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CH 18] Calculating Business 18-19

Example A: What is the (a) cost of purchasing two bonds of American Axle &
Manufacturing at its current price for a $1,000 bond, and given its coupon
rate what will be the (b) percent return of Interest paid for 1 year?

Solution Algorithm:

(a) Current Price % x $1,000/bond x 2 bonds = Cost to Purchase
99.25% x $1,000/bond x 2 bonds =
0.9925 x $1,000/bond x 2 bonds = $1985.00 (Cost to Purchase)

(b) Coupon Rate(%) x 2 Bonds x $1,000 = One year’s Interest
6.25% x 2 x $1,000 =
0.0625 x 2 x $1,000 = $125.00 (one year’s interest)
(One year’s Interest ÷ Cost to Purchase) x 100% = % return
($125.00 ÷ $1,985.00) x 100% = 6.30% return

In Example A, American Axel & Manufacturing is selling at 99.25% of the face value of
the bond and has a coupon rate of 6.25%. This company is paying 6.25% interest to the
bond holder per $1,000 bond. In this example American Axel & Manufacturing is paying
(0.0625 x $1,000 =) $62.50 per $1,000 bond.

This yields the bondholder a return of
The reason for being higher is
([$62.50 ÷ $992.50] x 100% = ) 6.30%. that the investor purchased
$1,000 bonds for $992.50.
This amounts to an interest rate that is
(6.30% − 6.25% =) 0.05% higher than the coupon rate.

Example B: What is the (a) cost of purchasing two bonds of AerCap Ireland Capital DAC
at its current price for a $1,000 bond and given its coupon rate what will be
the (b) percent return of Interest paid for 1 year?

Solution Algorithm:

(a) Current Price % x $1,000/bond x 2 bonds = Cost to Purchase
199% x $1,000/bond x 2 bonds =
1.99 x $1,000/bond x 2 bonds = $3,980.00 (Cost to Purchase)

(b) Coupon Rate(%) x 2 Bonds x $1,000 = One year’s Interest
3.875% x 2 x $1,000 =
0.03875 x 2 x $1,000 = $77.50 (one year’s interest)
(One year’s Interest ÷ Cost to Purchase) x 100% = % return
($77.50 ÷ $3,980.00) x 100% = 1.95% return

In Example B, AerCap Ireland Capital DAC has their bonds trading at 199% of the face
value of bond and has a coupon rate of 3.875%. This company is paying 3.875% interest to
the bond holder per $1,000 bond. In this example AerCap Ireland Capital DAC is paying
(0.03875 x $1,000 =) $38.75 interest per $1,000 bond. This yields the bondholder a return
of (($38.75 ÷ $1,990) x 100% = ) 1.95%. This amounts to an interest rate that is (3.875% -
1.950% =)1.925% lower than the coupon rate.

The idea of a bond, which is unique to Corporations, is that it allows the corporation to
borrow money from the public and pay the interest which the investor receives. Companies
borrow billions of dollars from the public through bonds, which represents a loan just as a
mortgage on real estate or a loan for an automobile. The coupons represent an interest only
payment to the bondholder. Each bond has a maturity date which is the date set on the
bond to redeem the bond by paying the bond holder the full amount of the bond in cash or,
if it is a convertible bond, giving shares of stock that will satisfy the bond value. A bond that 18
is convertible to stock will have cv in the terms of the bond.

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