.
Since the bond has semiannual payments, the coupon payment, the interest rate, and
the number of periods must all be expressed in semiannual terms:
Bond price=PV of coupon payments + PV of face value
=C × ((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t
=[(.0740 × $1,000) / 2] × [[1 / (.1200 / 2)] – (1 / {(.1200 / 2)[1 + (.1200 / 2)]
=$767.56
}
(8 × 2)
b.
Bond price=PV of coupon payments + PV of face value
$767.56=C × ((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t
=[(.0740 × $1,000) / 2] × [[1 / (r / 2)] – (1 / {(r / 2)[1 + (r / 2)] })] + (.8200 × $
(8 × 2)
