The Investment FAQ - Advice

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Subject: Advice - Beginning Investors

Last-Revised: 1 Aug 1998
Contributed-By: Steven Pearson, E. Green, [email protected]

Investing is just one aspect of personal finance. People often seem to
have the itch to try their hand at investing before they get the rest of
their act together. This is a big mistake. For this reason, it's a
good idea for "new investors" to hit the library and read maybe three
different overall guides to personal finance - three for different
perspectives, and because common themes will emerge (repetition implies
authority?). Personal finance issues include making a budget, sticking
to a budget, saving money towards major purchases or retirement,
managing debt appropriately, insuring your property, etc. Appropriate
books that focus on personal finance include the following (the links
point to

* Janet Bamford et al.
The Consumer Reports Money Book: How to Get It, Save It, and Spend
It Wisely (3rd edn)
* Andrew Tobias
The Only Investment Guide You'll Ever Need
* Eric Tyson
Personal Finance for Dummies

Another great resource for learning about investing, insurance, stocks,
etc. is the Wall Street Journal's Section C front page. Beginners
should make a special effort to get the Friday edition of the WSJ
because a column named "Getting Going" usually appears on that day and
discusses issues in, well, getting going on investments. If you don't
want to spend the dollar or so for the WSJ, try your local library.

What I am specifically NOT talking about is most anything that appears
on a list of investing/stock market books that are posted in
misc.invest.* from time to time. This includes books like Market Logic,
One Up on Wall Street, Beating the Dow, Winning on Wall Street, The
Intelligent Investor, etc. These are not general enough. They are
investment books, not personal finance books.

Many "beginning investors" have no business investing in stocks. The
books recommended above give good overall money management, budgeting,
purchasing, insurance, taxes, estate issues, and investing backgrounds
from which to build a personal framework. Only after that should one
explore particular investments. If someone needs to unload some cash in
the meantime, they should put it in a money market fund, or yes, even a
bank account, until they complete their basic training.

While I sympathize with those who view this education as a daunting
task, I don't see any better answer. People who know next to nothing
and always depend on "professional advisors" to hand-hold them through
all transactions are simply sheep asking to be fleeced (they may not
actually be fleeced, but most of them will at least get their tails
bobbed). In the long run, an individual is the only person ultimately
responsible for his or her own financial situation.

Beginners may want to look further in The Investment FAQ for the
articles that discuss the basics of mutual funds , basics of stocks ,
and basics of bonds . For more in-depth material, browse the Investment
FAQ bookshelf with its recommended books about personal finance and

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Subject: Advice - Errors in Investing

Last-Revised: 2 Aug 1999
Contributed-By: [email protected] , tprice at

The Wall Street Journal of June 18, 1991 had an article on pages C1/C10
on Investment Errors and how to avoid them. As summarized from that
article, the errors are:
* Not following an investment objective when you build a portfolio.
* Buying too many mutual funds.
* Not researching a one-product stock before you buy.
* Believing that you can pick market highs and lows (time the
* Taking profits early.
* Not cutting your losses.
* Buying the hottest {stock, mutual fund} from last year.

Here's a recent quote that underscores the last item. When asked
"What's the biggest mistake individual investors make?" on Wall $treet
Week, John Bogle, founder and senior chairman of Vanguard mutual funds,
said "Extrapolating the trend" or buying the hot stock.

On a final note, get this quote on market timing:

In the 1980s if you were out of the market on the ten best
trading days of the decade you missed one-third of the total

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Subject: Advice - Using a Full-Service Broker

Last-Revised: 23 Mar 1998
Contributed-By: Bill Rini (bill at, [email protected]

There are several reasons to choose a full-service broker over a
discount or web broker. People use a full-service broker because they
may not want to do their own research, because they are only interested
in long-term investing, because they like to hear the broker's
investment ideas, etc. But another important reason is that not
everybody likes to trade. I may want retirement planning services from
my broker. I may want to buy 3 or 4 mutual funds and have my broker
worry about them. If my broker is a financial planner, perhaps I want
tax or estate advice on certain investment options. Maybe I'm saving
for my newborn child's education but I have no idea or desire to work
out a plan to make sure the money is there when she or he needs it.

A huge reason to stick with a full-service broker is access to initial
public offerings (IPOs). These are generally reserved for the very best
clients, where best is defined as "someone who generates lots of
revenue," so someone who trades just a few times a year doesn't have a
chance. But if you can afford to trade frequently at the full-service
commission rates, you may be favored with access to some great IPOs.

And the real big one for a lot of people is quite simply time . Full
service brokerage clients also tend to be higher net worth individuals
as well. If I'm a doctor or lawyer, I can probably make more money by
focusing on my business than spending it researching stocks. For many
people today, time is a more valuable commodity than money. In fact, it
doesn't even have to do with how wealthy you are. Americans, in
general, work some pretty insane hours. Spending time researching
stocks or staying up on the market is quality time not spent with
family, friends, or doing things that they enjoy. On the other hand
some people enjoy the market and for those people there are discount

The one thing that sort of scares me about the difference between full
service and discount brokers is that a pretty good chunk of discount
brokerage firm clients are not that educated about investing. They look
at a $20 commission (discount broker) and a $50 commission (full service
broker) and they decide they can't afford to invest with a full service
broker. Instead they plow their life savings into some wonder stock
they heard about from a friend (hey, it's only a $20 commission, why
not?) and lose a few hundred or thousand bucks when the investment goes
south. Not that a broker is going to pick winners 100% of the time but
at least the broker can guide or mentor a beginning investor until they
learn enough to know what to look for and what not to look for in a
stock. I look at the $30 difference in what the two types of brokerage
firms charge as the rebate for education and doing my own research. If
you're not going to educate yourself or do your own research, you don't
deserve the rebate.

For more insights from Bill Rini, visit The Syndicate:

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Subject: Advice - One-Line Wisdom

Last-Revised: 22 Aug 1993
Contributed-By: Maurice Suhre

This is a collection of one-line pieces of investment wisdom, with brief
explanations. Use and apply at your own risk or discretion. They are
not in any particular order.

Hang up on cold calls.
While it is theoretically possible that someone is going to offer
you the opportunity of a lifetime, it is more likely that it is
some sort of scam. Even if it is legitimate, the caller cannot
know your financial position, goals, risk tolerance, or any other
parameters which should be considered when selecting investments.
If you can't bear the thought of hanging up, ask for material to be
sent by mail.
Don't invest in anything you don't understand.
There were horror stories of people who had lost fortunes by being
short puts during the 87 crash. I imagine that they had no idea of
the risks they were taking. Also, all the complaints about penny
stocks, whether fraudulent or not, are partially a result of not
understanding the risks and mechanisms.
If it sounds too good to be true, it probably is [too good to be true].
Also stated as ``There ain't no such thing as a free lunch
(TANSTAAFL).'' Remember, every investment opportunity competes with
every other investment opportunity. If one seems wildly better
than the others, there are probably hidden risks or you don't
understand something.
If your only tool is a hammer, every problem looks like a nail.
Someone (possibly a financial planner) with a very limited
selection of products will naturally try to jam you into those
which s/he sells. These may be less suitable than other products
not carried.
Don't rush into an investment.
If someone tells you that the opportunity is closing, filling up
fast, or in any other way suggests a time pressure, be very leery.
Very low priced stocks require special treatment.
Risks are substantial, bid/asked spreads are large, prices are
volatile, and commissions are relatively high. You need a broker
who knows how to purchase these stocks and dicker for a good price.

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Subject: Advice - Paying for Investment Advice

Last-Revised: 25 Apr 1997
Contributed-By: [email protected]

I'm no expert, but there's a simple rule that you should use to evaluate
all advice that is offered to you, especially advice for which someone
who doesn't know you is asking significant sums of money. Ask yourself
why the person is selling or giving it to you. If it sounds like a sure
ticket to riches, then why is the person wasting their time on YOU when
they could be out there making piles of dough?

Of course I'm offering advice here in this article, so let's turn the
tables on me right now. What's in it for me? Well, if you're reading
this article from my web site, look up at the top of the page. If you
have images turned on, you'll see a banner ad. I get a tiny payment
each time a person loads one of my pages with an ad. So my motivation
is to provide informative articles in order to lure visitors to the
site. Of course if you're reading this from the plain-text version of
the FAQ, you won't see any ads, but please do stop by the site sometime!

So if someone promises you advice that will yield 10-20% monthly
returns, perhaps at a price of some $3,000, you should immediately get
suspicious. If this were really true - i.e., if you pay for the advice
you'll immediately start getting these returns - you would be making
over 300% annually (compounded). Hey, that would sure be great, I
wouldn't have a day job anymore. And if it were true, wouldn't you
think that the person trying to sell it to you would forget all about
selling and just watch his or her money triple every year? But they're
not doing that, which should give you a pretty good idea about where the
money's being made, namely from you .

I'm not trying to say that you should never pay for advice, just that
you should not overpay for advice. Some advice, especially the sort
that comes from $15 books on personal finance and investments can easily
be worth ten times that sum. Advice from your CPA or tax advisor will
probably cost you a 3 or even 4-digit figure, but since it's specialized
to your case and comes from a professional, that's probably money well

It seems appropriate to close this article with a quote that I learned
from Robert Heinlein books, but it's probably older than that:

TANSTAAFL - there ain't no such thing as a free lunch.

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Subject: Advice - Researching a Company

Last-Revised: 3 Jun 1997
Contributed-By: George Regnery (regnery at

This article gives a basic idea of some steps that you might take to
research a company. Many sites on the web will help you in your quest
for information, and this article gives a few of them. You might look
for the following.
1. What multiple of earnings is the company trading at versus other
companies in the industry? The site does
this comparison reasonably well, and they base it on forward
earnings instead of historical earnings, which is also good.
2. Is the stock near a high or low, and how has it done recently.
This is usually considered technical analysis. More sophisticated
(or at least more complicated) studies can also be performed.
There are several sites that will give you historical graphs; one
3. When compared with other companies in the industry, how much times
the book value or times sales is the company trading? For this
information, the site is a good place to
4. Does the company have good products, good management, good future
prospects? Are they being sued? Do they have patents? What's the
competition like? Do they have long term contracts established? Is
their brand name recognized? Depending on the industry, some or all
of these questions may be relevant. There isn't a simple web site
for this information, of course. The Hoover's profiles have some
limited information to at least let you get a feel for the basics
of the company. And the SEC has lots of information in their Edgar
5. Management. Does the company have competent people running it? The
backgrounds of the directors can be found in proxy statements
(14As) in the Edgar database. Note that proxies are written by the
companies, though. Another thing I would suggest looking at is the
compensation structure of the CEO and other top management. Don't
worry so much about the raw figure of how they are paid -- instead,
look to see how that compensation is structured. If the management
gets a big base but bonuses are a small portion, look carefully at
the company. For some industries, like electric utilities, this is
OK, because the management isn't going to make a huge difference
(utilities are highly regulated, and thus the management is
preventing from making a lot of decisions). However, in a high
tech industry, or many other industries, watch your step if the
mgmt. gets a big base and the bonus is insignificant. This means
that they won't be any better off financially if the company makes
a lot of profits vs. no profits (unless, of course, they own a lot
of stock). This information is all in the Proxies at the SEC.
Also check to see if the company has a shareholder rights plan,
because if they do, the management likely doesn't give a damn about
shareholder rights, but rather cares about their own jobs. (These
plans are commonly used to defend against unfriendly takeovers and
therefore provide a safety blanket for management.) These
suggestions should get you started. Also check the article elsewhere in
this FAQ on free information sources for more resources away from the

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Subject: Advice - Target Stock Prices

Last-Revised: 25 Jun 2000
Contributed-By: blash404 at

A target price for a stock is a figure published by a securities
industry person, usually an analyst. The idea is that the target price
is a prediction, a guess about where the stock is headed. Target prices
usually are associated with a date by which the stock is expected to hit
the target. With that explanation out of the way..

Why do people suddenly think that the term du jour "target price" has
any meaning?? Consider the sources of these numbers. They're ALWAYS
issued by someone who has a vested interest in the issue: It could be an
analyst whose firm was the underwriter, it could be an analyst whose
firm is brown-nosing the company, it could be a firm with a large
position in the stock, it could be an individual trying to talk the
stock up so he can get out even, or it could be the "pump" segment of a
pump-and-dump operation. There is also a chance that the analyst has no
agenda and honestly thinks the stock price is really going places. But
in all too many cases it’s nothing more than wishful guesswork (unless
they have a crystal ball that works), so the advice here: ignore target
prices, especially ones for internet companies.

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Subject: Analysis - Annual Reports

Last-Revised: 31 Oct 1995
Contributed-By: Jerry Bailey, [email protected]

The June 1994 Issue of "Better Investing" magazine, page 26 has a
three-page article about reading and understanding company annual
reports. I will paraphrase:

1. Start with the notes and read from back to front since the front is
management fluff.
2. Look for litigation that could obliterate equity, a pension plan in
sad shape, or accounting changes that inflated earnings.
3. Use it to evaluate management. I only read the boring things of
the companies I am holding for long term growth. If I am planning
a quick in and out, such as buying depressed stocks like BBA, CML,
CLE, etc.), I don't waste my time.
4. Look for notes to offer relevant details; not "selected" and
"certain" assets. Revenue and operating profits of operating
divisions, geographical divisions, etc.
5. How the company keeps its books, especially as compared to other
companies in its industry.
6. Inventory. Did it go down because of a different accounting
7. What assets does the company own and what assets are leased?

If you do much of this, I really recommend just reading the article.

The following list of resources may also help.
* John A. Tracy has written an an easy-to-read and informative book
named How to Read a Financial Report (4th edn., Wiley, 1993). This
book should give you a good start. You won't become a graduate
student in finance by reading it, but it will certainly help you
grasp the nuts and bolts of annual reports.
* ABC News offers the following article:
* IBM offers a web site with much information about understanding
financial reports:

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Subject: Analysis - Beta and Alpha

Last-Revised: 22 Oct 1997
Contributed-By: Ajay Shah ( ), R. Shukla, Bob
Pierce (rbp at

Beta is the sensitivity of a stock's returns to the returns on some
market index (e.g., S&P 500). Beta values can be roughly characterized
as follows:

* b less than 0
Negative beta is possible but not likely. People thought gold
stocks should have negative betas but that hasn't been true.
* b equal to 0
Cash under your mattress, assuming no inflation
* beta between 0 and 1
Low-volatility investments (e.g., utility stocks)
* b equal to 1
Matching the index (e.g., for the S&P 500, an index fund)
* b greater than 1
Anything more volatile than the index (e.g., small cap. funds)
* b much greater than 1 (tending toward infinity)
Impossible, because the stock would be expected to go to zero on
any market decline. 2-3 is probably as high as you will get.

More interesting is the idea that securities MAY have different betas in
up and down markets. Forbes used to (and may still) rate mutual funds
for bull and bear market performance.

Alpha is a measure of residual risk (sometimes called "selecting risk")
of an investment relative to some market index. For all the gory
details on Alpha, please see a book on technical analysis.

Here is an example showing the inner details of the beta calculation

Suppose we collected end-of-the-month prices and any dividends for a
stock and the S&P 500 index for 61 months (0..60). We need n + 1 price
observations to calculate n holding period returns, so since we would
like to index the returns as 1..60, the prices are indexed 0..60. Also,
professional beta services use monthly data over a five year period.

Now, calculate monthly holding period returns using the prices and
dividends. For example, the return for month 2 will be calculated as:
r_2 = ( p_2 - p_1 + d_2 ) / p_1
Here r denotes return, p denotes price, and d denotes dividend. The
following table of monthly data may help in visualizing the process.
(Monthly data is preferred in the profession because investors' horizons
are said to be monthly.)

Nr. Date Price Div.(*) Return
0 12/31/86 45.20 0.00 --
1 01/31/87 47.00 0.00 0.0398
2 02/28/87 46.75 0.30 0.0011
. ... ... ... ...
59 11/30/91 46.75 0.30 0.0011
60 12/31/91 48.00 0.00 0.0267
(*) Dividend refers to the dividend paid during the period. They are
assumed to be paid on the date. For example, the dividend of 0.30 could
have been paid between 02/01/87 and 02/28/87, but is assumed to be paid
on 02/28/87.

So now we'll have a series of 60 returns on the stock and the index
(1...61). Plot the returns on a graph and fit the best-fit line
(visually or using some least squares process):

| * /
stock | * * */ *
returns| * * / *
| * / *
| * /* * *
| / * *
| / *
+------------------------- index returns

The slope of the line is Beta. Merrill Lynch, Wells Fargo, and others
use a very similar process (they differ in which index they use and in
some econometric nuances).

Now what does Beta mean? A lot of disservice has been done to Beta in
the popular press because of trying to simplify the concept. A beta of
1.5 does not mean that is the market goes up by 10 points, the stock
will go up by 15 points. It doesn't even mean that if the market has a
return (over some period, say a month) of 2%, the stock will have a
return of 3%. To understand Beta, look at the equation of the line we
just fitted:

stock return = alpha + beta * index return

Technically speaking, alpha is the intercept in the estimation model.
It is expected to be equal to risk-free rate times (1 - beta). But it
is best ignored by most people. In another (very similar equation) the
intercept, which is also called alpha, is a measure of superior

Therefore, by computing the derivative, we can write:
Change in stock return = beta * change in index return

So, truly and technically speaking, if the market return is 2% above its
mean, the stock return would be 3% above its mean, if the stock beta is

One shot at interpreting beta is the following. On a day the (S&P-type)
market index goes up by 1%, a stock with beta of 1.5 will go up by 1.5%
+ epsilon. Thus it won't go up by exactly 1.5%, but by something

The good thing is that the epsilon values for different stocks are
guaranteed to be uncorrelated with each other. Hence in a diversified
portfolio, you can expect all the epsilons (of different stocks) to
cancel out. Thus if you hold a diversified portfolio, the beta of a
stock characterizes that stock's response to fluctuations in the market

So in a diversified portfolio, the beta of stock X is a good summary of
its risk properties with respect to the "systematic risk", which is
fluctuations in the market index. A stock with high beta responds
strongly to variations in the market, and a stock with low beta is
relatively insensitive to variations in the market.

E.g. if you had a portfolio of beta 1.2, and decided to add a stock
with beta 1.5, then you know that you are slightly increasing the
riskiness (and average return) of your portfolio. This conclusion is
reached by merely comparing two numbers (1.2 and 1.5). That parsimony
of computation is the major contribution of the notion of "beta".
Conversely if you got cold feet about the variability of your beta = 1.2
portfolio, you could augment it with a few companies with beta less than

If you had wished to figure such conclusions without the notion of beta,
you would have had to deal with large covariance matrices and nontrivial

Finally, a reference. See Malkiel, A Random Walk Down Wall Street , for
more information on beta as an estimate of risk.

Here are a few links that offer information about beta.
* Barra Inc. offers historical and predicted beta values for stocks
that make up the major indexes. Visit this URL:
* For a brief discussion of using Beta and Alpha values to pick
stocks, visit this URL:

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Subject: Analysis - Book-to-Bill Ratio

Last-Revised: 19 Aug 1993
Contributed-By: Timothy May

The book-to-bill ration is the ratio of business "booked" (orders taken)
to business "billed" (products shipped and bills sent).

A book-to-bill of 1.0 implies incoming business = outgoing product.
Often in downturns, the b-t-b drops to 0.9, sometimes even lower. A
b-t-b of 1.1 or higher is very encouraging.

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Subject: Analysis - Book Value

Last-Revised: 23 Mar 1998
Contributed-By: Art Kamlet (artkamlet at

In simplest terms, Book Value is Assets less Liabilities.

The problem is Assets includes, as stated, existing land & buildings,
inventory, cash in the bank, etc. held by the company.

The problem in assuming you can sell off these assets and receive their
listed value is that such values are accounting numbers, but otherwise
pretty unrealistic.

Consider a company owning a 40 year old building in downtown Chicago.
That building might have been depreciated fully and is carried on the
books for $0, while having a resale value of millions. The book value
grossly understates the sell-off value of the company.

On the other hand, consider a fast-changing industry with 4-year-old
computer equipment which has a few more years to go before being fully
depreciated, but that equipment couldn't be sold for even 10 cents on
the dollar. Here the book value overstates the sell-off value.

So consider book value to be assets less liabilities, which are just
numbers, not real items. If you want to know how much a company should
be sold off for, hire a good investment banker, which is often done on
take-over bids.

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Subject: Analysis - Computing Compound Return

Last-Revised: 30 Dec 1995
Contributed-By: Paul Randolph (paulr4 at

To calculate the compounded return on an investment, just figure out the
factor by which the original investment multiplied. For example, if
$1000 became $3200 in 10 years, then the multiplying factor is 3200/1000
or 3.2. Now take the 10th root of 3.2 (the multiplying factor) and you
get a compounded return of 1.1233498 (12.3% per year). To see that this
works, note that 1.1233498 ** 10 = 3.2 (i.e.,
1.233498 raised to the 10th power equals 3.2).

Here is another way of saying the same thing. This calculation assumes
that all gains are reinvested, so the following formula applies:
TR = (1 + AR) ** YR
where TR is total return (present value/initial value), AR is the
compound annualized return, and YR is years. The symbol '**' is used to
denote exponentiation (2 ** 3 = 8).

To calculate annualized return, the following formula applies:
AR = (TR ** (1/YR)) - 1
Thus a total return of 950% in 20 years would be equivalent to an
annualized return of 11.914454%. Note that the 950% includes your
initial investment of 100% (by definition) plus a gain of 850%.

For those of you using spreadsheets such as Excel, you would use the
following formula to compute AR for the example discussed above (the
common computer symbol used to denote exponentiation is the caret or hat
on top of the 6).
= TR ^ (1 / YR) - 1
where TR = 9.5 and YR = 20. If you want to be creative and have AR
recalculated every time you open your file, you can substitute something
like the following for YR:
( (*cell* - TODAY() ) / 365)
Of course you will have to replace '*cell*' by the appropriate address
of the cell that contains the date on which you bought the security.

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Subject: Analysis - Future and Present Value of Money

Last-Revised: 28 Jan 1994
Contributed-By: [email protected]

This note explains briefly two concepts concerning the
time-value-of-money, namely future and present value. Careful
application of these concepts will help you evaluate investment
opportunities such as real estate, life insurance, and many others.

Future Value
Future value is simply the sum to which a dollar amount invested today
will grow given some appreciation rate.

To compute the future value of a sum invested today, the formula for
interest that is compounded monthly is:
fv = principal * [ (1 + rrate/12) ** (12 * termy) ]

fv = future value
principal = dollar value you have now
termy = term, in years
rrate = annual rate of return in decimal (i.e., use .05 for

Note that the symbol '**' is used to denote exponentiation (2 ** 3 = 8).

For interest that is compounded annually, use the formula:
fv = principal * [ (1 + rrate) ** (termy) ]


I invest 1,000 today at 10% for 10 years compounded monthly.
The future value of this amount is 2707.04.

Note that the formula for future value is the formula from Case 1 of
present value (below), but solved for the future-sum rather than the
present value.

Present Value
Present value is the value in today's dollars assigned to an amount of
money in the future, based on some estimate rate-of-return over the
long-term. In this analysis, rate-of-return is calculated based on
monthly compounding.

Two cases of present value are discussed next. Case 1 involves a single
sum that stays invested over time. Case 2 involves a cash stream that
is paid regularly over time (e.g., rent payments), and requires that you
also calculate the effects of inflation.

Case 1a: Present value of money invested over time.
This tells you what a future sum is worth today, given some rate of
return over the time between now and the future. Another way to
read this is that you must invest the present value today at the
rate-of-return to have some future sum in some years from now (but
this only considers the raw dollars, not the purchasing power).

To compute the present value of an invested sum, the formula for
interest that is compounded monthly is:
pv = ------------------------------
(1 + rrate/12) ** (12 * termy)

* future-sum = dollar value you want to have in termy
* termy = term, in years
* rrate = annual rate of return that you can expect,
in decimal


I need to have 10,000 in 5 years. The present value of
10,000 assuming an 8% monthly compounded rate-of-return
is 6712.10. I.e., 6712 will grow to 10k in 5 years at

Case 1b: Effects of inflation
This formulation can also be used to estimate the effects of
inflation; i.e., compute the real purchasing power of present and
future sums. Simply use an estimated rate of inflation instead of
a rate of return for the rrate variable in the equation.


In 30 years I will receive 1,000,000 (a megabuck). What
is that amount of money worth today (what is the buying
power), assuming a rate of inflation of 4.5%? The answer
is 259,895.65

Case 2: Present value of a cash stream.
This tells you the cost in today's dollars of money that you pay
over time. Usually the payments that you make increase over the
term. Basically, the money you pay in 10 years is worth less than
that which you pay tomorrow, and this equation lets you compute
just how much less.

In this analysis, inflation is compounded yearly. A reasonable
estimate for long-term inflation is 4.5%, but inflation has
historically varied tremendously by country and time period.

To compute the present value of a cash stream, the formula is:
month=12 * termy paymt * (1 + irate) ** int ((month - 1)/
pv = SUM
month=1 (1 + rrate/12) ** (month - 1)

* pv = present value
* SUM (a.k.a. sigma) means to sum the terms on the
right-hand side over the range of the variable
'month'; i.e., compute the expression for month=1,
then for month=2, and so on then add them all up
* month = month number
* int() = the integral part of the number; i.e., round
to the closest whole number; this is used to compute
the year number from the month number
* termy = term, in years
* paymt = monthly payment, in dollars
* irate = rate of inflation (increase in
payment/year), in decimal
* rrate = rate of return on money that you can expect,
in decimal


You pay $500/month in rent over 10 years and estimate
that inflation is 4.5% over the period (your payment
increases with inflation.) Present value is 49,530.57

Two small C programs for computing future and present value are
available. See the article Software - Archive of Investment-Related
Programs in this FAQ for more information.

--------------------Check for updates------------------

Subject: Analysis - Goodwill

Last-Revised: 18 Jul 1993
Contributed-By: John Keefe

Goodwill is an asset that is created when one company acquires another.
It represents the difference between the price the acquiror pays and the
"fair market value" of the acquired company's assets. For example, if
JerryCo bought Ford Motor for $15 billion, and the accountants
determined that Ford's assets (plant and equipment) were worth $13
billion, $2 billion of the purchase price would be allocated to goodwill
on the balance sheet. In theory the goodwill is the value of the
acquired company over and above the hard assets, and it is usually
thought to represent the value of the acquired company's "franchise,"
that is, the loyalty of its customers, the expertise of its employees;
namely, the intangible factors that make people do business with the

What is the effect on book value? Well, book value usually tries to
measure the liquidation value of a company -- what you could sell it for
in a hurry. The accountants look only at the fair market value of the
hard assets, thus goodwill is usually deducted from total assets when
book value is calculated.

For most companies in most industries, book value is next to
meaningless, because assets like plant and equipment are on the books at
their old historical costs, rather than current values. But since it's
an easy number to calculate, and easy to understand, lots of investors
(both professional and amateur) use it in deciding when to buy and sell

--------------------Check for updates------------------

Subject: Analysis - Internal Rate of Return (IRR)

Last-Revised: 25 June 1999
Contributed-By: Christopher Yost (cpy at, Rich Carreiro
(rlcarr at

If you have an investment that requires and produces a number of cash
flows over time, the internal rate of return is defined to be the
discount rate that makes the net present value of those cash flows equal
to zero. This article discusses computing the internal rate of return
on periodic payments, which might be regular payments into a portfolio
or other savings program, or payments against a loan. Both scenarios
are discussed in some detail.

We'll begin with a savings program. Assume that a sum "P" has been
invested into some mutual fund or like account and that additional
deposits "p" are made to the account each month for "n" months. Assume
further that investments are made at the beginning of each month,
implying that interest accrues for a full "n" months on the first
payment and for one month on the last payment. Given all this data, how
can we compute the future value of the account at any month? Or if we
know the value, what was the rate of return?

The relevant formula that will help answer these questions is:
F = -P(1+i)**n - [p(1+i)((1+i)**n - 1)/i]
In this formula, "F" is the future value of your investment (i.e., the
value after "n" months or "n" weeks or "n" years--whatever the period
over which the investments are made), "P" is the present value of your
investment (i.e., the amount of money you have already invested), "p" is
the payment each period, "n" is the number of periods you are interested
in, and "i" is the interest rate per period. Note that the symbol '**'
is used to denote exponentiation (2 ** 3 = 8).

Very important! The values "P" and "p" should be negative . This
formula and the ones below are devised to accord with the standard
practice of representing cash paid out as negative and cash received (as
in the case of a loan) as positive. This may not be very intuitive, but
it is a convention that seems to be employed by most financial programs
and spreadsheet functions.

The formula used to compute loan payments is very similar, but as is
appropriate for a loan, it assumes that all payments "p" are made at the
end of each period:
F = -P(1+i)**n - [p((1+i)**n - 1)/i]
Note that this formula can also be used for investments if you need to
assume that they are made at the end of each period. With respect to
loans, the formula isn't very useful in this form, but by setting "F" to
zero, the future value (one hopes) of the loan, it can be manipulated to
yield some more useful information.

To find what size payments are needed to pay-off a loan of the amount
"P" in "n" periods, the formula becomes this:
p = ------------
(1+i)**n - 1
If you want to find the number of periods that will be required to
pay-off a loan use this formula:
log(-p) - log(-Pi - p)
n = ----------------------

Keep in mind that the "i" in all these formula is the interest rate per
period . If you have been given an annual rate to work with, you can
find the monthly rate by adding 1 to annual rate, taking the 12th root
of that number, and then subtracting 1. The formula is:
i = ( r + 1 ) ** 1/12 - 1
where "r" is the rate.

Conversely, if you are working with a monthly rate--or any periodic
rate--you may need to compound it to obtain a number you can compare
apples-to-apples with other rates. For example, a 1 year CD paying 12%
in simple interest is not as good an investment as an investment paying
1% compounded per month. If you put $1000 into each, you'll have $1120
in the CD at the end of the year but $1000*(1.01)**12 = $1126.82 in the
other investment due to compounding. In this way, interest rates of any
kind can be converted to a "simple 1-year CD equivalent" for the
purposes of comparison. (See the article "Computing Compound Return"
for more information.)

You cannot manipulate these formulas to get a formula for "i," but that
rate can be found using any financial calculator, spreadsheet, or
program capable of calculating Internal Rate of Return or IRR.

Technically, IRR is a discount rate: the rate at which the present value
of a series of investments is equal to the present value of the returns
on those investments. As such, it can be found not only for equal,
periodic investments such as those considered here but for any series of
investments and returns. For example, if you have made a number of
irregular purchases and sales of a particular stock, the IRR on your
transactions will give you a picture of your overall rate of return.
For the matter at hand, however, the important thing to remember is that
since IRR involves calculations of present value (and therefore the
time-value of money), the sequence of investments and returns is

Here's an example. Let's say you buy some shares of Wild Thing
Conservative Growth Fund, then buy some more shares, sell some, have
some dividends reinvested, even take a cash distribution. Here's how to
compute the IRR.

You first have to define the sign of the cash flows. Pick positive for
flows into the portfolio, and negative for flows out of the portfolio
(you could pick the opposite convention, but in this article we'll use
positive for flows in, and negative for flows out).

Remember that the only thing that counts are flows between your wallet
and the portfolio. For example, dividends do NOT result in cash flow
unless they are withdrawn from the portfolio. If they remain in the
portfolio, be they reinvested or allowed to sit there as free cash, they
do NOT represent a flow.

There are also two special flows to define. The first flow is positive
and is the value of the portfolio at the start of the period over which
IRR is being computed. The last flow is negative and is the value of
the portfolio at the end of the period over which IRR is being computed.

The IRR that you compute is the rate of return per whatever time unit
you are using. If you use years, you get an annualized rate. If you
use (say) months, you get a monthly rate which you'll then have to
annualize in the usual way, and so forth.

On to actually calculating it...

We first have the net present value or NPV:

NPV(C, t, d) = Sum C[i ]/(1+d)^t[i ]

C[i ] is the i-th cash flow (C[0] is the first, C[N] is the
d is the assumed discount rate.
t[i ] is the time between the first cash flow and the i-th.
Obviously, t[0]=0 and t[N]=the length of time under
consideration. Pick whatever units of time you like, but
remember that IRR will end up being rate of return per chosen
time unit.

Given that definition, IRR is defined by the equation: NPV(C, t, IRR) =

In other words, the IRR is the discount rate which sets the NPV of the
given cash flows made at the given times to zero.

In general there is no closed-form solution for IRR. One must find it
iteratively. In other words, pick a value for IRR. Plug it into the
NPV calculation. See how close to zero the NPV is. Based on that, pick
a different IRR value and repeat until the NPV is as close to zero as
you care.

Note that in the case of a single initial investment and no further
investments made, the calculation collapses into:

(Initial Value) - (Final Value)/(1+IRR)^T = 0 or
(Initial Value)*(1+IRR)^T - (Final Value) = 0
Initial*(1+IRR)^T = Final
(1+IRR)^T = Final/Initial
And finally the quite familiar:
IRR = (Final/Inital)^(1/T) - 1

A program named 'irr' that calculates IRR is available. See the article
Software - Archive of Investment-Related Programs in this FAQ for more

--------------------Check for updates------------------

Subject: Analysis - Paying Debts Early versus Making Investments

Last-Revised: 14 July 2000
Contributed-By: Gary Snyder, Thomas Price (tprice at,
[email protected] , John A. Weeks III (john at

This article analyzes the question of whether you should apply any extra
cash you might have lying around to making extra payments on a debt, or
whether you should instead leave the debt on its regular payment
schedule and invest the cash instead. An equivalent question is whether
you should cash out an existing investment to pay down debt, or just let
it ride. We'll focus on the example of a first mortgage on a house, but
the analysis works (with some changes) for a car loan, credit-card debt,

Before we compare debts with investments, it's important to frame the
debate. A bit of financial planning is appropriate here; there are
several articles in the FAQ about that. To start with, an individual
should have an emergency fund of 3-6 months of living expenses.
Emergency funds need to be readily available (when was the last
emergency that you could plan for), like in a bank, credit union, or
maybe a money market fund. And most people would not consider these
investments. So the first thing to do with cash is arguably to
establish this sort of rainy-day fund. If you have to cash out a stock
to get this fund, that's ok; remember, emergencies rarely happen at
market tops.

Before we run numbers, I'd like to point out two important issues here.
The most important issue to remember is risk. Making early payments to
a loan exposes you to relatively few risks (once the loan is paid, it
stays paid), but two notable risks are liquidity and opportunity. The
liquidity risk is that you might not have cash when you need it (but see
above for the mitigation strategy of a rainy-day fund). The opportunity
risk is the possibility that a better opportunity might present itself
and you would be unable to take advantage of it since you gave the bank
your extra cash. And when you invest money, you generally expose
yourself to market risk (the investment's price might fall) as well as
other risks that might cause you to lose money. Of course the other
important issue (you probably guessed) is taxes. The interest paid on
home mortgages is deductable, so that acts to reduce the cost of the
loan below the official interest rate on the loan. Not true for
credit-card debt, etc. Also, monies earned from an investment are
taxed, so that acts to reduce the return on the investment.

One more caveat. If you simply cannot save; i.e., you would cash out
the investments darned quick, then paying down debt may be a good
choice! And owning a home gives you a place to live, especially if you
plan to live in it on a modest income.

Finally, all you can do in advance is estimate, guess, and hope. No one
will never know the answer to "what is best" until long after it is too
late to take that best course of action. You have to take your shot
today, and see where it lands tomorrow.

Now we'll run some numbers. If you have debt as well as cash that you
will invest, then maintaining the debt (instead of paying it) costs you
whatever the interest rate on the loan is minus whatever you make from
the investment. So to justify your choice of investing the cash,
basically you're trying to determine whether you can achieve a return on
your investment that is better than the interest rate on the debt. For
example, you might have a mortgage that has an after-tax rate of 6%, but
you find a very safe investment with a guaranteed, after-tax return of
9% (I should be so lucky). In this case, you almost certainly should
invest the money. But the analysis is never this easy -- it invariably
depends on knowing what the investments will yield in the future.

But don't give up hope. Although it is impossible to predict with
certainty what an investment will return, you can still estimate two
things, the likely return and the level of risk. Since paying down any
debt entails much lower risk than making an investment, you need to get
a higher level of return to assume the market risk (just to name one) of
an investment. In other words, the investment has to pay you to assume
the risk to justify the investment. It would be foolish to turn down a
risk-free 10% (i.e., to pay off a debt with an after-tax interest rate
of 10%) to try to get an after-tax rate of 10.5% from an investment in
the stock market, but it might make very good sense to turn down a
risk-free 6.5%. It is a matter of personal taste how big the difference
between the return on the investment and the risk-free return has to be
(it's called the risk premium), but thinking like this at least lets you
frame the question.

Next we'll characterize some investments and their associated risks.
Note that characterizing risk is difficult, and we'll only do a
relatively superficial job it. The purpose of this article is to get
you thinking about the options, not to take each to the last decimal

Above we mentioned that paying the debt is a low-risk alternative. When
it comes to selecting investments that potentially will yield more than
paying down the debt, you have many options. The option you choose
should be the one that maximizes your return subject to a given level of
risk (from one point of view). Paying off the loan generates a
rock-solid guaranteed return. The best option you have at approximately
this level of risk is to invest in a short-term, high-grade corporate
bond fund. The key market risk in this investment is that interest
rates will go up by more than 1%; another risk of a bond fund is that
companies like AT&T will start to default on their loans. Not quite
rock-solid guaranteed, but close. Anyway, these funds have yielded
about 6% historically.

Next in the scale of risk is longer-term bonds, or lower rated bonds.
Investing in a high-yield (junk) bond fund is actually quite safe,
although riskier than the short-term, high grade bond fund described
above. This investment should generate 7-8% pre-tax (off the top of my
head), but could also lose a significant amount of money over short
periods. This happened in the junk bond market during the summer of
1998, so it's by no means a remote possibility.

The last investment I'll mention here are US stock investments.
Historically these investments have earned about 10-11%/year over long
periods of time, but losing money is a serious possibility over periods
of time less than three years, and a return of 8%/year for an investment
held 20 years is not unlikely. Conservatively, I'd expect about an 8-9%
return going forward. I'd hope for much more, but that's all I'd count
on. Stated another way, I'd choose a stock investment over a CD paying
6%, but not a CD paying 10%.

Don't overlook the fact that the analysis basically attempted to answer
the question of whether you should put all your extra cash into the
market versus your mortgage. I think the right answer is somewhere in
between. Of course it's nice to be debt free, but paying down your
debts to the point that you have no available cash could really hurt you
if your car suddenly dies, etc. You should have some savings to cushion
you against emergencies. And of course it's nice to have lots of
long-term investments, but don't neglect the guaranteed rate of return
that is assured by paying down debt versus the completely unguaranteed
rate of return to be found in the markets.

The best thing to do is ask yourself what you are the most comfortable
with, and ignore trying to optimize variables that you cannot control.
If debt makes you nervous, then pay off the house. If you don't worry
about debt, then keep the mortgage, and keep your money invested. If
you don't mind the ups and downs of the market, then keep invested in
stocks (they will go up over the long term). If the market has you
nervous, pull out some or all of it, and ladder it into corporate bonds.
In short, each person needs to find the right balance for his or her

--------------------Check for updates------------------

Subject: Analysis - Price-Earnings (P/E) Ratio

Last-Revised: 27 Jan 1998
Contributed-By: E. Green, Aaron Schindler, Thomas Busillo,
[email protected]

P/E is shorthand for the ratio of a company's share price to its
per-share earnings. For example, a P/E ratio of 10 means that the
company has $1 of annual, per-share earnings for every $10 in share
price. Earnings by definition are after all taxes etc.

A company's P/E ratio is computed by dividing the current market price
of one share of a company's stock by that company's per-share earnings.
A company's per-share earnings are simply the company's after-tax profit
divided by number of outstanding shares. For example, a company that
earned $5M last year, with a million shares outstanding, had earnings
per share of $5. If that company's stock currently sells for $50/share,
it has a P/E of 10. Stated differently, at this price, investors are
willing to pay $10 for every $1 of last year's earnings.

P/Es are traditionally computed with trailing earnings (earnings from
the past 12 months, called a trailing P/E) but are sometimes computed
with leading earnings (earnings projected for the upcoming 12-month
period, called a leading P/E). Some analysts will exclude one-time
gains or losses from a quarterly earnings report when computing this
figure, others will include it. Adding to the confusion is the
possibility of a late earnings report from a company; computation of a
trailing P/E based on incomplete data is rather tricky. (I'm being
polite; it's misleading, but that doesn't stop the brokerage houses from
reporting something.) Even worse, some methods use so-called negative
earnings (i.e., losses) to compute a negative P/E, while other methods
define the P/E of a loss-making company to be zero. The many ways to
compute a P/E may lead to wide variation in the reporting of a figure
such as the "P/E for the S&P whatever." Worst of all, it's usually next
to impossible to discover the method used to generate a particular P/E
figure, chart, or report.

Like other indicators, P/E is best viewed over time, looking for a
trend. A company with a steadily increasing P/E is being viewed by the
investment community as becoming more and more speculative. And of
course a company's P/E ratio changes every day as the stock price

The price/earnings ratio is commonly used as a tool for determining the
value the market has placed on a common stock. A lot can be said about
this little number, but in short, companies expected to grow and have
higher earnings in the future should have a higher P/E than companies in
decline. For example, if Amgen has a lot of products in the pipeline, I
wouldn't mind paying a large multiple of its current earnings to buy the
stock. It will have a large P/E. I am expecting it to grow quickly. A
common rule of thumb is that a company's P/E ratio should be
approximately equal to that company's growth rate.

PE is a much better comparison of the value of a stock than the price.
A $10 stock with a PE of 40 is much more "expensive" than a $100 stock
with a PE of 6. You are paying more for the $10 stock's future earnings
stream. The $10 stock is probably a small company with an exciting
product with few competitors. The $100 stock is probably pretty staid -
maybe a buggy whip manufacturer.

It's difficult to say whether a particular P/E is high or low, but there
are a number of factors you should consider. First, it's useful to look
at the forward and historical earnings growth rate. For example, if a
company has been growing at 10% per year over the past five years but
has a P/E ratio of 75, then conventional wisdom would say that the
shares are expensive. Second, it's important to consider the P/E ratio
for the industry sector. For example, consumer products companies will
probably have very different P/E ratios than internet service providers.
Finally, a stock could have a high trailing-year P/E ratio, but if the
earnings rise, at the end of the year it will have a low P/E after the
new earnings report is released. Thus a stock with a low P/E ratio can
accurately be said to be cheap only if the future-earnings P/E is low.
If the trailing P/E is low, investors may be running from the stock and
driving its price down, which only makes the stock look cheap.

--------------------Check for updates------------------

The Investment FAQ is a collection of frequently asked questions and
answers about investments and personal finance. This is a plain-text
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