Page 89 - DMGT501_OPERATIONS_MANAGEMENT

Unit 3: Capacity Planning

Profit = P*Q – V *Q – F = (P – V) – Q – F Notes
Where, P is the Selling price per unit
V is the Variable cost per unit
(P – V) is the Contribution margin per unit
Q is the Quantity of product sold (units of goods or services)
F is the Total fixed costs
We use the profit equation to plan for different volumes of operations. CVP analysis can be
performed using either:
1. Units (quantity) of product sold
2. Revenues (in Rupees)

3.9.1 CVP Analysis in Units

We begin with the preceding profit equation. Assuming that fixed costs remain constant, we
solve for the expected quantity of goods or services that must be sold to achieve a target level of
profit.
Profit equation: Profit = (P – V) – Q – F
Solving for Q: Q = F + Profit/P – V = Quantity (units) required to obtain target profit

We must note that the denominator in this formula, (P – V), is the contribution margin per unit.

Example: Suppose that a shirt manufacturer ABC Apparels wants to produce a new
warm feel shirt and has forecast the following information.
Price per shirt = 800
Variable cost per shirt = 300
Fixed costs related to shirt production = 5,500,000
Target profit = 200,000

Estimated sales = 12,000 shirts
We determine the quantity of shirts needed for the target profit as follows:
Quantity = (5,500,000 + 200,000) / (800 – 300) = 11,400 shirts

3.9.2 CVP Analysis in Revenue

The Contribution Margin Ratio (CMR) is the percent by which the selling price (or revenue) per
unit exceeds the variable cost per unit, or contribution margin as a percent of revenue. For a
single product, it is
CMR = P – V / P

To analyze CVP in terms of total revenue instead of units, we substitute the contribution margin
ratio for the contribution margin per unit. We rewrite the equation to solve for the total amount
of revenue we need to cover fixed costs and achieve our target profit as:
Revenue = F + Profit/[(P – V)/ P] = F + Profit / CMR

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