Since the total losses to the layer will be unchanged and the loss ratio is to be maintained, this means that the total premiums (including reinstatement premiums) will therefore also need to be the same. If R is the new rate on line, then the initial premium received will be R*£5m. If C is the total amount of cover that needs to be reinstated over an n-year period based on an event set of past claims, then the total reinstatement premiums payable (@50%) are RC*0.5, which equates to RC/2n per year on average. Add this average annual reinstatement premium payable to the initial premium to get a total estimated annual premium of 5R + RC/2n. This needs to equal the original premium for layer 1 which was £1m (= £5m*20%). Then rearrange the equation to solve for R.
