Answer to new quiz

This is a classic retail arithmetic puzzle that touches on the difference between Percentage Margin and Cash Contribution (the Deckungsbeitrag you mentioned).

Here is the breakdown of your scenarios.

1. The Initial Agreement

Yes, on this we agree.

If you sell the exact same quantity at the same Turnover Speed (TOS):

 * Sustainable: €4 Selling - €2 Buying = €2 Profit/unit

 * Other: €3 Selling - €1 Buying = €2 Profit/unit

Since the cash profit per unit is identical (€2), the total profitability is identical. 

(Even though the Other product actually has a much higher margin percentage in this specific scenario, the cash result is the same).

2. The Question: Equal Profitability at Same Margin %

Now we move to your second scenario where the margin percentages are equal (50%), but the cash amounts differ.

The Context:

 * Sustainable (M): Buying €2 / Selling €4. (Margin: €2 per unit).

   * Current TOS: 5

   * Current Fundspeed: 250%

 * Other (L): Buying €1 / Selling €2. (Margin: €1 per unit).

The Calculation:

To be "equally profitable" in terms of Deckungsbeitrag (Cash Contribution)—which is what pays the bills—the "Other" socks must generate the same total amount of cash over the year as the "Sustainable" socks.

Since the "Other" socks only generate half the cash per unit (€1 vs €2), they must turn over twice as fast to generate the same total pile of money.

The Answer:

 * Turnover Speed (TOS): 10

 * Fundspeed (GMROII): 500%

The Breakdown

Here is the step-by-step math comparing the two to prove they generate the same cash contribution (Deckungsbeitrag):

| Metric | Sustainable (M) | Other (L) |

|---|---|---|

| Buying Price | € 2.00 | € 1.00 |

| Selling Price | € 4.00 | € 2.00 |

| Margin % | 50% | 50% |

| Cash Margin (per unit) | € 2.00 | € 1.00 |

| Turnover Speed (TOS) | 5 | 10 |

| Total Cash Generated | € 10.00 | € 10.00 |

| Fundspeed (Margin % x TOS) | 250% | 500% |

Comparison Summary

For the "Low" product to be as profitable as the "Medium" product while maintaining the same margin percentage, it must work twice as hard

.

 * TOS: Must increase from 5 to 10.

 * Fundspeed: Must increase from 250% to 500%.