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I'm trying to put the following situation into one simple formula:

Imagine a store that sells a product for X. They pay Y for it and profit Z (which may or may not be greater than Y). The store receives the payment A days after the sale.

What is the formula that will calculate how much money has been generated if every single penny is reinvested into more items to sell as soon as the payment is received and if the store invests in N items per day until its funds F run out (which always happens before M) and the profits are reinvested for M days, which is always greater than or equal to A? Any money still tied to products that have not yet been paid for after M days can be included as well.

So, let's say a store sells a product for 120 dollars, for which they pay 100 and from which they profit 20 dollars. The store only receives payment after 30 days so when they deliver a product they are out 100 dollars. If they sell 5 products a day, they will be out 15000 dollars when they start receiving back their money along with their profits 30 days later. They will continue investing 600 USD a day on new products until their initial funds of 10,000 USD run out.

So, to clarify:

Day 1 - 5 items invested in and sold

Day 2 - 5 items invested in sold

Day 3 - 5 items invested in sold

...

Day 20 - Funds run out as last 5 items are invested in and sold.

...

Day 31 - the 5 first items are paid for by the client, everything is reinvested and 6 items sold

Day 32 - the second 5 items are paid for by the client, everything is reinvested and 6 items sold

...

The things is, as soon as they receive their first 120 USD * 5 products = 600 USD, they will reinvest it into 6 more products and sell them immediately and so on so the store is always growing. Any money that is not enough to buy a product to sell is saved until there is sufficient money. How much would they make in a year?

I tried all sort of approaches for like 5 hours but putting this into one single formula is, unfortunately, beyond me at the moment.

Can it be done (I imagine so)?

InSaNo
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  • Can $M$ be less than $A$ or are they always equal? – Aman Kushwaha Aug 19 '21 at 06:03
  • Sorry, M is always greater than or equal to A – InSaNo Aug 19 '21 at 06:13
  • Since the store is investing all the money it receives including the profit, the money generated after $M$ days will be only in the form of investment, i.e, the number of products accumulated. Also what about the amount it invested before it received its first payment, Is that supposed to be subtracted? – Aman Kushwaha Aug 19 '21 at 06:25
  • I am not sure what you mean by your first assertion. I am so confused that maybe I explained it wrong. I edited the question and I think it makes more sense now.

    As to the amount, up to you.

     – InSaNo Aug 19 '21 at 06:33
  • Day 50: last day of receiving payment (of day 20th specifically) 5 items are paid for, 6 items purchased and sold... Day 51 : no funds left (the store never had "stored funds", it was using the payment received on daily basis) no payment, no investing, no selling. Day 61: 6 items are paid for, reinvested, 7.2 items purchased and sold (actually 7 items purchased) after every 5 days money for buying a whole item would be available. So, Day 65 6 items are paid for, 8 items purchased and sold. As a result On day 95 store will receive more money than day 94 or 96. – Aman Kushwaha Aug 19 '21 at 08:43
  • Thanks a lot for replying! What if it starts with 10,000 USD in funds and it invests in 5 items more for 20 days until the funds run out, then it keeps reinvesting the profits for a year and then stops and collects everything? – InSaNo Aug 19 '21 at 08:49

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