Cap Winestone of Universal Learning is preparing a bid for a new building to accommodate its expanding operations. As luck has it, the headquarters of former competitor Empire Learning is for sale through a sealed bid auction. The building is well suited to Universal's needs, containing computing equipment, network infrastructure and other important e-learning accessories.
Cap estimates the building is worth about $900,000 to him, and is trying to decide what bid to place. To simplify his decision, he narrows down his bid choices to four possible bids. He muses: "With lower bids I gain more value. If I bid $600,000, I'll get a building worth $900,000 to me, so I gain $300,000 in value. In terms of the value I gain, the lower the bid, the better.
"On the other hand," Cap continues, "With a low bid I'm not likely to win. From the point of view of winning the bid, the higher the bid the better. How do I balance these two opposing factors?
Cap lays out a decision tree with the possible bid amounts, the likelihood of winning for each bid, and the outcome values. What amount should Cap bid?
a. $600,000
his is not the best answer. Think about the value of paying $600,000 for a building worth $900,000 to you, and the likelihood of winning the building with a $600,000 bid.
b. $700,000
This is not the best answer. Think about the value of paying $700,000 for a building worth $900,000 to you, and the likelihood of winning the building with a $700,000 bid.
c. $800,000
This is the best answer. d. $900,000
This is not the best answer. Think about the value of paying $900,000 for a building worth $900,000 to you, and the likelihood of winning the building with a $900,000 bid.
Folding back the tree, we find the $800,000 bid gives the highest expected monetary value. the $800,000 bid best balances the value gained against the probability of winning.
Sensitivity Analysis
Still in Leo's office after you initially calculated the expected monetary value of launching the Chez Tethys, you listen to Leo's growing concerns about the estimates that inform his decision. Leo the Skeptic: The Uncertain Estimates Problem
Now that you've mapped out the possible downside and its probability for me, I'm a little discouraged. Sure, the analysis indicates that ventures like the Tethys will be profitable on average, but the fact that I have almost a two-thirds chance of an $800,000 loss scares me.
What if the potential loss is even greater? Or, what if it's even more likely that the Chez Tethys will just be a passing "Fad?"
Both points are well taken, Leo. I'll tell you what: let's break for lunch, and then delve a little deeper into our analysis.
A Decision's Sensitivity to Outcome Estimates
Over lunch, Alice comments on Leo's reaction to your analysis. "Leo's questions bring us to a crucial component of decision analysis: sensitivity analysis."
Seth Chaplin has all but decided how to produce the film Cloven. Based on his initial analysis, he is inclined to produce Cloven in partnership with K2 Classics, thereby retaining part
ownership of the film. The EMV of the K2 option is $1.4 million. The EMV of the alternative option — in which Seth's company produces Cloven for Pony Pictures and relinquishes ownership in the film — is $1.0 million.
But Seth's calculations were based on estimates. The probabilities and the outcome values he used in his analysis were educated guesses. No matter how detailed and rigorous the methodology, a decision analysis is only as
good as the data on which it is based. What if Seth isn't completely certain about these data?
Seth is particularly unsure about the $6 million value he used to represent the profits associated with a "Blockbuster" film. What would the EMV of the K2 option be if $4 million were a more representative value for "Blockbuster" profits?
Enter the EMV in $millions as a decimal number with one digit to the right of the decimal point (e.g., enter ''$5,500,000'' as ''5.5''). Round if necessary.
If $4 million is the expected value of S&C's profits for the "Blockbuster" scenario, then the EMV of a "Blockbuster" drops to $800,000, less than the $1 million EMV of the Pony option. Note that if the "Blockbuster" profit figure drops to $4 million, Seth's optimal decision
changes: he should now choose the Pony option. Seth has learned that his optimal decision is sensitive to the figure he uses to represent S&C's profits if Cloven attains "Blockbuster" status.
If Seth's optimal decision switches when the "Blockbuster" profit figure drops to $4 million, he might reasonably wonder what his decision would be for other values. What about $5 million? $4.5 million? How low would the "Blockbuster" profit figure have to be to make the Pony option preferable to the K2 option in terms of the EMV? At what "Blockbuster" profit figure does Seth's optimal decision switch?
Enter the EMV in $millions as a decimal number with two digits to the right of the decimal point (e.g., enter ''$5,500,000'' as ''5.50''). Round if necessary.
To answer that question, we first write the EMV of the K2 option with a variable, B, to represent "Blockbuster" profits in millions of dollars.
Now, we compare the EMV of the K2 option to the EMV of the Pony option. The K2 EMV is greater than the Pony EMV when the "Blockbuster" profit figure is greater than $4.67 million.
We call $4.67 million the breakeven value for "Blockbuster" profits: above it, the EMV criterion recommends the K2 option; below it, the EMV criterion recommends the Pony option.
Seth may not be sure if the "Blockbuster" profits are best represented by $6 million or $5 million or $4.8 million, but as long as he is confident that the figure is greater than $4.67 million, he need not lose any sleep over finding a more accurate value. Knowing that his estimates for the "Blockbuster" profit figure are firmly on one side of the breakeven value allows him to stop worrying about the precise value of that number in the decision analysis, since knowing that number with greater precision will not change his decision.
On the other hand, if Seth thinks the "Blockbuster" profit figure could be below $4.67 million, he may wish to invest additional resources to find a more accurate figure to represent "Blockbuster" profits.
If Seth thinks the true number is around the breakeven value of $4.67 million, but isn't certain if it's slightly above or slightly below that figure, he can also stop worrying about the precise value of the number. As long as the figure is around $4.67 million, Seth should be indifferent between the K2 and Pony deals, since the EMVs of the two options are about the same.
In fact, a good way to check that we have calculated a breakeven value correctly is to substitute the value into the EMV calculation: if the options have the same EMV, the breakeven value is correct.
Once we calculate a breakeven value, we know whether or not expending additional time and other resources to find a more accurate estimate is worthwhile. The breakeven value establishes a comfort zone: as long as we are confident that the value we are estimating is within the zone, we can feel comfortable choosing the option recommended by our initial analysis, based on our original estimate.
If we think the value we are estimating could be close to the breakeven value, we need to be more cautious. If the true value we are trying to estimate could lie outside of the comfort zone, we might want to try to make our estimate of that value more accurate before we reach a final decision.
How confident we are that the true value we are estimating lies inside the comfort zone given by the breakeven analysis is a matter of judgment and experience. Sometimes, we might collect sample data to estimate an outcome value. In this case, we should look closely at the variation in the data to see how widely and in what way the data can vary.
Calculating a breakeven value for data used in a decision analysis is called sensitivity analysis: for each estimated value in the analysis, we check to see by how much it would have to
change to affect our decision, assuming our estimates for all the other data are correct. Sensitivity analysis is an important and powerful tool for management decision-making. Managers who base decisions on an initial analysis without performing sensitivity analysis on critical data risk lulling themselves into a false sense of security in their decisions.
Summary
After completing an initial decision analysis, always conduct a sensitivity analysis for each outcome value estimate you are uncomfortable with. First, calculate the outcome value's
breakeven value: the value for which the EMV of the option initially recommended by the decision analysis ceases to be the best EMV. The breakeven value defines a comfort zone: If we believe that the actual outcome value might be outside that zone — thereby changing the optimal decision — we should reconsider our analysis and refine our estimate of the
outcome value in question.
Evaluating Non-Monetary Consequences
During his negotiations with K2 and Pony, Seth realized that he did not particularly look forward to working with the K2 team. Based on past experience, he knows that interpersonal frictions can be highly frustrating and can make a collaboration unpleasant. This frustration is clearly a cost — albeit a non-monetary cost — associated with the K2 option.
Sensitivity analysis can give us a "reality check" on how highly we value non-monetary consequences such as frustration, reputation costs and benefits, and sentimental values. Although it may be difficult to assign a value to such consequences, we can often answer questions about the most we'd be willing to pay to avoid (or to obtain) them by calculating a threshold value.
Clearly Seth wouldn't want to spoil any magical Hollywood days just to make an additional $5 in profits. But the more the K2 option pays relative to the alternatives, the more willing Seth might be to suffer working with the K2 team. How can Seth determine whether he should accept the K2 deal and bear the resulting
interpersonal trials and tribulations?
Sensitivity analysis can help us analyze non-monetary consequences such as frustration. Let's use "F" to represent the frustration cost (in $millions) Seth will incur if he has to work with the K2 team. Since
frustration will occur in any scenario involving the K2 option, $F million must be subtracted from all outcomes associated with the K2 option.
How large must the cost of frustration be for Seth's optimal decision to switch to the Pony option?
Enter F, the cost of frustration, in $millions as decimal number with one digit to the right of the decimal point (e.g., enter ''$5,500,000'' as ''5.5''). Round if necessary.
Adding $F million to the outcomes changes the EMV of the K2 option to $1.4 million - $F million. For Seth's decision to switch from the K2 deal to the Pony deal, the EMV of the K2 option, $1.4 million - $F million, must drop below $1.0 million. In other words, F must satisfy the inequality below.
In order to lower the EMV of the K2 option below the EMV of the Pony option, the cost of frustration would have to be valued at least at $400,000. Seth needs to ask himself if he would pay $400,000 to avoid the frustration of working with K2. Sensitivity analysis provides a clear, monetary upper bound against which he can measure the strength of his feelings.
In the end, Seth decides that he can learn to love the K2 team for $400,000. Summary
To incorporate non-monetary consequences into a decision, first find the option with the best EMV. Then, add the non-monetary consequence to the outcome values of all
scenarios affected by that non-monetary consequence, and calculate the breakeven value for which the option recommended by the initial decision analysis ceases to have the best EMV. The breakeven value defines a comfort zone: If we believe that the actual value of the non-monetary consequences might be outside that zone — thereby changing the optimal decision — we should try to gain a firm estimate of the non-monetary
consequence's value.
A Decision's Sensitivity to Probability Estimates
Seth is somewhat unsure about his estimates for the probabilities of how successful Cloven will be. He is quite sure that the probability of the film flopping is around 20%, but he's less sure about the probabilities of "Lackluster" and "Blockbuster" performance levels. He wants to know how sensitive his decision to choose the K2 deal is to the values of these
probabilities.
Let's call the probability of a "Blockbuster" "p." Seth is confident that the probability of a "Flop" is 20%. What is the probability of a "Lackluster" outcome?
a. 1.0 — p
b. 0.8 — p
This is the correct answer. c. p — 0.2
This is not the correct answer. Think about what probabilities must add up to 1.0. d. The answer cannot be determined from the information provided.
This is not the correct answer. Think about what probabilities must add up to 1.0.
Since the three outcomes are mutually exclusive and collectively exhaustive, their
probabilities must add to 100%. Seth is confident that the probability of a "Flop" is 20%, so he knows that the probabilities of the remaining two outcomes ("Blockbuster" and
"Lackluster") must add to 80%. Thus, the probability of a "Lackluster" performance is 0.8 - p.
Using p to denote the probability of a "Blockbuster" outcome and 0.8 - p to denote the probability of a "Lackluster" outcome, what is the EMV of the K2 option?
a. p * $6 million - $0.4 million
This is the correct answer. b. p * $6 million + $0.4 million
This is not the correct answer. Remember that the ''Flop'' scenario involves a loss. c. $0.08 million - p * $6 million
This is not the correct answer. Remember that p is the probability of a ''Blockbuster.'' d. $0.08 million + p * $6million
This is not the correct answer. Remember that p is the probability of a ''Blockbuster.'' The EMV of the K2 option is p * $6 million - $0.4 million. For what values of p, the
probability of Cloven becoming a "Blockbuster" film, is the Pony option preferred to the K2 option on the basis of EMV?
a. p > 0.233
This is not the best answer. The higher the probability of a ''Blockbuster'', the more attractive the K2 option becomes relative to the Pony option.
b. p < 0.233
This is the best answer. c. p > 0.300
This is not the best answer. The higher the probability of a ''Blockbuster'', the more attractive the K2 option becomes relative to the Pony option.
This is not the best answer. At 0.29, for instance, the K2 option is still preferable to the Pony option. The breakeven value for the probability of a "Blockbuster" hit is 23.3%: when the probability is above 23.3%, the EMV of the K2 option is higher; when the probability is below 23.3%, the EMV of the Pony option is higher. If Seth is confident that the probability of a "Blockbuster" is at least 23.3%, he can feel comfortable choosing the K2 option. He need not expend additional effort trying to further refine his estimates for the probabilities of different levels of success.
Decision-making is an iterative, multi-step process. When analyzing a decision, we should first construct and analyze a decision tree based on our best estimates of the outcomes and probabilities involved. After reaching a tentative decision, it is critical to scrutinize the data used in a decision analysis and conduct sensitivity analyses for each estimate that we feel unsure about.
As long as we are comfortable that the true value we are estimating is within the range specified by the breakeven calculation, we can confidently proceed with our decision. If not, we should focus our efforts on refining our estimates for those values to which our decisions are most sensitive.
Finally, we should note that managers sometimes need to test the sensitivity of their decisions to two or more estimates simultaneously. Sensitivity analysis techniques can be extended to address these situations; these techniques are beyond the scope of this course.
Summary
After completing an initial decision analysis, always conduct a sensitivity analysis for each probability value you are uncomfortable with. First calculate the probability's breakeven value: the probability for which the EMV of the option initially recommended by the
decision analysis ceases to be the best EMV. The breakeven value defines a comfort zone: If we believe that the actual probability might be outside that zone — thereby changing the optimal decision — we should reconsider our analysis and refine our estimate of the probability in question.
Solving the Uncertain Estimates Problem
Sensitivity analysis helps managers cope with the uncertainty that surrounds the estimates they base decisions on. With your new knowledge, you're ready to turn to Leo's problem. Your initial analysis recommends that Leo launch his floating restaurant, but Leo has expressed some doubt about the estimate of the losses he'd incur if the Tethys turns out to be a passing "Fad."
How high do the losses have to be in the "Fad" scenario to make launching the Tethys ill-advised in terms of EMV?
a. Greater than $0.70 million.
This is not the best answer. When you compute the EMV, make sure you are weighting the ''Fad'' outcome value by the likelihood that it will occur.
b. Less than $0.70 million.
This is not the best answer. When you compute the EMV, make sure you are weighting the ''Fad'' outcome value by the likelihood that it will occur.
c. Greater than $1.08 million. This is the best answer. d. Less than $1.08 million.
This is not the best answer. Think about how the outcome value of a ''Fad'' would have to change to make launching the Tethys unprofitable in terms of the EMV.
Launching the Tethys would be less attractive than not launching it if the EMV of launching is less than $0, the EMV of not launching. Solving the inequality below, we find that the losses in the event that the Tethys is just a "Fad" would have to exceed $1.08 million for Leo to abandon the project based on the EMV criterion.
Assume that, in fact, Leo's estimate — that he will incur an $800,000 loss if Chez Tethys turns out to be a "Fad" — is correct. For what probability of a "Fad" does launching the Tethys cease to be a worthwhile venture, in terms of the EMV?
a. Greater than 71%. This is the best answer. b. Less than 71%.
This is not the best answer. Think about how the probability of a ''Fad'' would have to change to make the EMV of launching the Tethys higher than the EMV of not launching.
c. Greater than 29%.
This is not the best answer. Make sure you are finding the probability of a ''Fad'' rather than the probability of a ''Phenomenon.
d. Less than 29%.
This is not the best answer. Make sure you are finding the probability of a ''Fad'' rather than the probability of a ''Phenomenon.''
Launching the Tethys is less attractive than not launching it if the EMV of launching is less than $0, the EMV of not launching. Solving the inequality below, we find that the probability of a "Fad" would have to be higher than 71% for Leo to prefer to abandon the project based on the EMV criterion.