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Calculating Category CAGR from Aggregate Unit Costs

Article Quant Q&A · Author: Flynn Rausch
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Summary

The document asks how to calculate a category-wide compound annual growth rate for unit costs across multiple items. It gives the standard CAGR relationship between a starting value, ending value, and elapsed time, and notes that averaging individual item CAGRs or summing annual unit prices may not produce a meaningful category rate.

The responses suggest calculating CAGR from the category's base-year and ending-year values, with one proposing the average price of a basket as the aggregate series. The central practical issue is defining that aggregate consistently: the result depends on whether items receive equal weights, volume weights, or another weighting scheme, and whether the basket composition changes over time. The document does not specify those details or provide an example calculation, so its suggestions do not establish a single correct category measure without further information about the cost data and intended aggregation.

Key ideas

  • CAGR uses the starting value, ending value, and elapsed number of years.
  • A category-level CAGR should be calculated from aggregate values at the endpoints.
  • Averaging item-level CAGRs is not necessarily equivalent to calculating CAGR for the category.
  • A basket average can serve as an aggregate series, but its weighting and composition need definition.

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Full text
# Overall CAGR calculation


# Overall CAGR calculation












I'm one of those data analysts who doesn't have a MBA, so I'm still figuring out the basics of finance as work gets assigned to me.

Here's the exact wording I was given:

> What's the unit cost inflation (CAGR) between 2010 and 2014?

In this case, I've got 20 rows, I've got the unit costs for each year. I got the year-over-year and 4-year CAGRs for each row no problem per the formula:

$$\textrm{CAGR}(t_0, t_n) = \left( \frac{V(t_n)}{V(t_0)} \right) ^{\frac{1}{t_n - t_0}} - 1$$

Now my problem arises: I need to get the CAGR for the entire category. I'm going to assume it's neither as simple as just summing/averaging the CAGR for each item, nor summing up the unit prices by year and running them through the formula.

## Answer by Mehdi Zare (score 1)

https://quant.stackexchange.com/a/49715

CAGR is the growth rate that when applied to the base year and compounded over the entire time, generates the final value. So to get CAGR you need to plugin base value, final value and duration to the formula to get the rate.

## Answer by Jamulive (score 0)

https://quant.stackexchange.com/a/51513

If you need an overall CAGR for the category, it sounds like you can get an average price of the basket, and calculate the CAGR of this average price.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.