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Why do convertible note terms include both valuation caps and discounts?


We are raising initial funds and interested investors have proposed a convertible note that includes a valuation cap that works as a maximum for the price at which their note would convert to equity as well as a discount rate that gives the investors a discount for their note conversion from the price of shares offered to other investors in a future funding round. Why are they asking for both when it seems that the discount rate gives them all the benefits that they need as early investors (favorable share pricing terms to any future investors)?