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Let say you manage a supermarket chain and want to estimate profitability of a store over time, not only by using revenue and cost for a given unit of time - but also to include the initial investment for opening a given store.

How do you properly annualize the initial cost?

I see two problems:

  1. Even if given inflation figures for each year since opening, I'm not sure how to properly divide the initial investment and apply inflation.

  2. When comparing stores, longer running stores have 'positive bias' on profitability (all else kept equal), as the initial investment is divided by more units so the annualized cost is artificially lower.

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How you apply initial investment depends on the nature of that investment. You could consider the initial investment as a fixed cost (if that’s actually the case), then calculate the net present value of all revenues and subtract/ compare to the fixed cost. This requires taking care of inflation of course.

An alternative is to consider the initial investment as part of the capital costs. For example, the initial investment may have been borrowed and you are currently paying interest on that loan. Or you can imagine that you bought capital (e.g. land and machines) with the investment and are renting those out to yourself, which you would subtract from your profits. This way you capture the (opportunity) cost of that capital. In a classic economics profit function, that corresponds to the $r*K$ part of the profit equation $\Pi = p*y -w*L - r*K$, where p are prices, y are output units, w are wages and L are labor amounts.

As for your first point, you apply inflation as you normally would anytime you want to compare monetary amounts across time for any reason.

For example, suppose you made the investment last year and have profits this year. To compare them, you can convert this year’s profits to last year’s dollars. To do so, you can divide this year’s profits with 1+cpi inflation percentage, or multiply it by the (gdp) deflator.

On your second point, the difference is not artificial. You are describing very real economies of scale, which increase profitability.

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