Consider the case of the Cast Iron Company. On each nondelinquent sale, Cast Iro
ID: 2793645 • Letter: C
Question
Consider the case of the Cast Iron Company. On each nondelinquent sale, Cast Iron receives revenues with a present value of $1,230 and incurs costs with a present value of $1,000. Cast Iron’s costs have increased from $1,000 to $1,080. Assuming that there is no possibility of repeat orders and that the probability of successful collection from the customer is p = 0.95, answer the following.
a-1. What is the expected profit of granting credit? (Do not round intermediate calculations.)
a-2. Should Cast Iron grant or refuse credit?
Grant
Refuse
b. What is the break-even probability of collection? (Enter your answer as a percent rounded to 1 decimal place.)
Explanation / Answer
a-1 Expected profit will be profit if collection is successful plus loss if collection is unsuccessful multiplied by their respective probabilities -
Profit if successful = $1230 - $1080 = $150
Loss if unsuccessful = (-)$1080
Expected profit = $150 x 0.95 + (-$1080 x 0.05) = $88.50
b) Since expected profit is positive, the company should grant credit.
c) Let probability of success be p. Then, probability of no success would be (1 - p). For break even, the expected profit should be zero. So, we have -
Expected Profit = 0
or, $150 x p + (- $1080) x (1 - p) = 0
or, $150p - $1080 + $1080p = 0
or, $1230p = $1080
or, p = 0.87804878048 or 0.88
Therefore, break-even probability of collection is 0.88.