1. The insurance company evaluates a stolen item as worth: N.
2. They pay us a value of: 4/5N*.
3. We buy a replacement item worth M.
3a. If M <= 4/5 N, we receive no additional payment. Net total received: 4/5N*.
3b. If 4/5N < M <= N, we receive an additional payment of (M - 4/5N). Net total received: M*.
3c. If N < M, we receive an additional payment of 1/5N. Net total received: N*.
*less D, the deductible.
There must be a game mechanic in there.