Traditional NPV vs Decision tree analysis

Several approaches of deal with uncertainties have been described above. In the following, we will use a simple example to make a deeper understanding of NPV. A petroleum

The managers would like to know whether invest now or wait one year to get more information and then make a decision. The cost for waiting one year will be decided later.

Based on the traditional NPV method, we can get following net present value.

NPV=

I million

Since NPV is positive, it seems that this company should go head to do the investment. In fact, this conclusion is not correct, however, because the calculations above ignore the option that wait and keep open possibility of doing not invest if the market environment is not so good.

Decision tree analysis is also an approach to help management determine which alternative at any particular choice point make the greatest profit. It is quite an easy way to present all the possibilities of outcome as an expansion to a simple calculation of NPV. We still use the same example in the following and see how it works. After the initial investment, this petroleum company finds that the successful chance of this project is 30 percent. In the next phase, this company will invest $3.5 million in building up a processing plant which may generate expected annual cash flow of $0.5 million. Assuming no important change in the company’s situation, but management in this company has a deeper consideration of the cash flow forecasts. There is a 60% chance of a large market in the long run and a 40%

chance of a low demand, offering a year-5 expected value of $10 million and -$4 million separately. Here the appropriate risk-adjusted discount rate is assumed to 10%.

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

I0=0.1 C1=0.5 C2=0.5 C3=0.5 C4=0.5 C5=0.5

Figure 2.4 shows the basic decision tree in which problem this petroleum company is facing with.

Figure 2.4: Decision tree of project

Under decision tree analysis, we start from the back of the tree and NPV for each outcome is multiplied by the probability. It could be calculated, starting from the right of the decision tree and roll back to the left. Because of the market demand, expected cash flow in the fifth year is the outcome multiplies probability and accumulates these two values.

Therefore, the present value in year 5 is

E₅ (PV) = 0.6*10+0.4*(-4) = 4.4

Step back to year 4, using risk-adjusted discount rate k=0.1, we can get the expected NPV that,

Now we know the net present value in the fourth year and roll back the third year which is at node “B”. To build a plant, it will cost $ 3.5 million. Similar to last step, the expected NPV at node “B” in year 3 is

Finally, step back to the initial node “A” which we may get the expected NPV at present: negative value means that the managers in this company should refuse this project. Here there is only one choice that to invest now or never invest. According to the result of NPV, this company should not invest forever. In fact, the result of NPV is still not correct because of the wrong discount rate.

The discount rate should be an important factor in this case and it is difficult to determine the right discount rate. It is assumed that the discount rate is the same for all stages but actually different stages should have different rates. The reason is that high risks require high discount rate and low risks require low discount rate. It is not reasonable to use the same rate because different levels of risks exist in different stages of the project. Another reason is this method is lack of considering changes in the project’s own riskiness over time. Managers pay more attention on the risks which have great impact on the entire project but ignore those risks that are associated to the project. Therefore, if the project takes a wrong risk-adjusted discount rate, the calculation will be in a wrong direction.

On the other hand, even the net present value is positive, it is not necessary to run the entire project forever. Actually, there is an option that stops the project for a while and waits and sees how is the market will be if supply exceeds demand and gas price is low. If the price goes up again, this company could start to run the project again and invest more.

Otherwise, he could shut down the processing plant and sell this project to other petroleum companies if possible and he could also get money from selling this project. Although the result is negative in this case, it does not mean that it is not feasible to invest in this project.

Considering the flexibility to abandon to the project in this case, what if its salvage value at any time exceeds the present value of expected subsequent cash flows, including the

abandon value at the end of fifth year (Trigeorgis Lenos, 1996). Taking this condition into account, the initially undesirable project seems become acceptable. The above discussion shows that the traditional NPV rules kill the flexibility option such as waiting one year or abandon the project before the end of useful life time. Of course, there are situations in which this company cannot wait or wait for a long time to invest because his competitor may enter this market and invest first. To delay with less time and the cost for delaying will affect the investment decision (Pindyck Pobert S., 1991). In the next section we will explore this point into detail with general model. The opportunity cost will be defined in which is worth to invest next year rather than invest right now or never.