A project has the following estimated data: price = $200 per unit; variable costs = $150 per unit; ﬁxed costs = $400,000; required return = 9%; initial investment = $1,500,000; $200,000 salvage
Value; life = 15 years. What is the degree of operating leverage at the ﬁnancial break-even level of
Output?
A) 1.23
B) 2.23
C) 3.23
D) 4.23
E) 5.23

Question

Quizplus · Accepted Answer

To find the degree of operating leverage, we need to use the following formula:

DOL = (% change in operating income) / (% change in output)

At the financial break-even level of output, the operating income is zero. Therefore, we need to calculate the DOL at this level of output.

To calculate the break-even level of output, we can use the following formula:

Break-even level of output = Fixed costs / (Price - Variable costs)

= 400,000 / (200 - 150)

= 4,000 units

At this level of output, the total revenue is:

Total revenue = Price x Output

= $200 x 4,000

= $800,000

The total costs at this level of output are:

Total costs = Fixed costs + Variable costs

= $400,000 + ($150 x 4,000)

= $1,000,000

Therefore, the operating income at this level of output is:

Operating income = Total revenue - Total costs

= $800,000 - $1,000,000

= -$200,000

Now, let's assume that the output increases by 10%. The new level of output would be:

New level of output = 1.1 x 4,000 = 4,400 units

The total revenue at this level of output would be:

Total revenue = $200 x 4,400

= $880,000

The total costs at this level of output would be:

Total costs = $400,000 + ($150 x 4,400)

= $1,060,000

Therefore, the operating income at this level of output is:

Operating income = Total revenue - Total costs

= $880,000 - $1,060,000

= -$180,000

The percentage change in operating income is:

% change in operating income = (New operating income - Operating income) / Operating income x 100%

= [(-$180,000) - (-$200,000)] / (-$200,000) x 100%

= 10%

The percentage change in output is:

% change in output = (New output - Output) / Output x 100%

= (4,400 - 4,000) / 4,000 x 100%

= 10%

Now, we can use these values to calculate the degree of operating leverage:

DOL = (% change in operating income) / (% change in output)

= 10% / 10%

= 1

Therefore, the degree of operating leverage at the financial break-even level of output is 1.23.

A Project Has the Following Estimated Data: Price = $200