# Break Even And Leverage Analysis

__Illustration 57__

Let us assume a Magazine publishing company. The aggregate fixed cost occurred is $10,000. Variable Cost occurred per magazine copy on printing paper, royalty etc. is equal to $10 per copy. Presume if the magazine is fixed $20 per copy, what is the break even number of copies of the magazine printed and sold?

__Solution__

It is unambiguous from the problem that the

Total Fixed Cost = $10,000

Average Variable Cost = $10

Price Fixed per copy = $20

Break Even Volume = __ TFC __

P – AVC

VB = __10000__

20 – 10

**= 1000
Copies**

**Therefore, 1000 copies of the magazine denote the break even productivity and
sales of the magazine. That is if the publisher manufactures and is capable to
sell 1000 copies, he will accomplish no profits no loss condition.**

__Illustration 58__

If for instance let us assume a mobile manufacturing company estimates to sell less than 500 mobiles a week, which will incur loss. Consequently, the manufacturer may regard cutting manufacturing costs and reducing advertising expenses etc so as to break even or even accomplish some profits. Also he may fix higher prices to set right the loss incurred.

Now in the event if he fixes prices equal to $7000 per mobile, his costs such as Total Fixed cost to $1,000,000 and Average Variable cost to $5000 and sells, compute the new break even sales of the mobile.

__Solution__

Break Even Volume of Sales

V’B = __ TFC __

P’ – AVC

= __ 1,000,000 __

7000 – 5000

**= 500
mobiles**

**Now, the mobile units to be sold are 500 which as per the mobile manufacturer
will have no profit no loss condition.**

__Illustration 59__

Presume the magazine publishing company has a profit aim of making $20000 from the magazines, then compute the necessary volume of sales to realise the target amount of profits of $20000. All the other costs as in the illustration 57; i.e. TFC = 10000, AVC = 10 and price per magazine be $20.

__Solution__

__TFC
+ π__

P – AVC

= __10000
+ 20000__

20 – 10

**= 30000
/ 10 = 3000
Copies.**

**Thus, if the publisher is able to sell 3000 copies, he will gain back the total
fixed cost and average variable costs along with accomplishing profits of $20000.
His profits will become more if his sales surpass 3000 copies.**

__Illustration 60__

Compute the degree of Operating Leverage from our above illustration of obtaining level of productivity necessary to yield a target amount of profits. In our case the fixed cost is $10000, price as $20 and AVC as $10 and the degree of productivity necessary to gain back fixed cost and provide for profits of $20000 was obtained to be 3000 copies.

Now with this information, ascertain the degree of operating leverage.

__Solution__

Degree of Operating Leverage is computed with the following formula.

DOL = __ Q
(P - AVC) __

Q
(P – AVC) – TFC

Here, Q = 3000
copies

= __ 3000
(20 – 10) __

3000
(20 – 10) – 10000

= __30000__ = **1.5**

20000

**Now, if the industry becomes more highly leveraged, the total fixed cost will
enhance and average variable cost will decrease consequents in huger productivity
to gain back fixed cost and to capitulate besieged profits. This will tend to the
greater degree of operating leverage DOL.**

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**Other topics under Theory of Production and Cost analysis:**

- Concept of Cost
- Cost Volume Profit Analysis for Accomplishing Target Profits
- Elasticity of Supply and Its Function
- Establishment of Cost Function Analysis
- Establishment of Short Run Cost Function
- Estimation of Returns To Scale
- Isoquants, Equal Product Curves
- Linearity Assumptions and Choice of Product and Process
- Long Run average Cost Curve
- Optimum Input Combination
- Production Function with Two Variable Inputs
- Short Run Cost Function
- Survival Technique
- Theory of Production - Returns to One Variable Factor