EX 21-16 Break-even analysis

Sprint Nextel is one of the largest digital wireless service providers in the United States. In a recent year, it had approximately 33.3 million direct subscribers (accounts) that generated revenue of $32,563 million. Costs and expenses for the year were as follows (in millions):


Cost of revenue $17,492
Selling, general, and administrative expenses 9,418
Depreciation 5,074



Assume that 75% of the cost of revenue and 25% of the selling, general, and administrative expenses are variable to the number of direct subscribers (accounts).

a. What is Sprint Nextel’s break-even number of accounts, using the data and assumptions above? Round units (accounts) and per-account amounts to one decimal place.
b. How much revenue per account would be sufficient for Sprint Nextel to break even if the number of accounts remained constant?


Answer:

Fixed Costs
a. Break-Even = Revenue per Account – Variable Cost per Account
$16,510.5 million 3
Break-Even = $977.91 – $464.7 2
Break-Even = 32.2 million (rounded) accounts
1 Revenue per account (in millions):
$32,563 million ÷ 33.3 million = $977.9 (rounded)
2 Variable cost per account (in millions, except variable cost per account):
Cost of revenue……………………………………………… $17,492 × 75% = $13,119.0
Selling, general, and administrative expenses………… 9,418 × 25% = 2,354.5
Total variable cost…………………………………………… $15,473.5
Divided by number of accounts…………………………… ÷ 33.3
Variable cost per account (rounded)……………………… $ 464.7
3 Fixed costs (in millions):
Cost of revenue……………………………………………… $17,492 × 25% = $ 4,373.0
Selling, general, and administrative expenses………… 9,418 × 75% = 7,063.5
Depreciation…………………………………………………… 5,074 × 100% = 5,074.0
Total fixed costs……………………………………………… $16,510.5
b. Break-Even = Fixed Cost
Revenue per Account – Variable Cost per Account
33.3 million accounts = $16,510.5 million
X – $464.7
33.3X – $15,474.5 =
33.3X =
X =
$16,510.5 million
$31,985.0
$960.5 (rounded)