# Markup on COGS or investment?

I'm reading the Innovator's Dilemma by Clayton Christensen and came across the following text and table:

Discounters didn't accept lower profits than those of traditional retailers, however; they just earned their profits through a different formula. In the simplest terms, retailers cover their costs through the gross margin, or markup, they charge over the cost of the merchandise they sell. Traditional department stores historically marked merchandise up by 40 percent and turned their inventory over four times in a year - that is, they earned 40 percent on the amount they invested in inventory, four times during the year, for a total return on inventory investment of 160 percent. ... Discount retailers earned a return on inventory investment similar to that of department stores, but through a different model: low gross margins and high inventory turns. Table 5.1 summarizes the three positions.

I think I get the point: you can cover the costs associated with running a store either by having higher margins or by having a higher inventory turnover. If your inventory turnover is low, the inventory that you sell needs to have a higher gross margin to cover the costs of holding that inventory vs if your inventory turnover is high. However, the explanation in this book confuses me as it appears to use inconsistent definitions.

In the text "markup" is defined as the gross margin charged over the cost of the merchandise that is sold. If traditional department stores historically marked merchandise up by 40 percent then that would mean that if they bought \$100 worth of product they would sell it for \$140. If this is the correct interpretation of the definition then the ROI of 160% makes no sense. Suppose that a full inventory is valued at \$100. If they ... turned their inventory over four times in a year then that would mean that they would sell an entire inventory four times, meaning that they would incur costs of \$400 and achieve a revenue of \$560. ROI = (\$560 - \$400) / \$400 = 40% and not 160%.

The only way in which this works is if the markup is calculated with respect to the costs associated with holding a particular inventory for an entire year (like cost of space, administrative costs, etc). If the markup is relative to the total costs that you would incur from running the stores and not costs of goods sold then the 160% ROI makes sense. However in this statement the 40% markup is clearly defined as the margin charged over the cost of merchandise they sell which I would interpret as COGS.

The idea is that I only need \$100, not \$400, since I recoup the \$100 with each sale. 1. I have \$100. This is my capital, I will only use this in the business for a year.
2. I buy one set of goods for \$100, I have \$0 left.
3. I sell the goods for \$140. 4. I buy a new set of goods for \$100, I have \$40 left. 5. I sell the goods for \$140.
6. I buy a new set of goods for \$100, I have \$80 left.
7. I sell the goods for \$140. 8. I buy a new set of goods for \$100, I have \$120 left. 9. I sell the goods for \$140.
10. I now have \$260, and I started out with \$100, thus the ROI is 160%.