# Decision Tree

DecisionTree

Decisiontrees are analysis diagrams that help an individual analyze theviability of projects by determining which project has the lowestcost and which one has the highest cost. It also determines whichproject realizes the highest returns or net present value and choosesthat with the lowest cost and the highest NPV. In this, I have beengiven three investment opportunities, which I am required todetermine the most lucrative one among the three. Option A has aninitial cost outlay of \$ 0.75 million, with three probabilistic NPVs,namely: High NPV of \$ 5 million at a probability of 0.5, average NPVof \$ 2 million at a probability of 0.3, and low NPV of \$ 0 million ata probability of 0.2. Option B has an initial cost of \$ 0.55 million,with three probabilistic NPVs, namely: high NPV of \$ 3 million at aprobability of 0.75, average NPV of \$ 2 million at a probability of0.15, and low NPV of \$ 1 million at a probability of 0.1. Lastly,option C has an initial outlay of \$ 0.75 million, with oneprobabilistic NPV of \$ 1.5 million at a probability of 1.0.

Analysis

Toanalyze this, two rationales and logics are used. One, for mutuallyexclusive projects, an investor should choose the one with thehighest positive net present value (NPV). Second, for dependentprojects, the investor ought to choose those investment projectswhich positive net present values (NPV). Since these investmentportfolios are from three independent industries or securities thatis option A is from the real estate development industry, option B isthe retail franchise for just hats while option C is from high yieldmunicipal bonds, they would be considered mutually exclusive projects(Ghiami,&amp Beullens, 2016).This implies that to make my decision I would choose the option withthe highest positive net present value (NPV).

Inthis analysis, we assume that the net present value is uncertain orprobabilistic in nature. To determine the highest net present values(NPV) of the expected net present value (ENPV) and choose the mosttop. Here, the decision tree has three options. Each option has thepresent values of the cash flows, the initial cost outlay, and theprobabilistic net present values. Option A as per the excel file hasan initial cost outlay of \$ 0.75 million (Ghiami,&amp Beullens, 2016).It also has uncertain NPVs: one, which is high of \$ 5 million at aprobability of 0.5, one that is medium of \$ 2 million at aprobability of 0.3, and one, which is low of \$ 0 million at aprobability of 0.2. Since this analysis requires us to show thecosts, we will also show the present values (Ghiami,&amp Beullens, 2016).To determine the present values of the cash inflows, one needs tofind the expected net present value (ENPV) and then add the initialcost outlay as shown below.

OptionB as per the excel file attached has a cost outlay of \$ 0.55 million(Ghiami,&amp Beullens, 2016).It also has probabilistic NPVs: a high NPV of \$ 3 million at aprobability of 0.75, a medium of \$ 2 million at a probability of0.15, and a minimum of \$ 1 million at a probability of 0.1. As donein option A, one needs to determine the expected net present value(ENPV) and then add the initial cost outlay to find the PV as shownbelow.

OptionC has a cost of \$ 0.75 million (Ghiami,&amp Beullens, 2016).It also has an uncertain NPV of \$ 1.5 million at a probability of1.0. As done in option A and B above, one needs to calculate theexpected net present value (ENPV) and then add the initial outlay soas to find the PV of cash inflow as shown below.

Recommendations

Aninvestor is advised to invest in the investment project with thehighest expected net present value since these are mutually exclusiveprojects (Ghiami,&amp Beullens, 2016).Based on the analysis above, option A has an expected net presentvalue of \$ 3.1 million, option B has projected the net present valueof \$ 2.65 million, while the expected net present value of option Cis \$ 1.5 million. I should, therefore, invest in option A since itsexpected net present value (ENPV) of \$ 3.1 million is the highest(Ghiami,&amp Beullens, 2016).Despite the investment option A having one of the highest cost outlayof \$ 0.75 million, it is capable of realizing the highest returns of\$ 3.1 million based on its expected net present value (ENPV). Iwould, therefore, invest in the real estate development sector sinceit has the highest payoff despite the highest risk (Ghiami,&amp Beullens, 2016).

References

Ghiami,Y., &amp Beullens, P. (2016). Planning for shortages? Net PresentValue analysis for a deteriorating item with partialbacklogging.&nbspInternationalJournal of Production Economics,&nbsp178,1-11. Retrieved on 3 November 2016.