Will paying cash for a deal punish us on Cash on Cash returns?

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Is it harder to get a ten percent or more Cash on Cash return when doing cash deals?  Seems like the only way we can up our Cash on Cash is to calculate the purchase with a much lower down payment... but we want to sink our own cash into the deal.  I am struggling to see if it is a bad deal or if we need to accept lower Cash on Cash returns when we invest all-cash deals... Thanks!