# Decision Trees and portfolio theory

Q1

A company has developed two types of synthetic fuel. However it has not developed efficient manufacturing processes for either of them. It has has the option to develop the manufacturing process for both, either or none of them.

They estimate that if they try to develop a process for fuel A then their probability of success is 0.46. If they do succeed then they expect that they could sell the process to another company for $43,600. Alternatively they could manufacture the fuel themselves, in which case they estimate that if the market is strong then they will achieve a revenue stream with a net present value (NPV) of $68,200, or if the market is week a NPV of $28,100. They estimate the probability of the market being strong for fuel A as being 0.45. Attempting to develop the process is expected to cost $38,800. This amount needs to be deducted from all of the above returns to determine the profit for each situation ... Continued in word file

Q2

A particular security gives an average return of $14.65 per year and has a beta of 0.5. The return on the market portfolio is 0.07 and the risk free rate is 0.05. What should be the value of this security? What would your answer for the value of the security be if you were given the additional information that the probability of default is 0.04?

https://brainmass.com/statistics/probability/decision-trees-and-portfolio-theory-276857

#### Solution Preview

1:

Fuel A:

First you need to determine the EMV for the "Make Decision"

EMV = 0.45*(68,200-38,800)+.55*(28,100-38,800) = 7,345

EMV for Selling to another company will simply be 43,600-38,800 =4,800

Since the EMV to "Make" is higher, company would chose to make fuel A themselves.

Thus now the EMV for attempting to develop a process for Fuel A only is:

EMV = 0.46*7,345 + .54*(-38,800) = $-17,573.3

Fuel B:

First you need to determine the EMV for the "Make Decision"

EMV = ...

#### Solution Summary

The solution goes into a considerable amount of detail in order to explain the concepts of decision tree and portfolio theory. Detailed step-by-step calculations are shown for both the questions asked. EMV is calculated for all options and steps are clearly shown. Overall, an excellent response that must be downloaded for anyone looking to better understand these concepts.