Last Month Audited RGI Growth / Annual RGI Growth Target, scaled
Exponentially
Exponential Scaling is applied to this KPI in order to have greater
reduction in KPI achievement depending on how much it falls short of
the target.
Example1: Actual RGI Growth = -1%; RGI Growth Target = 4%; KPI = 57%
Example2: Actual RGI Growth = 0.02%; RGI Growth

To calculate the KPI with exponential scaling, we need to apply an exponential function to the ratio of the actual RGI growth to the target RGI growth. Here's a step-by-step process to achieve this:

1. **Identify the Variables:**
   - Actual RGI Growth (\( RGI_{actual} \))
   - RGI Growth Target (\( RGI_{target} \))

2. **Calculate the Ratio:**
   - \( \text{Ratio} = \frac{RGI_{actual}}{RGI_{target}} \)

3. **Apply Exponential Scaling:**
   - Use an exponential function to scale the ratio. The function could be of the form:
     \[
     KPI = 100 \times e^{-\alpha (1 - \text{Ratio})}
     \]
     where \( \alpha \) is a constant that determines the steepness of the scaling.

Let's use the provided examples to determine \( \alpha \):

### Example 1:
- Actual RGI Growth (\( RGI_{actual} \)) = -1%
- RGI Growth Target (\( RGI_{target} \)) = 4%
- KPI = 57%

Calculate the ratio:
\[
\text{Ratio} = \frac{-1}{4} = -0.25
\]

Using the given KPI:
\[
57 = 100 \times e^{-\alpha (1 - (-0.25))}
\]
\[
0.57 = e^{-\alpha \times 1.25}
\]
\[
\ln(0.57) = -\alpha \times 1.25
\]
\[
\alpha = -\frac{\ln(0.57)}{1.25}
\]
\[
\alpha \approx 0.379
\]

### Example 2:
Let's verify using another example:
- Actual RGI Growth (\( RGI_{actual} \)) = 0.02%
- RGI Growth Target (\( RGI_{target} \))

Let's assume we need to find the KPI.

Calculate the ratio:
\[
\text{Ratio} = \frac{0.02}{RGI_{target}}
\]

Using the found \(\alpha\):
\[
KPI = 100 \times e^{-\alpha (1 - \text{Ratio})}
\]
\[
KPI = 100 \times e^{-0.379 (1 - \frac{0.02}{RGI_{target}})}
\]

Now you can use the same process to determine the KPI for any given actual RGI growth and target using the \(\alpha\) found from the examples.

Would you like to input specific values to get a calculated KPI? Do you need any more details or explanations?

Here are 5 numbered questions you might consider asking next:
1. Can you provide more examples for verification?
2. What are the exact values for your second example?
3. How do we choose the best value for \(\alpha\)?
4. Can you explain how exponential scaling impacts KPI calculation in more detail?
5. How can we apply this KPI calculation method in real-world scenarios?

**Tip:** When dealing with exponential functions, small changes in the input can lead to large changes in the output. It's essential to choose your parameters carefully.

Learn how to calculate Key Performance Indicator (KPI) with exponential scaling using real-world examples. Includes step-by-step formulas and calculations for different scenarios of actual vs. target RGI growth.

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