Question

Cast Iron Company, on each nondelinquent sale, receives revenues with a present value of $1,210 and incurs costs with a value of $1,055. 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 0.81. But if the payment is made, the probability that the customer will pay for the second order is 0.96.

a. Calculate the minimum probability at which credit can be extended assuming there is no possibility of repeat orders. (Enter your answer as a percent rounded to 1 decimal place.)

b. If it costs $12.25 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.)

Answer 1

Casse 1 Payment is made

Probability = p

Profit = P1 = Revenue - cost

  = $1210 - $1055

= $155

Case 2 Payment is not made

Probability = 1 - p

Profit = P2 = Revenue - cost

= 0 - $1055

= - $1055

Part (a)

Expected profit = p x P1 + (1 - p) x P2

= p x $155 + (1 - p) x (-$1055)

=$1210p - $1055

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, $1210p - $1055 =

Hence, The Minimum Probability, p = $1055 / $1210 = 87.19%

Part (b)

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

Expected profit = $1,210p - $1,055

p = 0.96 for the Secound Order

Hence, expected profit = $1,210 x 0.94 - $1,055 = $82.40

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 82.40 x N = 12.25

Hence, N = 12.25 / (82.40 x 0.04) =3.717

Hence, Break even point = N = 3.72 units