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					Example of Sensitivity Analysis Using Harrah's Analysis

Objective: To assess the effectiveness of the frequency upside program
Source: Exhibit 2C data            Assume: Old Redemption             40 $/offer (we called this X in class)

Diagnostics

Step 1: Compute Simple "Pre" and "Post" Averages

                         PRE             POST
#Guest                     31             130
Trip/Guest                  1              1.2
Theo Win               $8,075.00       $49,830.00
Theo Win / Trip         $286.00         $323.00

Redemption              10.40%           47.00%
Comp Rewards            17.00%           21.00%

Step 2: Compute Incremental Costs and Benefits

Inc. Revenue              32663.45 (See case slideshow for formula)
Inc. Cost                  5736.64
Net Benefit               26926.81

Step 3: Sensitivity Analysis

Procedure: Identify all factors that you may have uncertainties above, and all possible states of the world
Example: Suppose I suspect that the long run POST redemption rates could be anywhere between 45% and 55%
…..and the POST trips / guest could range between 1 and 1.3
Further, assume that all states of the world are equally likely.
We can use the spreadsheet to change one item at a time to calculate net benefit

                                      Redemption
                          45              50           55
T/G = 1                 $28,112        $27,592        $27,072
T/G = 1.1               $27,644        $27,072        $26,500
T/G = 1.2               $27,176        $26,552        $25,928
T/G = 1.3               $26,708        $26,032        $25,356

Step 4: Descriptive Statistics

If all the above numbers are equally likely, then

Mean                      $26,812
Standard Deviation           $794
Now you can calculate the probability of, say, the benefit being greater that $27,000 (use normalized Z and a z-table)
You have just converted a point estimate into a probability estimate.

The standard deviation as a percent of mean is      2.96%
And six standard deviations represent an error of  $4,764
This can be thought of as the cost of being inaccurate (since it represents the 6 SD range)
You can also plot the data to look at trends



                                               Sensitivity


           $28,500
           $28,000
           $27,500
           $27,000
            $26,500
            $26,000
            $25,500
            $25,000
                                                                    T/G = 1.3
            $24,500
                                                                  T/G = 1.2
            $24,000
                                                               T/G = 1.1
            $23,500
                                                             T/G = 1
                              45
                                           50
                                                      55
                      Redemption Rate
en 45% and 55%




ized Z and a z-table)

				
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