The short course continues to evolve. New
examples are added each time it is offered and the (somewhat)
complex mathematics that is standard in this field is being
replaced by simple arguments that relate to familiar business
concepts. As an example, the esoteric theory of valuation, which is
usually taught in classrooms in terms of partial differential
equations or continuous matching of securities, is now presented in
the course in terms of discounting. It is also shown how proper
valuation relates to ROE (return on equity) and to firm growth.
There is also a stronger emphasis on the structure of projects-the
various types of options and how they can be treated easily.
April and September Investment Science for
Industry will be offered at Stanford April 22-23 and September
16-17. Detailed information can be obtained from the web site:
information about Investment Science for Industry Course
Past participants are encouraged to bring this
course to the attention of their colleagues. We have had several
such referrals in the past.
Projects and Research
In addition to the projects that we have
discussed in previous newsletters, a new initiative has been
generated this year. A special project course (for Stanford
students) will be offered in the Spring quarter. This course is
available to a select number of students who have completed two
quarters of Investment Science in the department. The course is
being taught primarily by Robert Luenberger. The course will use
real examples from industry, so if your company would like to have
a group of 5 students work on a short (3 month) investment project,
please contact me at Stanford, or Rob at Onward
(email@example.com). Of course we are available for more
comprehensive projects, but this special opportunity may be a good
way to get Investment Science started in your company.
Our current research and outside applications
include involve banking decisions, environmental compliance issues
in electric power, electric power trading, contract design, general
project evaluation, capital investments in cyclic industries (such
as the petrochemical industry), and the strategic deployment of
Information Technology. New applications are being discovered every
month, and of course many of these ideas have evolved from
participants' discussions at the short course.
The last issue of this newsletter
discussed the "two-rate" method of discounting, which is a simple
way of modifying traditional discounted cash flow analysis to
properly account for degrees of uncertainty. This method seems to
appeal to many people.
Now, we shall discuss an even more
powerful method of discounting: Risk-Time Discounting, (referred to
as the Two Step Method in the last newsletter). This method is
still simple to understand and simple to implement. In some
respects it builds on the two-rate method, but it can handle
complex cash flows that are subject to saturation, curtailment,
expansions, options, and other nonlinearities.
The basic idea of the method is simple:
discount all component cash flows first for risk and then for time;
hence the name, "risk-time discounting".
To describe the method, let us review the
two basic principles of discounting.
1. Market Uncertainty
Suppose a cash flow is a perfect market
cash flow; that is, it is proportional to the value of a stock. For
example, the revenue of a new product one year from now might be
estimated to be equal to that of 1,000 shares of the company stock
in one year--reflecting the fact that if the market is strong for
the company in general it is likely to be strong for the new
product as well. The present value of such a market cash flow is
equal to current value of the market variable. In the example that
means that the cash flow has a present value equal to the current
value of 1,000 shares of stock. (The reason is that the stock and
the project are perfect substitutes in terms of what cash they
generate in a year. Therefore, the current values of this cash flow
must be equal.)
Now translate this into discounting. If the
company stock is expected to increase at some rate, say 14%, then
we discount the expected value of the cash flow by this same 14%.
For example if the current value of the stock is $100, we expect it
will be $114 at the end of the year. If we expect the project cash
flow to be equal to 1,000 shares, that will be $114,000. The
present value of the cash flow is $100,000, obtained by discounting
back by the 14% that it rose.
Suppose now that the cash flow is a
private cash flow, which means that it is independent of any
variable in the market. For example, the cash flow might be the
cost of repairs to machinery, which depends only on whether or not
the machinery breaks down. The expected values of such cash flows
should be discounted at the risk-free rate. Hence if the risk-free
rate is 5%, and the expected value of a private cash flow in one
year is $100, then the present value is $100/1.05 = $95.24
These two types of uncertainty and the
related discounting principles are the basis for all discounting.
All cash flows can be represented as combinations of these two
Now let us describe the risk-time
discounting procedure. We first discount all cash flow processes
for risk. For a market variable this means that we discount by its
growth rate minus the risk-free rate. For the stock that increases
by 14% per year when the risk-free rate is 5%, we discount by 14%-
5% = 9%. For a private variable we discount by the risk-free rate,
which is 5% in our example--no risk-adjustment is required. Then,
after necessary risk discounts are made, we find the aggregate
resulting cash flow and discount that for time, using the risk-free
It may seem like a belabored process to
discount the market cash flows in two steps: 9% for risk followed
by 5% for time. But the advantage is that then the result is valid
for cash flows subject to options, saturation, expansions, and
various other nonlinearities, which are the meat of modern project
evaluation, representing a large part of a project's
The reason this risk-time technique works
is that we discount the underlying market process for risk before
it enters our spreadsheet as a cash flow. It is discounted before
being subject to options and other distortions inherent in our
project. It is discounted for market risk "out in the market" not
in our project. It is a market uncertainty, not a private one, and
should be discounted in the market, not in our private project.
This explanation is of course merely suggestive; the real
explanation is based on some fairly deep mathematics. But this
simple explanation is easy to remember. Discount market uncertainty
for risk out in the market, not in your private project.
Let us see how to do this in a simple
example. Consider a call option on a stock. (An example that is
similar to one worked several ways in the text Investment
Suppose the stock has a current price of
$62.00, is expected to grow at 20%, and has a volatility of 20%.
The risk-free rate is 5%. The option has a strike price of $60 and
a time to maturity of 5 months. This is a nonlinear payoff that
might be typical of projects as well. In this case the payoff is
positive only if the stock ends up higher than $60, in which case
we get the surplus over $60.
The value of the option can be found by
risk-time discounting. In this case the only cash flow occurs at
the end of 5 months and is a pure market uncertainty. We discount
the market variable "in the market" before it gets to the option.
The expected growth rate of the stock is 20% and the risk-free rate
is 5%; hence we discount the stock by 20%-5% =15%. The remaining
expected growth rate of the stock is then equal to the risk-free
rate (of 5%). Now, we can use simulation or the lattice method to
carry out the discounting. In simulation, we would run many
simulations of the stock (after it is discounted for risk down to a
5% expected growth rate). We would find the value of the payoff
(cash flow) in each simulation run and discount that for time (at
5%). The average of all these discounted values (averaged over the
various simulation runs) is the value of the option.
Remember the principle: Discount for risk
and then for time. But discount market risk outside-in the
market-before it encounters non-market characteristics such as