Department of Management Science & Engineering

Number 2/Spring 1998

Investment Science Newsletter

By Professor David G. Luenberger

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Discount at a Higher Rate?

This is the second newsletter describing events in the Investment Science program at Stanford. In each issue we report on the nature of research underway and projects that we have been addressing. There will also be a short article related to Investment Science concepts (see "Why Discount at the Risk-Free Rate?" in this issue.)

We welcome comments and examples related to practical applications of Investment Science.

Investment Science Published

The text, Investment Science, is the most visible outreach of our program and has received excellent reviews. For example, there are outstanding reviews at which continues to be a popular source for the book. The text is crrently being used for the first time in its published form in several universities. At Stanford there are nearly 250 students taking the course this quarter.

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Short Course News

The course, Investment Science for Industry, has been evolving at a rapid pace in response to the thoughtful feedback from participants. This year the course will relate the modern concepts of finance more directly to conventional methods of accounting procedures used in most firms. We will not compromise on theory, but instead reformulate the theory so that it is more accessible, more intuitive, and more in line with conventional approaches. Hence, the new approach will show how to modify existing methods (primarily discounting methods) so that they are in line with modern financial concepts and more truly reflect the economic consequences of actions.


Investment Science for Industry was taught in Taiwan, hosted by Yuan-Ze Institute, last September. There were 30 participants in a beautiful setting on the top floor of the Far Eastern International Center in Taipei. The participants were from investment banks, consulting organizations, high-tech industry, and large conventional industries. The participants and instructors had very fruitful interchanges of ideas and shared some excellent cuisine. We also had the opportunity to meet with several of Taiwan's business leaders and were heartened by their enthusiastic reaction to investment science.

April and November
Investment Science for Industry will be offered at Stanford April 30-May1, 1998 and November 12-13, 1998.

Update on Projects

Projects with industry sponsorship which are underway include:

CHEVRON has sponsored research on real options and commodity price cycles which is being carried out primarily by Marius Holtan in his role as a post-doctoral fellow. We have found that the issue of commodity price cycels is a concern of major industries. Our approach is not to predict the exact price pattern (which is probably impossible) but to understand its statistical character and translate this into appropriate strategy (for plant construction, commodity purchase, contract design, hedging, or acquisition) using investment science methods. Superior strategies can lead to substantial company value.

NATIONAL SEMICONDUCTOR is working with us on the development of superior methods for analysis of mergers and acquisitions using investment science methods.

We have worked with Hewlett-Packard on a number of innovative projects, including design of commodity contracts, supplier policies, and general business strategy.

ENRON has sponsored general research, which this year focused on evaluation of foreign investments subject to specific country risk as well as other technological and market risks. This research has been carried out by Kian Esteghamat.

Current Graduate Research

Student research is devoted mainly to evaluation of projects and development of project portfolio design. The work on evaluation focuses on how to account for uncertainty that is partially related to market variables and partially to private uncertainty unique to that project. In the past, we have developed methods for determining the value of such projects from a market perspective -- that is, how much such a project should be worth in an open market -- which is consistent with the viewpoint of methods that attempt to generalize Net Present Value. Currently, we are developing methods that determine the value of projects, taking into account the fact that the project is in a particular firm, not in the market by itself.

The work on project portfolio design goes to the heart of company strategy. Every company must manage its portfolio of business units, R&D projects, new business initiatives, and acquisitions. The rewards for proper management can be substantial. However, such management requires a clear understanding of business uncertainties and how they interact. We have new methods for clarifying the possibilities and for determining suitable actions.

Why Discount at the Risk-Free Rate?

In conversations with business people and participants in the short course, we teach that the cash flows of small risky projects should be discounted at the risk-free rate provided that the risk is private risk, not related to market variables. For example, if the cash flow is dependent only on whether a certain technlogy, currently in development, will work as planned, the uncertainty can be considered as a private risk. Or as another example, if the cash flow depends only on the amount of oil at a specific site, the uncertainty is again private risk. Of course, most projects have both market and private risk, but still, the portion of the cash flow due to private risk should be discounted at the risk-free rate -- that is what we teach.

This simple rule seems to trouble many people as being non-intuitive -- for after all, the project is resky and some account should be made of that risk, it seems.

So, here is a question we hear frequently (and the answer).

Question: Why should our company discount private risk at the risk-free rate?

Answer: There are two views: the outside view (by your stockholders) and the inside view (by management's objectives).


Each part of your company's portfolio is a portion of the outside investor's portfolio. Outsiders value risk-free investments at the risk-free rate. Also the stock in your company is a very small part of the average outsider's portfolio. When you take on a private risk investment, it combines with all the other private risk investments in the world, and through diversification, each outside investor will obtain very close to the average value of these risky cash flows; the private risks "'average out" for them and the result is essentially risk-free. hence, investors will value our private risks according to their averages, and treat them as essentially risk free. You should too, if you are concerned with the market value of a project.


Your company is striving for growth and value. It has many high-potential opportunities, and for this reason it borrows money -- to fund additional opportunities. But the list of viable opportunities is limited, and borrowing increases overall volatility; as a consequence your company decides on a best level of debt. It decided (assuming that managment is rational) that the current debt-equity ratio represents a good tradeoff between borrowing risk-free and investing in additional typically risky projects. Hence, risk-free components of a new project should be regarded as part of the trade-off and measured just like debt is measured: at the risk-free rate. (Of course, your company pays a premium over the risk-free rate for its debt; but ignore that for this discusssion. It does not materially change the answer.)

If a portion of a project has private risk, that is somewhat different than being risk-free. If the project is a small one, then -- just like outside investors -- managment should lump all the internal private risks together and determine that, as a group, they are essentialy risk-free. Hence, for small projects, private risk should be discounted at the risk-free rate.

Discount at a Higher Rate?

If the project is not small, the uncertainty associated with private risk is definitely important to the future of the company. In general, the impact of such rusk is related to the magnitude of the risk compared to the asset base of the company. However, the true value of such a risk is not accurately measured by imposing a higher discount rate. This is easy to see, because, for example, tow cash flows of $1 million that have separate private risks are more desirable together (because of diversification) than one cash flow of $2 million with comparable risk. Discounting would treat the two cases equally, adding up the cash flows without accounting for diversification. In a proper valuation, each private risk must be accounted for separately. This can be done with a software program and the result related to the growth potential of the firm. But the best way to treat large projects is to consider them together and determine the best mix for company growth and value as part of a strategic plan. Discounting is, in every case, useful only as a beginning measure, and primarily for small projects.