## Decision Trees

We have considered potential sources of value in NPV analysis. Moreover, we pointed out that there is a connection between the stock market and a firm's capital budgeting decisions. A savvy CEO can learn from the stock market. Now our interest is in coming up with estimates of NPV for a proposed project. A fundamental problem in NPV analysis is dealing with uncertain future outcomes. Furthermore, there is usually a sequence of decisions in NPV project analysis. This section introduces the device of decision trees for identifying the sequential decisions in NPV analysis.

Imagine you are the treasurer of the Solar Electronics Corporation (SEC), and the engineering group has recently developed the technology for solar-powered jet engines. The jet engine is to be used with 150-passenger commercial airplanes. The marketing staff has proposed that SEC develop some prototypes and conduct test marketing of the engine. A corporate planning group, including representatives from production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase. They estimate that this preliminary phase will take a year and will cost \$100 million. Furthermore, the group believes there is a 75-percent chance that the reproduction and marketing tests will prove successful.

Based on its experience in the industry, the company has a fairly accurate idea of how much the development and testing expenditures will cost. Sales of jet engines, however, are subject to (1) uncertainty about the demand for air travel in the future, (2) uncertainty about

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204 Part II Value and Capital Budgeting

■ Table 8.1 Cash Flow Forecasts for Solar Electronics Corporation's Jet Engine Base Case (millions)*

 Investment Year 1 Year 2 Revenues \$6,000 Variable costs (3,000) Fixed costs (l,79l) Depreciation 00(030000) Pretax profit 909 Tax (Tc= 0.34) 00(030090) Net profit \$ 600 Cash flow \$ 900 Initial investment costs -\$1,500

*Assumptions: (1) Investment is depreciated in years 2 through 6 using the straight-line method; (2) tax rate is 34 percent; (3) the company receives no tax benefits on initial development costs.

*Assumptions: (1) Investment is depreciated in years 2 through 6 using the straight-line method; (2) tax rate is 34 percent; (3) the company receives no tax benefits on initial development costs.

future oil prices, (3) uncertainty about SEC's market share for engines for 150-passenger planes, and (4) uncertainty about the demand for 150-passenger planes relative to other sizes. Future oil prices will have a substantial impact on when airlines replace their existing fleets of Boeing 727 jets, because the 727s are much less fuel efficient compared with the new jets that will be produced over the next five years.

If the initial marketing tests are successful, SEC can acquire some land, build several new plants, and go ahead with full-scale production. This investment phase will cost \$1,500 million. Production will occur over the next five years. The preliminary cash flow projection appears in Table 8.1. Should SEC decide to go ahead with investment and production on the jet engine, the NPV at a discount rate of 15 percent (in millions) is

\$900

Note that the NPV is calculated as of date 1, the date at which the investment of \$1,500 million is made. Later we bring this number back to date 0.

If the initial marketing tests are unsuccessful, SEC's \$1,500 million investment has an NPV of -\$3,611 million. (You will see how to calculate this number in the section.) This figure is also calculated as of date 1.

Figure 8.1 displays the problem concerning the jet engine as a decision tree. If SEC decides to conduct test marketing, there is a 75-percent probability that the test marketing will be successful. If the tests are successful, the firm faces a second decision: whether to invest \$1,500 million in a project that yields \$1,517 million NPV or to stop. If the tests are unsuccessful, the firm faces a different decision: whether to invest \$1,500 million in a project that yields -\$3,611 million NPV or to stop.

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Corporate Finance, Sixth Budgeting Using Net Present Value Companies, 2002

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Chapter 8 Strategy and Analysis in Using Net Present Value 205

Now 1 year 2 years

Test and Initial Production development investment

Test and Initial Production development investment

Open circles represent decision points; closed circles represent receipt of information.

As can be seen from Figure 8.1, SEC has the following two decisions to make:

1. Whether to test and develop the solar-powered jet engine.

2. Whether to invest for full-scale production following the results of the test.

One makes decisions in reverse order with decision trees. Thus, we analyze the second-stage investment of \$1,500 million first. If the tests are successful, it is obvious that SEC should invest, because \$1,517 million is greater than zero. Just as obviously, if the tests are unsuccessful, SEC should not invest.

Now we move back to the first stage, where the decision boils down to a simple question: Should SEC invest \$100 million now to obtain a 75-percent chance of \$1,517 million one year later? The expected payoff evaluated at date 1 (in millions) is

(Probability Payoff \ / Probability Payoff \

success successful failure failure

The NPV of testing computed at date 0 (in millions) is

1.15

Thus, the firm should test the market for solar-powered jet engines.

Warning 1 We have used a discount rate of 15 percent for both the testing and the investment decisions. Perhaps a higher discount rate should have been used for the initial testmarketing decision, which is likely to be riskier than the investment decision.

Warning 2 It was assumed that after making the initial investment to produce solar engines and then being confronted with a low demand, SEC could lose money. This worst-case scenario leads to an NPV of -\$3,611 million. This is an unlikely eventuality. Instead,

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Corporate Finance, Sixth Budgeting Using Net Present Value Companies, 2002

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206 Part II Value and Capital Budgeting it is more plausible to assume that SEC would try to sell its initial investment—patents, land, buildings, machinery, and prototypes—for \$1,000 million. For example, faced with low demand, suppose SEC could scrap the initial investment. In this case, it would lose \$500 million of the original investment. This is much better than if it produced the solar-powered jet engines and generated a negative NPV of \$3,611 million. It is hard for decision trees to capture all of the managerial options in changing environments.

q ! ? • What are two potential problems in using decision trees?

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