Break-even analysis for a service company Sprint Nextel is one of the largest di

Question

Break-even analysis for a service company

Sprint Nextel is one of the largest digital wireless service providers in the United States. In a recent year, it had approximately 32.5 million direct subscribers (accounts) that generated revenue of $35,345 million. Costs and expenses for the year were as follows (in millions):

Cost of revenue $20,841

Selling, general, and administrative expenses 9,765

Depreciation 2,239

Assume that 70% of the cost of revenue and 30% of the selling, general, and administrative expenses are variable to the number of direct subscribers (accounts). In part (a) and (b), round all interim calculations and final answers to one decimal place.

a. What is Sprint Nextel's break-even number of accounts, using the data and assumptions given?

27.9

million accounts

b. How much revenue per account would be sufficient for Sprint Nextel to break even if the number of accounts remained constant?

$

941.7

million per account

Break-Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold 500,000 units at a price of $94 per unit during the current year. Its income statement is as follows:

Sales $47,000,000

Cost of goods sold 25,000,000

Gross profit $22,000,000

Expenses:

Selling expenses $4,000,000

Administrative expenses 3,000,000

Total expenses 7,000,000

Income from operations $15,000,000

The division of costs between variable and fixed is as follows:

Variable Fixed

Cost of goods sold 70% 30%

Selling expenses 75% 25%

Administrative expenses 50% 50%

Management is considering a plant expansion program for the following year that will permit an increase of $3,760,000 in yearly sales. The expansion will increase fixed costs by $1,800,000 but will not affect the relationship between sales and variable costs.

Required:

1. Determine the total variable costs and the total fixed costs for the current year.

Total variable costs $

22,000,000

Total fixed costs $

10,000,000

2. Determine (a) the unit variable cost and (b) the unit contribution margin for the current year.

Unit variable cost $

44

Unit contribution margin $

3. Compute the break-even sales (units) for the current year.

200,000

units

4. Compute the break-even sales (units) under the proposed program for the following year.

236,000

units

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $15,000,000 of income from operations that was earned in the current year.

536,000

units

6. Determine the maximum income from operations possible with the expanded plant.

$

7. If the proposal is accepted and sales remain at the current level, what will the income or loss from operations be for the following year?

$

Income

8. Based on the data given, would you recommend accepting the proposal?

In favor of the proposal because of the reduction in break-even point.

In favor of the proposal because of the possibility of increasing income from operations.

In favor of the proposal because of the increase in break-even point.

Reject the proposal because if future sales remain at the current level, the income from operations will increase.

Reject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales.

Choose the correct answer.

Explanation / Answer

Calculation of total variable expenses:
Variable cost of revenue = $20,841 x 70% = $14588.7 million
Variable selling, general and administrative expenses = $9,765 x 30% = $2,929.5
Total variable expenses = $17,518.2 million
Contribution = Revenue – Variable costs
Contribution = $35,345 – 17,518.2 = $17,826.8
Total fixed costs:
Fixed cost of revenue = $20,841 x 30% = $6,252.3 million
Fixed selling, general and administrative expenses = $9,765 x 70% = $6,835.5
Depreciation = $2,239
Total fixed expenses = $15,326.8

Contribution per account =17,826.8 / 32.5= $548.5
Break even number of accounts = 15,326.8 / 548.5 = 27.9 million

Part 2:
1. Total variable cost for the current year:
Cost of goods sold = 25,000,000 x 70% = $17,500,000
Selling expenses = 4,000,000 x 75% = $3,000,000
Administrative expenses = 3,000,000 x 50% = $1,500,000
Total variable expenses = $22,000,000
Total fixed expenses = (25,000,000 – 17,500,000) + (4,000,000 – 3,000,000) + (3,000,000 -1,500,000) = $10,000,000
2. Contribution = $47,000,000 – 22,000,000 = $25,000,000
Contribution margin ratio = 25,000,000 / 47,000,000 = 53.2%
Unit variable cost = 22,000,000 / 500,000 = $44
Unit contribution margin = $94 -44 = $50 per unit
3. Break even sales in units = 10,000,000 / 50 = 200,000 units
4. New fixed cost = 10,000,000 + 1,800,000 = $11,800,000
New Break even sales = 11,800,000 / 50 = 236,000 units
6. Maximum income from operations under expansion:
New sales = $47,000,000 + 3,760,000 = $50,760,000
In units = 50,760,000 / 94 = 540,000
New contribution = 540,000 x 50 = $27,000,000

Income from operations = 27,000,000 – 11,800,000 = $15,200,000
7. If sales remain at current level:
New Profit = Contribution – New fixed cost
New Profit = $25,000,000 – 11,800,000 = $13,200,000

8. In favor of the proposal because of the possibility of increasing income from operations.

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