Question

Corporate Finance class

Cast Iron Company, on each nondelinquent sale, receives revenues with a present value of $1,280 and incurs costs with a value of $1,090. Cast Iron has been asked to extend credit to a new customer. You can find little information on the firm, and you believe that the probability of payment is no better than .81. But if the payment is made, the probability that the customer will pay for the second order is .94.

a. Calculate the minimum probability at which credit can be extended assuming there is no possibility of repeat orders. (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)

Minimum probability= %

b. If it costs $14.00 to determine whether a customer has been a prompt or slow payer in the past, at how many units ordered should Cast Iron undertake such a check? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Break-even point= units not percent

Answer 1

Case 1: Payment is made

Probability = p

Profit = P1 = Revenues - Cost = 1,280 - 1,090 = 190

Case 2: Payment is not made

Probability = 1 - p

Profit = P2 = Revenues - Cost = 0 - 1,090 = -1,090

Part (a)

Expected profit = p x P1 + (1 - p) x P2 = p x 190 + (1 - p) x (-1,090) = 1,280p - 1,090

the minimum probability at which credit can be extended assuming there is no possibility of repeat orders, will be that value of p at which expected profit = 0

Or, 1,280p - 1,090 =

Hence, the minimum probability, p = 1,090 / 1,280 = 85.2%

Part (b)

Let N be the number of units ordered when Cast Iron should undertake such a check.

Expected profit = 1,280p - 1,090

p = 0.94 for the second order

Hence, expected profit = 1,280 x 0.94 - 1,090 = 113.20

The customer check will help us eliminate the non payment cases on second order.

Hence, (1 - p) x Expected profit x N = Cost of check

Hence, (1 - 0.94) x 113.20 x N = 14

Hence, N = 14 / (113.20 x 0.06) = 2.06125

Hence, Break even point = N = 2.06 units