Question

Hydro Systems Engineering Associates, Inc., provides consulting services to city water authorities. The consulting firm’s contribution-margin ratio is 30 percent, and its annual fixed expenses are $220,000. The firm’s income-tax rate is 45 percent. Required:

1. Calculate the firm’s break-even volume of service revenue.
2. How much before-tax income must the firm earn to make an after-tax net income of $128,000?
3. What level of revenue for consulting services must the firm generate to earn an after-tax net income of $128,000?
4. Suppose the firm’s income-tax rate changes to 35 percent. What will happen to the break-even level of consulting service revenue?

Answer 1

Answer:

1) the break even point = total fixed costs / contribution margin = $220,000 / 30% = $733,333.33

2) net income after taxes = before tax income x (1 - tax rate)

$128,000 = before tax income x (1 - 45%)

$128,000 = before tax income x 55%

before tax income = $128,000 / 55% = $232,727.27

3) when total revenue = $733,333.33, net income = $0

so we must add $232,727.27 of contribution margin to $733,333.33:

contribution margin = revenue x 30%

revenue = $232,727.27 / 30% = $775,757.58

total revenue = break even + additional revenue = $733,333.33 + $775,757.58 = $1,509,090.91

4) will remain the same, income tax rate only taxes net income, and at the break even level net income = $0

Answer 2

Hydro Systems Engineering Associates, Inc., provides consulting services to city water authorities is :

1. The firm’s break-even volume of service revenue is $733,333.33.
2. The before-tax income must the firm earn to make an after-tax net income is $232,727.27
3. The level of revenue for consulting services must the firm generate to earn an after-tax net income of $128,000 is $1,509,090.91.
4. The break-even level of consulting service revenue is zero.

"Revenue"

Answer 1)

The firm’s break-even volume of service revenue is :

Break even point = total fixed costs / contribution margin

Break even point = $220,000 / 30%

Break even point = $733,333.33

Answer 2)

The before-tax income must the firm earn to make an after-tax net income is :

Net income after taxes = before tax income x (1 - tax rate)$128,000 before tax income * (1 - 45%)$128,000

before tax income x 55%

before tax income = $128,000 / 55%

before tax income= $232,727.27

Answer 3)

The level of revenue for consulting services must the firm generate to earn an after-tax net income of $128,000 is :

Total revenue = $733,333.33

Net income = $0

Add : $232,727.27 of contribution margin to $733,333.33:

contribution margin = revenue x 30%

revenue = $232,727.27 / 30%

revenue = $775,757.58

Total revenue = break even + additional revenue

Total revenue = $733,333.33 + $775,757.58

Total revenue= $1,509,090.91

Answer 4)

The break-even level of consulting service revenue is :

Revenue will remain the same,

Income tax rate only taxes net income.

Break even level net income = $0

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