# week3 by dandanhuanghuang

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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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