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BDI and CDI example 1

Optional numerical practice

Extra drills; no claim that these exact questions or allocated marks appeared in TEE

Optional practice question. An area contains 10% of the relevant population, accounts for 15% of total brand sales and 20% of total category sales. Calculate BDI and CDI and interpret them. [3 practice marks]

Answer

Authored illustration: these numbers were chosen to explain a faculty-note concept. No matching supplied-data question was found in the 14 recovered APR papers. Standalone calculation drills are optional practice; their marks are author-set.

Given

Population shareBrand-sales shareCategory-sales share
10%15%20%

To find

Brand and category development indices.

Formula and why

\text{BDI}=\frac{B_{\%}}{P_{\%}}\times100,\qquad\text{CDI}=\frac{C_{\%}}{P_{\%}}\times100LaTeX: \text{BDI}=\frac{B_{\%}}{P_{\%}}\times100,\qquad\text{CDI}=\frac{C_{\%}}{P_{\%}}\times100

The common denominator is population share. Only the numerator changes between brand sales and category sales.

Step-by-step solution

Step 1. Substitute for BDI

\text{BDI}=\frac{15}{10}\times100LaTeX: \text{BDI}=\frac{15}{10}\times100

Step 2. Divide and scale BDI

1.5\times100=150LaTeX: 1.5\times100=150

Step 3. Substitute for CDI

\text{CDI}=\frac{20}{10}\times100LaTeX: \text{CDI}=\frac{20}{10}\times100

Step 4. Divide and scale CDI

2\times100=200LaTeX: 2\times100=200

Step 5. Compare each with 100

Both brand and category are over-represented relative to population.

Final answer: BDI = 150; CDI = 200.