A selling firm is taxable and wants to evaluate a credit applicant via the one-period, after-tax, net present-value approach. The appropriate discount rate for expected future flows is 10 percent per year. If the applicant does not pay in the normal course of business, it is expected that the applicant will be liquidated. The liquidation process will take two years, and trade creditors are expected to experience a 50 percent recovery rate, though the average recovery by the seller in such cases is 20 percent. If the applicant does not default, it is expected that payment will be received in 90 days. Based on a failure-forecasting function estimated with equal sample
sizes of defaulted and non defaulted firms, a probability of default of 80 percent for the applicant has been computed. However, only 1 percent of applicants actually default. The seller is in the 35 percent tax bracket, and the order amount is $30,000. The tax cost of the inventory to service the order will be $27.000, although the actual out-of-pocket cost to replenish inventory when the order is shipped will be only $26,000. Use a 360-day year.

a. Calculate the expected net present value of the sale if the firm accrues a reserve for bad debt based on average loss rates.

b. Calculate the expected net present value of the sale if the firm does not accrue a reserve, but instead writes off bad debts as they occur.