# Break-even Analysis Form

BREAK-EVEN ANALYSIS - 6

3

Proof: Using the definition of Total Profit (

A

) we can take the partial derivative of it with

respect to output:

M

A

/

M

Q =

M

(TR

!

TVC

!

TFC)/

M

Q. Since TFC is a constant (its

derivative is thus zero), we obtain

M

A

/

M

Q =

M

(TR

!

TVC)/

M

Q. Now, if P and Q do not

change with Q, this would become M

A

/MQ = (P ! AVC)(MQ/MQ) = P ! AVC. This simply

says that for an unit increase in output, profit will increase by an amount equal to the

difference between price and average variable cost. Substituting

M

A

/

M

Q = P

!

AVC back

into the definition of DOL (= (Q/

A

)(

M

A

/

M

Q)) and simplifying, we get the boxed property

given above.

4

Proof: Using, say, the definition DOL = (TR

!

TVC)/(TR

!

TC)] above, we take the

partial derivative of DOL with respect to AVC, obtaining: M(DOL)/M(TVC) = ! 1/(TR !

TC) which is clearly negative if the firm is making profit. Indeed, since Q is a constant, we

can rewrite this as M(DOL)/M(AVC) = ! Q/(P ! ATC) < 0.

DOL

TFC

Profit

TR TVC

TR TC

TR TVC

TR TVC TFC

= =

−

−

=

−

− −

are constant), it can be readily derived that:

3

(3)

Several conclusions can be drawn:

(1) The DOL generally depends on the output level, and is equal to zero at the profit-

maximizing output (because M

A

/MQ = 0 at that point)

(2) The DOL is negative (positive) below (above) the break-even level. Equation (3)

also yields an interesting result:

! Rule: For the same total cost, the Degree of Operating Leverage increases with fixed

costs and decreases with variable costs.

4

(3) Consider 2 (almost identical) plants, except that

Plant A (capital intensive): low fixed costs, high variable costs

Plant B (labor intensive) high fixed costs, low variable costs

Since fixed costs are outlays already made, if the firm chooses to built Plant A

instead of B, it can be said that the firm “gets more leverage” out of the resources

it already has.

(4) A plant with high fixed costs and low variable costs will also have a higher break-

even point than a plant with low fixed costs and high variable costs.

The significance of this relationship is that a firm with large fixed costs usually

breaks even at a higher output level. However, this firm’s DOL is also higher, its

profits rises at a relatively high rate when production rises above break-even.

Likewise, its profits declines more quickly during economic downturns, and the firm

would become unprofitable at a relatively large output quantity (since the break-even

Page 6/16

Free Download

## Break-even Analysis Form PDF

Favor this template? Just fancy it by voting!

(0 Votes)

0.0

Related Forms

39 Page(s) | 6415 Views | 32 Downloads