Profit Analysis of Delivery Services | CFA Level 1 Exam | Test Prep

Weighted Mean Profit per Delivery

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Question

A bottling company offers three kinds of delivery services-instant, same day and within five days. The profit per delivery varies according to the kind of delivery.

The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plan.

To find out what effect each type of delivery has on the profit picture, the company has made the following tabulation based on deliveries for the previous quarter.

Type of Number of Deliveries Profit per Delivery

Delivery During the Quarter -

Instant 100 $70 -

Same day 60 $100 -

Within five days 40 $160 -

What is the weighted mean profit per delivery?

Answers

Explanations

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A. B. C. D. E.

A

(100*70)+(60*100)+(40*160) = 1940. Mean is 1940/200 = 97

To find the weighted mean profit per delivery, we need to calculate the average profit per delivery taking into account the number of deliveries for each type.

The formula for calculating the weighted mean is:

Weighted Mean = (Sum of (Weight * Value)) / Total Weight

In this case, the value represents the profit per delivery, and the weight represents the number of deliveries.

Let's calculate the weighted mean profit per delivery step by step:

  1. Calculate the total profit for each type of delivery:

    • Instant: 100 deliveries * $70 profit per delivery = $7,000 total profit
    • Same day: 60 deliveries * $100 profit per delivery = $6,000 total profit
    • Within five days: 40 deliveries * $160 profit per delivery = $6,400 total profit

  2. Calculate the total number of deliveries: Total deliveries = 100 + 60 + 40 = 200

  3. Calculate the weighted mean profit per delivery using the formula: Weighted Mean = (Sum of (Weight * Value)) / Total Weight Weighted Mean = (($7,000 * 100) + ($6,000 * 60) + ($6,400 * 40)) / 200 Weighted Mean = ($700,000 + $360,000 + $256,000) / 200 Weighted Mean = $1,316,000 / 200 Weighted Mean = $6,580

Therefore, the weighted mean profit per delivery is $6,580.

None of the provided answers (A, B, C, D, E) match the calculated value, so it seems there may be an error in the answer options or a mistake in the calculation.

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