The answer for part D is given. please provide a logical explanation of why the deductible (D) is multiplied by 8% (13%-5%)

Your firm faces a(n) 13% chance of a potential loss of $5 million next year. If your firm implements new policies, it can reduce the chance of the loss to 5%, but these new policies have an upfront cost of $80,000. Suppose the beta of the loss is 0, and the risk-free interest rate is 4%. a. If the firm is uninsured, what is the NPV of implementing the new policies? b. If the firm is fully insured, what is the NPV of implementing the new policies? c. Given your answer to (b), what is the actuarially fair cost of full insurance? d. What is the minimum-size deductible that would leave your firm with an incentive to implement the new policies? e. What is the actuarially fair price of an insurance policy with the deductible in part (d)? d. What is the minimum-size deductible that would leave your firm with an incentive to implement the new policies? If the insurance policy has a deductible, then the firm will benefit from the new policies because it will avoid a loss, and therefore avoid paying the deductible, 8% of the time. Let D be the amount of the deductible. Then the NPV of the new policies is as follows: 8% XD NPV = - $80,000+ (1 +0.04) Setting the NPV to 0 and solving for D we get: D=$1.040 million