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What is the Discount Rate in equity crowdfunding SAFEs?

A common question I hear from investors is about what a discount rate is and how it works with SAFEs or convertible notes.
The discount rate for investors is shown on the terms of each Crowd SAFE or Convertible Note on portals such as Wefunder and Republic. It determines the discount that will be applied to the current valuation when calculating the number of shares
The SAFE or Convertible Note, when and if it converts to equity shares, will convert at the lesser of either the discount rate OR the valuation cap. That is the price used to calculate how many shares you get upon conversion – so the lower the price, the more shares you get.
For example, let’s say you invest in a company offering a Crowd SAFE with a 20% discount and a $10 million valuation cap.
When valuation cap is a better deal: if the company was raising their next financing round at a $20 million valuation and converting the SAFEs, then your SAFE would either convert at a 20% discount ($20M*.8 = $16M), or a $10M valuation cap. In this case – $16M vs. $10M – the valuation cap of $10M gives the investor a better deal and would be used to calculate how many shares you get. You are essentially getting twice as many shares as new investors at the $20M valuation.
When discount rate is a better deal: on the other hand, if the company converted and was at the same $10 million valuation, then your SAFE would convert at either the 20% discount ($10M*.8 = $8M) or the $10M cap. In this case – $8M vs. $10M – the discount rate gives the best deal to the investor and would be used when calculating how many shares you get upon conversion.