Department of Management Science & Engineering

Number 3/Autumn 1998

Investment Science Newsletter

By Professor David G. Luenberger
luen@stanford.edu

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CONTENTS

FORUM

INVESTMENT SCIENCE PUBLISHED

SHORT COURSE NEWS

PROJECTS

TOPICS OF INTEREST

THE TWO-RATE METHOD OF DISCOUNTING

This is the third 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 is also a short article of substance related to Investment Science concepts (see "The Two-Rate Method of Discounting" in this issue.)

A primary goal of the newsletter is to continue to build a network for exchanging ideas. We welcome comments and examples related to practical applications of Investment Science.


Investment Science Published

The text, Investment Science, was published by Oxford University Press in early June this year. This is good news to the students who in the past have had to put up with preliminary versions. The book can be purchased through the web at Amazon.com or through many bookstores.

Order Investment Science from Amazon.com Here


Short Course News

The new concepts introduced in Investment Science for Industry have been extremely well received. Participants are particularly pleased with the two-rate method of discounting, and the Double Step method. The two-rate method is simple and can be applied to many common investment situations. (It is discussed later in this newsletter.) The Double Step method is a revolutionary way of presenting and calculating modern option-type analysis. Originally, option theory was expressed in terms of the Black-Scholes equation, a differential equation that is beyond the mathematics familiar to most practitioners. The introduction of lattice methods was a tremendous step forward in terms of clarity and computational simplicity, although the required risk-neutral probabilities were difficult to understand because they were not directly related to normal discount factors. The Double Step method, on the other hand, expresses results in terms of familiar discount rates, easily understood by participants. The method is also easy to implement with simulation. The course has also added new examples from industry, and more are being added each time the course is taught.

November and April
Investment Science for Industry will be offered at Stanford November 12-13, 1998 and April 22-23, 1999. Past participants are encouraged to bring this course to the attention of their colleagues.

Projects

Several projects with industry that are follow-ups to the short course are currently underway at Stanford or with closely affiliated companies.

The project with Chevron focused on the cycles in the petrochemical industry. This work has led to a new fundamental understanding of cycles and, most importantly, to the development of strategies to use in cyclic industries.

Applied Materials has used investment science to investigate the economics of a new product in the dynamic environment of the semiconductor industry. Hewlett Packard used investment science to develop a method for evaluating commodity contracts.

The Energy Policy Research Institute (EPRI) is using investment science to evaluate the profitability of power plants in Poland. Enron Capital and Trade has sponsored research at Stanford on foreign investments subject to specific country risk as well as other technological and market risks.


Topics of Interest

Investment Science is applicable to a wide assortment of business issues. We have found especially strong interest in the following:

Project Evaluation. This is perhaps the core issue of many business problems. The question is often posed as "What is the correct discount rate for my project?" Of course, the issue is usually not that simple, as anyone who has taken the course Investment Science for Industry understands.

Real Options. Increasingly, people are aware that the options implicit in business often provide value. These "real options" include options to terminate the project if it goes poorly in the first phase, options to reduce or increase commodity order magnitudes, options to accelerate a project, and so forth. The presence of uncertainty actually increases value when options are available.

Portfolio Selection. Many firms are faced with dozens of potential projects every year, and not all can be funded. However, the projects often have interacting effects or correlations with various market segments. A sound basis for selecting among such projects is provided by investment science concepts.

Business Valuation. Methods for valuation of an entire business or firm is a topic of considerable importance and one of considerable debate. Traditional methods of discounted cash flow or use of comparables are of only limited value. Investment science can provide a new solid foundation for valuation based on how the market values growth and uncertainty.

Cycles. Industries requiring large capital investment are typically characterized by business cycles, caused by periods of relatively heavy investment followed by periods of low investment. If these markets are highly competitive, the average participant will lose money on average. Cycles cannot be predicted accurately, but they can be characterized statistically, and optimal investment strategies can be developed.

Growth. A key measure of business success is its growth rate--measured perhaps in terms of the growth in book value. The STAR method, a new tool of investment science, characterizes current growth and relates new projects, acquisitions, options, and debt to changes in overall growth. This tool can be used strategically to shape the trade-off between average growth and the risk associated with that growth.


The Two-Rate Method of Discounting

One of the simplest ways to improve conventional discounted cash flow analysis of projects is to use two discount rates instead of one. The method is intuitive, simple to implement, and in some cases can give vastly improved results compared to using a single rate. Very often, projects will be found to be less attractive when properly analyzed than when a single discount rate is used.

Here is how to use the method. Many projects have two types of risk:

  1. Revenue Risk (a combination of price and volume risk)
  2. Cost Risk (often associated with the technical risk of new products).

In some cases only one of these categories is actually risky, in which case the risk-free component is considered as one of the categories.

For example, the output of a factory producing a well-established product may be subject to substantial price risk (common in semiconductor and petrochemical industries, for example). The costs, on the other hand, may be relatively non-risky. In this case the two categories of risk are that associated with price and the risk-free category of costs.

As another example, an electric power plant may have a contract to deliver a fixed amount of power over several years at a predetermined price, but future fuel costs may be uncertain. In this case the revenue category is risk-free and the cost is associated with the risk of fuel cost.

When components of cash flow divide into two categories, it is natural to assign different discount rates to each of the categories. If the component is risk free, then the obvious rate to use is the risk free discount rate (around 5% to 10% these days). If the component is volatile, then it is appropriate to use the appropriate rate, determined usually by the market.

Some volatile components should also be discounted at the risk-free rate. This is true if the risk is independent of anything in the market. For example, technical risk or risk associated with unique private assets should be treated as if they are risk free if they constitute only a small (or medium) portion of a firm's total business portfolio. These private risks are automatically diversified if they are a small portion of the business. The classic example is the amount of oil at a particular oil well site. This amount is a private risk whose expected value should be discounted at the risk-free rate, provided it is but one of several projects at various unrelated sites.

If the risk is related to traded assets, then the market gives the appropriate discount rate. For example, if the risk is that associated with the price of semiconductors, then the average growth rate of a semiconductor stock index would serve as an appropriate interest rate for the discount factor.

Example. Suppose a firm is planning to build a new plant that will produce 10,000 units per year for the next 5 years. The price of these units has a volatility of 20% and mirrors the volatility of a stock index for the industry. The cost each year is fixed. The expected cash flows are shown in the spreadsheet below.

Year
0
1
2
3
4
5
Expected Price
0
20
22
24
26
29
Expected Revenue
0
200,000
220,000
240,000
260,000
290,000
Fixed Cost
500,000
10,000
80,000
80,000
80,000
80,000

Simple Project. The price is uncertain but is expected to increase. The costs are fixed.

Traditionally, this project might be analyzed by a single-rate discounted cash flow analysis. In such an analysis the yearly profit is determined and the then discounted. The discount rate is subject to debate but in this example an analyst might try 15% since that is a blend between the volatility of 20% and the fixed rate of 5%. This analysis, shown in the next spreadsheet, concludes that the project is profitable.

Year
0
1
2
3
4
5
Expected Price
0
20
22
24
26
29
Expected Revenue
0
200,000
220,000
240,000
260,000
290,000
Fixed Cost
500,000
10,000
80,000
80,000
80,000
80,000
Profit
-500,000
190,000
140,000
160,000
180,000
210,000
Discounted Profit
-500,000
165,217
105,860
105,203
102,916
104,407
NPV
83,603
         

Traditional Analysis. Discounting profit at 15% implies that the project is profitable.

In the two-rate method, we discount revenue at its natural rate of 20% and we discount the fixed costs at their natural rate of 5%. Then we sum up the difference. This is analysis is shown in the next spreadsheet. This analysis shows that the project is unprofitable.

Year
0
1
2
3
4
5
Expected Price
0
20
22
24
26
29
Expected Revenue
0
200,000
220,000
240,000
260,000
290,000
Discounted Revenue
0 166,667 152,778 138,889 125,386 116,544
Fixed Cost
500,000
10,000
80,000
80,000
80,000
80,000
Discounted Cost
-500,000
9,524
72,562
69,107
65,816
62,682
Two-rate Profit
-500,000
157,143
80,215
69,782
59,570
53,862
NPV
-79,428
         

Two-Rate Method. The expected revenue is discounted at 20% because that is how the market values that uncertainty. The fixed costs are discounted at 5% because that is the rate for fixed cash flows. The discounted cost is then subtracted from the discounted revenue to obtain the final value.

There are two ways to see why the results differ the way they do. First, fixed costs are not discounted as heavily in the two-rate method as in the single-rate method, and hence the present value of the costs are higher than with the earlier method. Likewise, the revenues are discounted more heavily in the two-rate method, and hence the present value of revenues is less than with the earlier method. As a result of these effects, the net value of the project is lower.

A second interpretation is that when fixed costs are subtracted from revenue, the resulting profit is more volatile than revenue itself. Higher volatility reduces the desirability of profit, and hence the appropriated discount rate should be greater than the 20% rate appropriate for revenue, not lower. Indeed, in this example a single discount rate of 30% will give approximately the same value as the two-rate method. However, the 30% figure cannot be determined before the analysis is conducted because it depends on the pattern of revenue and fixed costs. The two-rate method always gives the correct result.