Question

The Branding Iron Company selis its irons for $70 apiece wholesale. Production cost is $60 per iron. There is a 25% chance that

a. prospective customer will go bankrupt within the next half-year. The customer orders 1,000 irons and asks for 6 monthis' credit. Assume the discount rate is 7% per year, there is no chance of a repeat order, and the customer will either pay in full or not pay at ail, 0. Calculate the expected profit for the order. (A negntive amount should be indicoted by a minus sign. Do not round intermediate colculations. Round your onswer to 2 decimal ploces.)
b. Should the order be accepted? Yes

Answer 1

The expected profit is calculated by taking into account the profit per unit, the probability of the customer paying, the number of units ordered, and discounting the profit for the credit period. The example deals with expected profit under uncertainty and incorporates the relevant risks and time value of money.

Step-by-step explanation:

The expected profit for the Branding Iron Company's order with the customer can be calculated by considering the probabilities of the customer's payment and bankruptcy risk along with the discount rate. The profit per unit is the difference between the selling price and the cost to produce, which is $70 - $60 = $10. With a 25% chance of bankruptcy, there is a 75% chance the customer will pay. Thus, the expected profit is the profit per unit multiplied by the number of units and the probability of payment, discounted by the discount rate for the six-month period.

The expected profit (EP) can be expressed as EP = (Probability of payment * Number of units * Profit per unit) / (1 + Discount rate)Period, where Period is half a year or 0.5 in this case.

We would also consider whether the expected profit outweighs the risk of non-payment and if the profit margin justifies extending a credit line. Without factoring in the 25% bankruptcy risk, the nominal profit would be 1,000 units * $10 = $10,000. However, with the potential for bankruptcy, the expected profit would reduce to 75% * $10,000, and we would then apply a half-year discount at a 7% annual rate.