Your company is considering granting credit to a new customer. The price per unit is $165 and the variable cost per unit is $150. The monthly interest rate is 0.8%. The customer will pay in 30 days if he does not default. If the customer does not default, he will buy one unit every month forever. What is the break-even default percent?
A) 3.7%
B) 8.0%
C) 61.5%
D) 88.0%
E) 92.0%

Question

Quizplus · Accepted Answer

The break-even default percent can be calculated using the formula for the present value of a perpetuity: $PV = \frac{C}{r}$, where $PV$ is the present value, $C$ is the cash flow per period, and $r$ is the interest rate per period. Here, the cash flow per period ($C$) is the profit per unit, which is the selling price minus the variable cost ($165 - $150 = $15). The monthly interest rate ($r$) is 0.8%, or 0.008 in decimal form.First, calculate the present value of the perpetuity if the customer does not default: $PV = \frac{15}{0.008} = \$1875$.This present value represents the total value of all future profits from selling one unit per month forever at a profit of $15 per unit, discounted at the monthly interest rate of 0.8%.To find the break-even default percent, we need to determine what percentage of this present value can be lost to defaults before the deal becomes unprofitable. Since the cost to the company for each unit (if the customer defaults) is the variable cost of $150, the break-even point is when the loss equals the present value of the profits.The break-even default percent is calculated as the ratio of the variable cost per unit to the present value of the perpetuity: $\frac{150}{1875} = 0.08$ or 8%.However, this calculation seems to have been misunderstood in the context of the provided options, suggesting a mistake in the calculation process. Given the options and the correct approach to calculate the break-even default percent based on the provided formula and logic, the correct answer should reflect the proportion of the transaction that can be lost to defaults before the deal becomes unprofitable, considering the profit margin and the interest rate. The mistake in the calculation above indicates a reevaluation is necessary, focusing on the correct interpretation of the perpetuity value and the impact of defaults on it. Given the options and the typical approach to such financial calculations, the correct answer should align with the principles of financial analysis, but the provided calculation does not accurately lead to any of the given options directly. The correct approach involves assessing the net present value of the cash flows and determining the default rate at which the net present value would be zero, considering the profit per unit and the cost of capital. However, without the precise recalculated figures based on the correct formula application, the selection provided earlier was incorrect. The correct interpretation involves a deeper financial analysis, potentially incorporating the expected loss due to defaults and its impact on the net present value of the future cash flows.

Your Company Is Considering Granting Credit to a New Customer