# On the topic of bonds...

B

#### Bill Woessner

I'll be the first to admit that I know nothing about bonds. But the
more. I found some information on GM's bonds on their web site:

http://www.gm.com/corporate/investor_information/fixed-inc-sec/

Just for the sake of an example, let's look at XGM. According to
Google Finance, XGM closed at \$5.54 yesterday. That's on a par value
of \$25. The coupon rate is 7.25% and there's roughly 32.5 years left
to maturity.

One interesting thing I noticed is that the bond pays \$1.8125 per year
in interest. At that rate, it would only take 3 years to earn back
the current cost of the bond. In other words, as long as GM doesn't
default on these bonds in the next 3 years, you'll at least get your
principal back.

But assuming you hold on to the bond until maturity (and GM doesn't
default on it), what kind of return will you get? It seems simple
enough to calculate. The bond will pay \$1.8125 per year for 32.5
years. That's a total of \$58.90625 in interest. And when the bond
matures, you get the par value back. That's another \$25 for a grand
total of \$83.90625. That makes for an equivalent continuously
compounded interest rate of ln(83.90625 / 5.54) / 32.5 = 8.36%.

Except... there's a major difference. In a traditional compounded
interest scenario, you have to reinvest your interest. That's not the
case here. In fact, the concept of reinvesting interest isn't even
applicable unless you consider the case of buying new bonds. So maybe
this bond has MORE than an 8.36% rate of return? Not sure how to

Anyway, that was my first foray in to thinking about bonds. Is all of
This was just a thought exercise.

Thanks,
Bill

T

#### themightyatlast

I'll be the first to admit that I know nothing about bonds. But the
more. I found some information on GM's bonds on their web site:

http://www.gm.com/corporate/investor_information/fixed-inc-sec/

Just for the sake of an example, let's look at XGM. According to
Google Finance, XGM closed at \$5.54 yesterday. That's on a par value
of \$25. The coupon rate is 7.25% and there's roughly 32.5 years left
to maturity.

One interesting thing I noticed is that the bond pays \$1.8125 per year
in interest. At that rate, it would only take 3 years to earn back
the current cost of the bond. In other words, as long as GM doesn't
default on these bonds in the next 3 years, you'll at least get your
principal back.

But assuming you hold on to the bond until maturity (and GM doesn't
default on it), what kind of return will you get? It seems simple
enough to calculate. The bond will pay \$1.8125 per year for 32.5
years. That's a total of \$58.90625 in interest. And when the bond
matures, you get the par value back. That's another \$25 for a grand
total of \$83.90625. That makes for an equivalent continuously
compounded interest rate of ln(83.90625 / 5.54) / 32.5 = 8.36%.

Except... there's a major difference. In a traditional compounded
interest scenario, you have to reinvest your interest. That's not the
case here. In fact, the concept of reinvesting interest isn't even
applicable unless you consider the case of buying new bonds. So maybe
this bond has MORE than an 8.36% rate of return? Not sure how to

Anyway, that was my first foray in to thinking about bonds. Is all of
This was just a thought exercise.

Thanks,
Bill
Yep. That's the trick. If you compute the rate of return assuming you
can reinvest the dividends at the same rate, you will get some
staggering rate of return. I compute this as 33%. If you could
reinvest the interest for 32 years by buying more bonds, and the bonds
remain at a yield-to-maturity of 33% you will end up with \$47k in
principal repayment at the end of the 32 years, 86000 times what you
paid.

Of course the market is implying that there is an approximately 30%
chance of GM bonds becoming worthless each year for the next 32 years.
So the chances of riding this out would be something like 3 in a
million. So this is a giant accumulator bet, where you double your
money like every 2.5 years, but have a 50% chance of going bust every
2.5 years.

Nice exercise though. Haven't done something like this in Excel since
my MBA oh so many years ago. I guess it would have been Lotus 1-2-3 in
those days.

======================================= MODERATOR'S COMMENT:
A reminder to all posters: Please trim the post you respond to and try to be as succinct as possible.

T

#### themightyatlast

I'll be the first to admit that I know nothing about bonds. But the
more. I found some information on GM's bonds on their web site:

http://www.gm.com/corporate/investor_information/fixed-inc-sec/

Just for the sake of an example, let's look at XGM. According to
Google Finance, XGM closed at \$5.54 yesterday. That's on a par value
of \$25. The coupon rate is 7.25% and there's roughly 32.5 years left
to maturity.

One interesting thing I noticed is that the bond pays \$1.8125 per year
in interest. At that rate, it would only take 3 years to earn back
the current cost of the bond. In other words, as long as GM doesn't
default on these bonds in the next 3 years, you'll at least get your
principal back.

But assuming you hold on to the bond until maturity (and GM doesn't
default on it), what kind of return will you get? It seems simple
enough to calculate. The bond will pay \$1.8125 per year for 32.5
years. That's a total of \$58.90625 in interest. And when the bond
matures, you get the par value back. That's another \$25 for a grand
total of \$83.90625. That makes for an equivalent continuously
compounded interest rate of ln(83.90625 / 5.54) / 32.5 = 8.36%.

Except... there's a major difference. In a traditional compounded
interest scenario, you have to reinvest your interest. That's not the
case here. In fact, the concept of reinvesting interest isn't even
applicable unless you consider the case of buying new bonds. So maybe
this bond has MORE than an 8.36% rate of return? Not sure how to

Anyway, that was my first foray in to thinking about bonds. Is all of
This was just a thought exercise.

Thanks,
Bill
Forgot to account for taxes on my last post. At a 40% marginal tax
rate you would only accumulate 525 times your original investment. So
it wouldn't be any fun at all.

======================================= MODERATOR'S COMMENT:
A reminder to all posters: Please trim the post you respond to and try to be as succinct as possible.

R

#### Ron Peterson

I'll be the first to admit that I know nothing about bonds.  But the
more.  I found some information on GM's bonds on their web site:

http://www.gm.com/corporate/investor_information/fixed-inc-sec/

Just for the sake of an example, let's look at XGM.  According to
Google Finance, XGM closed at \$5.54 yesterday.  That's on a par value
of \$25.  The coupon rate is 7.25% and there's roughly 32.5 years left
to maturity.

One interesting thing I noticed is that the bond pays \$1.8125 per year
in interest.  At that rate, it would only take 3 years to earn back
the current cost of the bond.  In other words, as long as GM doesn't
default on these bonds in the next 3 years, you'll at least get your
principal back.

But assuming you hold on to the bond until maturity (and GM doesn't
default on it), what kind of return will you get?  It seems simple
enough to calculate.  The bond will pay \$1.8125 per year for 32.5
years.  That's a total of \$58.90625 in interest.  And when the bond
matures, you get the par value back.  That's another \$25 for a grand
total of \$83.90625.  That makes for an equivalent continuously
compounded interest rate of ln(83.90625 / 5.54) / 32.5 = 8.36%.

Except... there's a major difference.  In a traditional compounded
interest scenario, you have to reinvest your interest.  That's not the
case here.  In fact, the concept of reinvesting interest isn't even
applicable unless you consider the case of buying new bonds.  So maybe
this bond has MORE than an 8.36% rate of return?  Not sure how to

Anyway, that was my first foray in to thinking about bonds.  Is all of
This was just a thought exercise.
money-zine.com has a bond yield calculator that gives the yield at
32.7%.

D

#### dapperdobbs

Interesting ... I get an after 20% tax real rate of return discounted
at 3% inflation equal to about 7.4%.

Never really caught on about natural logarithms ... most girls found
them boring ... I used a NPV formula.

Hope I'm not being obtuse here, but what I find most interesting about
tracking into the unfamiliar land of bonds and yields is that the
original investment of \$5.45 turning into \$25 is an unadjusted 4.8%
return. Adjusted for 3% inflation, it would be a bit under 1.8%
annualized. Given that the current yield on the bond after 20% tax is
26%, I would have expected much more than a real return of 7.4%, of
which the 1.8% capital gain is a significant component. I never really
understood why I didn't like bonds that much - the nominal yield
stated decreases each year by the rate of inflation, eventually
approaching zero, and the interest is subject to tax bracket creep.
The principal declines as well, assuming par for par, so you get to a
zero return even faster.

By comparison, an investment in stocks - according the Siegel's
averages and so forth - has returned an equivalent percentage to the
exceptional XGM. A company that regularly increases its dividend
payout should keep the yield constant at least above the rate of
inflation (saving wear and tear on the calculators), and regular
increases in earnings provides the equivalent of continuous
compounding.

D

#### Douglas Johnson

Of course the market is implying that there is an approximately 30%
chance of GM bonds becoming worthless each year for the next 32 years.
So the chances of riding this out would be something like 3 in a
million. So this is a giant accumulator bet, where you double your
money like every 2.5 years, but have a 50% chance of going bust every
2.5 years.
A Credit Default Swap is a kind of insurance policy against a bond defaulting.
You make an up front payment and then an annual payment. If the bond defaults,
the seller of the CDS makes you whole.

Today, to insure \$1,000,000 of GMAC bonds, you need to pay \$450,000 up front and
\$50,000 a year there after. The market thinks GM is toast.

See http://www.reuters.com/article/bondsNews/idUSN3146536620081031.

-- Doug

T

Bill said:
Just for the sake of an example, let's look at XGM. According to
Google Finance, XGM closed at \$5.54 yesterday. That's on a par value
of \$25. The coupon rate is 7.25% and there's roughly 32.5 years left
to maturity.

total of \$83.90625. That makes for an equivalent continuously
compounded interest rate of ln(83.90625 / 5.54) / 32.5 = 8.36%.

Anyway, that was my first foray in to thinking about bonds. Is all of
this correct?

Bill, without even looking at your specific calculations...that's NOT
correct because you're using a financial calculation that applies to
less-risky issues - a \$25 trust-preferred selling for \$24.33, perhaps.

You have to throw that out the window when you look at the debt of
highly distressed companies - no doubt you're aware of GM/GMAC's issues,
it's front-page news. Their debt is NOT being priced based on the model
you're using, with 32.5 years of cash flows and a lump sum at the end.
Rather, those distressed prices signal the market's belief that there is
a very high risk of bankruptcy, suspended debt payments, restructuring,
etc. It's a highly speculative guess about what the current debt holders
might receive when the dust settles (which could be 32.5 years of
interest plus principal at maturity, but the pricing says that is
extremely unlikely).

I think this is a terrible place to head on your first foray into bonds!