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 = ?


To calculate the KPI with exponential scaling, given the conditions and the example, we need to establish a formula that can be used to compute the KPI. The goal is to create a greater reduction in the KPI achievement when the actual RGI growth falls short of the target. 

Given:
- Actual RGI Growth (\( RGI_{actual} \)) = -1%
- RGI Growth Target (\( RGI_{target} \)) = 4%

Let's denote the KPI as a function of the ratio between the actual growth and the target growth, scaled exponentially:

\[ KPI = 100 \times e^{-\alpha (1 - \text{Ratio})} \]

where 
\[ \text{Ratio} = \frac{RGI_{actual}}{RGI_{target}} \]
and \(\alpha\) is a constant that we can determine based on provided examples or desired scaling behavior.

### Step-by-Step Calculation:

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

2. **Determine \(\alpha\):**
   From the previous step, we derived \(\alpha \approx 0.379\).

3. **Apply the Exponential Scaling Formula:**
   \[ KPI = 100 \times e^{-0.379 (1 - (-0.25))} \]

4. **Simplify the Exponent:**
   \[ KPI = 100 \times e^{-0.379 \times 1.25} \]

5. **Calculate the Exponent:**
   \[ -0.379 \times 1.25 = -0.47375 \]

6. **Calculate the KPI:**
   \[ KPI = 100 \times e^{-0.47375} \]
   Using a calculator to find \( e^{-0.47375} \):
   \[ e^{-0.47375} \approx 0.6229 \]

7. **Final KPI Calculation:**
   \[ KPI = 100 \times 0.6229 \]
   \[ KPI \approx 62.29 \]

Therefore, for the given example where the Actual RGI Growth is -1% and the RGI Growth Target is 4%, the KPI, when scaled exponentially, is approximately 62.29%.

Would you like to see more examples, or do you have any other questions?

Here are 5 numbered questions you might consider asking next:
1. Can we use a different value for \(\alpha\) for a more aggressive or lenient scaling?
2. How do we interpret the KPI value in a business context?
3. Can you provide more examples with different actual RGI growth and target values?
4. How does the KPI change if the actual RGI growth is positive but less than the target?
5. Can you explain the implications of using exponential scaling versus linear scaling for KPI calculation?

**Tip:** When dealing with exponential scaling, always check if the chosen \(\alpha\) reflects the desired sensitivity and adjust accordingly for your specific needs.

Explore how to calculate KPI using exponential scaling with an example of actual RGI growth at -1% against a target of 4%. This guide breaks down the process step-by-step and covers key mathematical concepts like ratios and exponential functions, suitable for Grades 10-12.

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