Final answer:
The average nondiscounted gross profit during a customer's lifetime at Troista Mobile Accessories is an idealized $576, calculated by assuming a 60% gross margin on an annual spending of $240 and a 75% customer retention rate.
Step-by-step explanation:
To calculate the average nondiscounted gross profit during a customer's lifetime for Troista Mobile Accessories, we first need to find the yearly gross profit per customer. Given that a customer spends $12 on average per visit and visits the website 20 times each year, the total annual spending is $12 × 20 = $240. Troista makes a margin of 60%, so the annual gross profit from one customer is $240 × 0.60 = $144.
Next, we consider customer retention. With a 25% customer attrition rate yearly, the remaining customer retention rate is 75%. We can use the formula for the sum of a geometric series to find the lifetime value, S = a / (1 - r), where 'a' is the first term (annual gross profit) and 'r' is the common ratio (retention rate). Therefore, the lifetime gross profit is $144 / (1 - 0.75) = $576.
However, since we are looking for the average lifetime gross profit, and given that not all customers will stay for an infinite amount of years, this calculation is an idealized maximum average. In a practical sense, the calculation can vary widely based on the number of years a customer stays with the company. For accurate business planning, this simple model could be adjusted to take into account the actual average customer lifespan based on historical data.