Home Accounting Cost Analysis: Managerial and Cost Accounting

# Per Unit Revenue Shifts

Thus far, the discussion has focused on cost structure and changes to that structure. Another approach to changing the contribution margin is via changes in per unit selling prices. So long as these adjustments are made without impacting fixed costs, the results can be dramatic. Let's return to Leaping Lemming, and see how a 10% increase in sales price would impact the contribution margin and profitability for 20X2.

Notice that this 10% increase in price results in a doubling of the contribution margin and a tripling of the net income. Bingo: the solution to increasing profits is to raise prices while maintaining the existing cost structure - if it were only this easy! Customers are sensitive to pricing and even a small increase can drive customers to competitors. Before raising prices, a company must consider the "price elasticity" of demand for its product. This is fancy jargon to describe the simple reality that demand for a product will drop as its price rises.

So, the real question for Leaping Lemming is to assess how much volume drop can be absorbed when prices are increased. The appropriate analysis requires dividing the continuing fixed costs (plus target or current net income) by the revised unit contribution margin; this results in the required sales (in units) to maintain the current level of profitability. For Lemming to achieve a \$500,000 profit level at the revised pricing level, it would need to sell 5,000 units:

Units to Achieve a Target Income (Total Fixed Costs + Target Income) / Contribution Margin Per Unit 5,000 Units = (\$500,000 + \$500,000) / \$200

If Lemming sells at least 5,000 units at \$1,100 per unit, it will make at least as much as it would by selling 10,000 units at \$1,000 per unit. The unknown is what customer response will be to the \$1,100 pricing decision. Many a business has fallen prey to the presumption that they could raise prices with impunity; others have scored homeruns by getting away with such increases.

# Margin Beware

Some contracts provide for "cost plus" pricing, or similar arrangements that seek to provide the seller with an assured margin. These agreements are intended to allow the seller a normal and fair profit margin, and no more. However, they can have unintended consequences. Let's evaluate an example. Pioneer Plastics sells trash bags to Heap Compacting Service. Heap and Pioneer have entered into an agreement that provides Pioneer with a contribution margin of 20% on 1,000,000 bags.

Originally, the bags were anticipated to cost Pioneer \$1 each to produce, plus a fixed cost of \$100,000. However, increases in petroleum products necessary to produce the bags skyrocketed, and Pioneer's variable production cost was actually \$3 per unit. Let's see how Pioneer faired under their agreement:

 \$1 Scenario \$3 scenario Sales \$ 1,250,000 \$ 3,750,000 Variable costs (1,000,000 X \$1 vs. \$3) 1,000,000 3,000,000 Contribution margin (20% ofsales) \$ 250,000 \$ 750,000 Fixed costs 100,000 100,000 Net income \$ 150000 \$ 650 000

Notice the astounding change in Pioneer's net income - \$150,000 versus \$650,000. Such "cost plus" agreements must be carefully constructed, else the seller has little incentive to do anything but let costs creep up. Sometimes you will hear a company complain about cost increases negatively affecting their "margins;" before you assume the worst, take a closer look to see how the bottom line is being impacted. Even if Pioneer agreed to cut Heap a break and reduce their margin in half, their bottom line profit would still soar in the illustration.

# Margin Mathematics

In the preceding illustration, the contribution margin was 20% of sales. Accordingly, variable costs are 80% of sales. If total variable costs are \$1,000,000, then sales would be \$1,250,000 (\$1,000,000 divided by 0.80).

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