Cast Iron Compay on each nondelinquent sale receives revenue

Cast Iron Compay, on each nondelinquent sale, receives revenues with a present value of $1,230 and incurs with a value of $1,065. Cast Iron has been asked to extend cedit to a new customer. You can fidn little information on the firm, and you believe that the probability of payment is no better then 0.77. But if teh payment is made, the probability that the customer will pay for the second order is 0.94. It costs $15.25 to determine whether a customer has been a prompt or slow payer in the past.

Calculate the minimum probability at which credit can be extended. (round answer 2 decimal places)

Solution

Revenue receiving present value = 1230

Incurred value = 1065

Difference = 1230-1065

                  = 165

For a new customer let x be the credit extended

Expected payment from him = (0.77x-0.23x-0.06x+0.94x)0.5

= 0.71x

For this incurred value revenue received should be 0.71x(1230)/1165 = 0.749614x

If this is equal to 15.25 then no loss or gain

or when x = 20.34381

If x >20.34381, there is profit

Hence minimum credit should be extended = 20.34381