2. 1 So far, when selecting from alternative solutions, we have neglected uncertainty about costs. Yet: revenues may be different from estimates(economic changes etc); costs may be different from estimates (incorrect data etc); So, how do you know which will really be the best alternative solution in the end?

3. 2 Impossible to know which solution is the best with absolute certainty! So what can we do? Consider the following problem: Hotel A: City X; $20M initial cost; revenue = $1,000M NPV if a proposed airport is built but just $100M if it is not; probability of airport being built is 0.1. Hotel B: City Y; $30M initial cost; revenue = $175M NPV. Which would you select?

4. 3 One solution to this problem is to calculate the expected cost/profit of each alternative this is the average cost/profit experienced if the decision was made many times (assuming the outcomes may also change); no other strategy is more likely to provide greater profit over many projects; however, may not go for the choice with the highest expected cost if there is a risk that you will go, say, bankrupt.

5. 4 Sometimes the problem is too complicated to visualize what all the possible outcomes are: maybe many decisions; maybe many uncontrollable factors; and some decisions may follow other decisions. The solution to this is to use decision tree analysis: a graphical method of problem solving; lays decisions out in a logical frame; facilitates calculation of expected value of all combinations of decisions.

6. 5 = Decision Node: = Chance Node: = Link: Point in tree where choices for alternative solutions are available Example: build hotel A or B? Point in tree where uncontrollable alternative outcomes are represented Example: will airport be built? Branches in tree representing alternative choices or outcomes Examples: $1,000,000; or probability = 0.73 Expected cost = ? or probability = ? Cost A = ? Cost B = ? Etc.. BASIC COMPONENTS OF D.T.A.

7. 6 Build tree starting at main decision 1. First decision is?: Build hotel A or B? A = $ B = $ 2. First chance is?: Build airport? Initial Cost= $20M Build? No Build probability=0.9 NPV Revenue = $100M Build probability=0.1 NPV Revenue = $1,000M Initial Cost= $30M NPV Revenue = $175M Perform a reverse pass 1. Calculate expected revenue 0.9x$100M=$90M Decision node Chance node 2. Calculate total expected NPV 0.1x$1,000M=$100M $90M+$100M=$190M 1.0x$175M=$175M $170M $145M Therefore select A 3. Identify best alternative

8. 7 Consider the following leisure facility project: (note, all construction costs = $8.0M excluding foundation work):

9. 8 Site Ground obstrs.? Ground obstrs.? City Land avail.? Land avail.? A - $8.0M C - $8.0M -$2.0M 1 $47.0M 2 - $1.5M Buy? Econo.? avail (p=0.3) Light rail? Light rail? B - $8.0M -$2.0M $47.0M obstrs (p=0.2) -$2.5M no obstrs (p=0.8) -$1.5M not avail (p=0.7) $46M $44M no. yes -$7.0M good (p=0.5) $63.0M poor (p=0.5) $42.0M built in 5 yrs (p=0.2) $78.0M built in 10 yrs (p=0.4) $63.0M not built (p=0.4) $38.0M 0.2x-2.5=-0.5 0.8x-1.5=-1.2 -0.5-1.2=-1.7 47-1.7=45.3 0.7x46=32.2 44 0.5x63=31.5 0.5x42=21 31.5+21=52.5 52.5-7=45.7 0.4x63=25.2 13.7+32.2=45.9 45.9-1.5 =44.4 45.3-8=37.3 47-8-2=37 0.2x78=15.6 0.4x38=15.2 15.6+25.2+15.2 =56 56-8-2=46 0.3x45.7=13.7