Question

Rotelco is one of the largest digital wireless service providers in the United States. In a recent year, it had approximately 100 million direct subscribers (accounts) that generated revenue of $31,100 million. Costs and expenses for the year were as follows:

Cost of revenue	$14,600
Selling, general, and administrative expenses	10,000
Depreciation	3,400

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).

a. What is Rotelco's break-even number of accounts, using the data and assumptions above? Round to the nearest whole number.
million accounts

b. How much revenue per account would be sufficient for Rotelco to break even if the number of accounts remained constant? Round to the nearest dollar.
$ million per account

Answer 1

Solution:

Meaning Of Break Even Point: Break Even Point is the point at which total Sales Revenue is equal to total Costs. Means the point at which there will be no profit or no loss. It can be calculated in both number of units and dollar value.

Total Cost = Direct Material cost + Direct labor cost + Manufacturing overhead cost + selling and administration expenses.

Explaination :

1. Calculation of Total Contribution Margin:

Contribution Margin = Sales Revenue - Variable costs

= $31,100 - ( 70% x Cost of Revenue + 30% x selling, general and administrative expenses)

= $31,100 - ( 70% x $14,600 + 20% x $10,000)

= $31,100 - ( $10,220 + $2,000 )

= $31,100 - $12,220

= $18,880

2. Calculation of Contribution Margin per unit: (Number of Accounts in Million)

Contribution Margin per unit = Total Contribution Margin / Number of Direct Subscribers (accounts )

= $18,880 / 100 Million

=$188.80 per million accounts.

3. Calculation of Contribution Margin Ratio:

Contribution Margin Ratio = Total Contribution Margin / Sales Revenue

= $18,880 / $31,100

= $0.6070 or say $0.61

4. Calculation of Total Fixed Cost:

= Depreciation + ( 30% x cost of revenue + 70% x selling ,general and administrative expenses )

= $3,400 + ( 30% x $14,600 + 70% x $10,000 )

= $3,400 + ( $4,380 + $7,000 )

= $3,400 + $11,380

= $14,780

Answer (A) : Rotelco's Break Even Number of Accounts:

Break Even Point (In Units) = Total Fixed Cost / Contribution Margin per million account

= $14,780 / 188.80

= $78.28

or say $79

Answer (B): Revenue per account of Rotelco to Break Even:

= Total Fixed Cost / (Contribution Margin Ratio x Number of subscribers in million)

= $14,780 / (0.61 x 100 )

= $14,780 / 61

= $242.295

or say $242