Burnt_toast --
Thanks so much for the excellent and detailed clarification. You'll
often see researchers shun questions that seem to be easy because they
know that the question is much more complex; has many nuances; or is
open to several interpretations.
You've detailed your prime issues and that's enormously helpful.
INTRODUCTION
==============
The world of finance has become very intriguing since the early 1970s,
with very sophisticated predictive models being used. They're based
on modern statistics and they've helped expand the use of options and
futures trading; created new ways for corporations to manage
everything from product development to currency trading; and even
emerged in the "Moneyball" school of baseball management:
Amazon.com
"Moneyball," Michael Lewis
http://www.amazon.com/exec/obidos/ASIN/0393057658/qid=1089483408/sr=2-3/ref=sr_2_3/002-0939296-9742461
Much of the serious academic work developing and testing these
concepts was done at my alma mater, the University of Chicago's
Graduate School of Business.
To start, let's look at the "cost of capital."
COST OF CAPITAL
================
When money is borrowed, there's a cost for the opportunity to use it
month-after-month or year-after-year.
In finance questions, you'll see a reference to "opportunity cost" or
"discount rate" or "cost of capital" or even just "inflation rate."
Historically, the inflation rate will be the foundation on which all
of these capital costs are based. When inflation goes up, so does a
U.S. Treasury bill and so does the prime rate and so do mortgage
rates.
So too, should returns on projects at Ford or Microsoft. So too,
should the returns on stock investments. Any company still investing
to earn a 5% return when inflation has doubled to 10% is actually
squandering investors' money.
Why the different terms for "interest cost"? Because different
investments carry different risk. Here are some different interest
costs, taken from the latest Wall Street Journal -- and structured
from lowest-risk to highest-risk:
* 6-month Treasury bills: 1.6%
* prime rate: 4.25%
* 10-year Treasury bond: 4.48%
* 30-year Treasury bond: 5.22%
* Freddie Mac 30-year mortgage: 5.72%
* Class A corporate bonds: 5.1-6.3%
* High-yield corporate bonds: 5.8-6.6%
* Credit card lending: 20-22%
What factors increase risk? You can see from the Treasury pricing
that one factor is time. If the U.S. government borrows for 6 months,
the yield is only 1.6% because it's unlikely that inflation will
devalue your investment much in that short a time period.
In general, the U.S. Treasury rates are also considered "risk free."
If the government runs out of money, it can print more -- though then
inflation rises.
Corporation rates are higher because a corporation can declare
bankruptcy, even if debts are "secured" by assets of the company. And
this partly explains why unsecured credit card loans to individuals
are so high.
RISK
=====
It turns out that the risk factors are pretty standard for borrowed
money (bonds, mortgages, preferred stock, T-bills) and for stocks and
for options and for futures.
? inflation rate
? time
? market risk
? firm risk
There's a high-simplified version here in the Cost of Capital section
of this page, which discusses the Capital Asset Pricing Model (CAPM):
QuickMBA
"Corporate Finance" (undated)
http://www.quickmba.com/finance/cf/
And two guys received the Nobel Prize for broadening this theory to
cover options and futures (also called "derivatives.") Robert
Merton and Myron Scholes got the Nobel Prize for figuring this out
(Fischer Black's death in 1995 preceded the prize). They developed
what's called the Black-Scholes Option Pricing model while teaching at
the University of Chicago's GSB in the early 1970s:
American Mathematical Society
"1997 Nobel Prize in Economics"
http://www.ams.org/new-in-math/nobel1997econ.html
I'd mentioned previously that when inflation is at 10%, a company
can't be investing in projects that return only 5%. Returns to
investors must be substantially higher -- and company managers have to
make decisions to get those returns. Since a company is a collection
of investment decisions being made every day, each project must get
those higher returns. General Electric should NOT use company cash to
buy a fleet of vehicles if investors expect a stock return of 15%
today and the company can finance those trucks at 5% from Ford Motor.
I won't go into how market risk and firm risk is figured other than to
say that it involves statistical measures of how stocks perform. It's
a complex area on its own; I'll recommend a book at the end of this
Google Answer that will be helpful.
SOME EXAMPLES
==============
LOTTERY WINNER
---------------
You've seen the lottery example already. Imagine that you're
Geraldine Williams, who just had the choice of taking $294M either as
a lump-sum $168 million or $11 million per year over 26 years.
USA Today
"$294M lottery winner is 68-year-old cleaning woman," (July 9, 2004)
http://www.usatoday.com/news/nation/2004-07-09-lottery-winner_x.htm
Williams has lots of decisions to make:
? does she think taxes will rise or fall?
? what about inflation?
? her life expectancy is shorter than the 26 years, so how does she
want to plan for her family to inherit the money?
? is there a likelihood that inheritance taxes will rise -- or fall?
The first valuable piece of information for her is to calculate what
implied return she's getting on the $168M if the state hands this
investment over to an insurance firm to create a 26-year annuity.
Note that if she accepts the annual payout, she's receiving $157
million less because they'll still write a before-tax check of $11
million.
The lottery will hand a check for $157 million to an insurance firm
and they'll invest it to yield 4.77%:
http://wwww.mooneyevents.com/williams.xls
Geraldine could do that herself by buying T-bills, if you see the
rates noted above. But the insurance company will invest that money
expecting to make at least 8 to 12% in a portfolio of stocks and bonds
-- and make a handsome profit.
Geraldine could do as well herself but buying a small number of mutual
funds. Doing so would cover all risks except market risk. And a
timing strategy of investing gradually in mutual funds over a 3-5 year
period would help balance that risk.
---
The "present value" of the $11M being paid by the lottery goes down
every year by the interest rate here. Her second check in July, 2005
is worth:
$11,000,000/1.0477 = $10,499,189
2006: $11M/(1.0477 * 1.0477) = $10.0M
2007: $11M/(1.0477 * 1.0477 * 1.0477) = $9.7M
.
.
.
2029: $11M/(1.0477)^25 = $11M/3.2057 = $3.43M
---
To answer your question about a continuous annuity (Are you saying
that after 200 years of inflation, the $9 million is insignificant?)
-- yes. In this case it becomes $986 in today's money.
In the original case for Missmallprincess, the implied rate was 9% --
much higher than the 4.77% that lottery officials are using today.
The NPV of the annuity paid in year 200 on $11M is 36 cents.
But a little secret here for you: I did the calculation that way only
because I couldn't get my annuity function to work properly in Excel!
YOUR BROTHER'S COMPANY
-----------------------
Your brother, French_Toast is an experienced chef who's decided that
it's time to go out on his own and launch a restaurant. You're to be
the financier for him and are considering borrowing against the house
to fund the enterprise.
You can borrow at prime rate (4.25%) to raise $300,000 to let French
open his restaurant. What's the cost-of-capital?
It would be highly unwise to use 4.25%, first because the prime rate
moves with markets. But more important are three other factors:
? there are market risks that should be accounted for. The restaurant
business fluctuates with economic conditions and stocks such as
McDonalds or Applebees or Buca de Beppo reflect these risks (all are
publicly-traded).
? there are business risks because it's your brother's first
restaurant. He might be a great chef but sloppy about managing the
business's marketing or its stock of food and beverage. He might be a
poor accountant and think that he's making money when he's not. He
might be the victim of an unscrupulous business manager.
? business decisions get made every day: without a realistic
cost-of-money he might use your money instead of leasing furniture.
He might buy a pastry oven which seems to be profitable at 4.25% but
is a drain on the business at more-realistic rates of 12% or 15%.
---
I think that about the only item that I haven't touched on is IRR or
internal rate of return. It's one of several profitability models
that companies use to try to simplify day-to-day decisions for
managers. It's closely-related to net-present-value, using a
discounting of income streams.
(NPV)/(1 + IRR)^t = Initial outlay, where t = number of years and IRR
is the IRR expressed as a decimal (9% would be .09).
In the cases where there's continual investment (say upgrades in
tooling after an initial purchase), you're using your Cash/Cash Out
for each year's cash flows.
STOCK VALUATION & OTHER CONSIDERATIONS
=======================================
There are often many other considerations in these problems, the
most-common being taxes. Certainly Ms. Williams needs worry about
estate taxes, however she takes her lottery payoff.
For corporations, the impact of investment tax credits and
depreciation can be substantial.
But what a company is trying to do is maximize the payment of future
dividends to its shareholders. And what you're trying to do as an
investor is value the growth opportunities and management to judge a
fair price for the stock.
Consider: Microsoft. At some points during the 1980s the company had
revenues of $1 billion to $2 billion and market capitalization of more
than $30 billion, while most firms had price to EARNINGS (not
revenues) rations of 10:1 or 12:1.
Several factors were working for Microsoft:
* it had dominance in language, operating system and office applications markets.
* it was well-managed and generating cash.
* when penetration of personal computers was only 10-15% of the U.S.
market, there were clear opportunities for growth in the U.S. and
abroad.
* the software business has low variable costs in shipping another
unit (less than 10% of revenues) and is easily scaled up for higher
volumes.
RECOMMENDATIONS
================
This Answer has been deliberately short of links to other sources.
Many of the terms used here (and in the original question by
Missmallprincess) can be searched on Google. You'll probably get the
best results if you search using some of the key theorists in each
area of finance:
Milton Friedman + inflation
Milton Friedman + money supply
Black + Scholes + option pricing
Modigliani + Miller + CAPM
Also, I've done a large number of these financial questions and you
can use Google Answers search to help find them:
black + scholes + omnivorous-ga
IRR + NPV + omnivorous-GA
I'd also highly recommend Burton Malkiel's classic of finance, written
originally in 1973 but substantially updated in later versions with
the impact of new financial theory:
Amazon.com
"A Random Walk Down Wall Street," (Malkiel)
http://www.amazon.com/exec/obidos/ASIN/0393325350/qid=1089501103/sr=2-1/ref=sr_2_1/002-0939296-9742461
Malkield does an excellent job of explaining types of risk, including
markets-gone-crazy. Modern investment theory assumes markets are
efficient (while continually testing the assumption) but there have
been instances of whole markets acting irrationally -- including the
Dutch tulip market in the late 1600s and South Sea Co. bubble in
England. They are informative because often there are structural
reasons for runaway values.
Best regards,
Omnivorous-GA |
Clarification of Answer by
omnivorous-ga
on
11 Jul 2004 07:55 PDT
Burnt_toast --
1. The link to the spreadsheet should be working now.
2. I tried to make this point clear but suspect that I got into too
many extraneous points:
* the lowest cost of capital is usually the Treasury rate, as it's
risk-free, guaranteed by the full faith and credit of the government.
It usually approximates inflation or "expectations of inflation."
(This is actually a whole separate topic and brings in the issue of
why short-term rates are sometimes higher that long-term rates. Today
they're lower.)
* opportunity cost is what else you could do with the money. If you
borrow against your house you'd have to look at opportunity cost as
the 4.25% you'd pay to borrow. But opportunity cost is not a "cost of
capital" -- the "cost of capital" is the risk of what you're doing
with the money (investing in stocks; buying income property; investing
in your brother's restaurant).
* note that opportunity cost or finance rates are timed to the length
of the investment. In the way Geraldine Williams is being paid, it's
4.77% because the insurance companies are saying "if there were a
25-year T-bill that's what it would pay."
* "discount rate" is often used in finance questions as the quickest
and easiest finance measure. Often we just use a T-bill rate to avoid
arguments but in a corporate it should reflect the total cost of
capital and be substantially (50%-100%) higher.
* See the QuickMBA link under "Cost of Capital" for a precise
definition of how the cost of equity -- or the cost of stock is
calculated. Stocks are priced to add return based on:
1. market risk
2. firm risk
This is why I said that you should look at what Restaurant stocks are
returning (analyze the restaurant market risk), then also judge your
brother's experience (firm risk) to come up with a Cost of Capital for
the French_Toast Restaurant.
This is how Google or Yahoo or Amazon get priced by the market, though
it often seems that expectations for initial public offerings are
extraordinarily high to the casual observer. It's often because the
companies are going through a dramatic growth phase where it's
difficult to size their ultimate "market."
3. Finally, on NPV and IRR, your last comments are correct. You
calculate NPV by dividing each year's cash flow by the compounded
discount rate/opportunity cost/cost of capital. I prefer to use Year
0 to illustrate initial investment. What's important is to use the
timing of cash flows. For a good example, see this Google Answer on
financials of bringing in a tennis pro:
http://answers.google.com/answers/threadview?id=367089
When inflation is high or cash flows are "lumpy" (like all
subscriptions paid in January or all tax returns coming in April) NPVs
can be affected dramatically by when they arrive in a year.
Again, Malkiel's "Random Walk Down Wall Street" is highly recommended.
It's written in understandable English and has great historical
background, even if written by a Yale professor. There are lots of
reviews of it on the Internet, so if you're eager to get a peek at it,
just do a Google search for the book title.
Best regards,
Omnivorous-GA
|
