Exercise-1 (Target profit analysis, break-even point)

By: Rashid Javed | Updated on: September 8th, 2022

PNG electric company manufactures a number of electric products. Rechargeable light is one of the PNG’s products that sells for $180/unit. Total fixed expenses related to rechargeable electric light are $270,000 per month and variable expenses involved in manufacturing this product are $126 per unit. Monthly sales are 8,000 rechargeable lights.

Required:

  1. Compute break-even point of the company in dollars and units.
  2. According to a research conducted by sales department, a 10% reduction in sales price will result in 25% increase in unit sale. Prepare two income statements in contribution margin format, one using the current price and one using proposed price (10% below the old sales price).
  3. Compute the number of rechargeable lights to be sold to earn a net operating income of $189,000 per month (use original data).

Solution:

(1). Computation of break-even point:

a. Break even point in units:

Break even point in units can be computed by using either equation method or contribution margin method. Both the methods are given below:

i. Equation method:

Sales = Variable expenses + Fixed expenses
$180Q = $126Q + 270,000
$180Q – $126Q = $270,000
$54Q = $270,000
Q = $270,000/$54
Q = 5,000 Units

ii. Contribution margin method:

Break even point = Fixed expenses/Contribution margin per unit
270,000 / 54*
= 5,000 units

*$180 – $126

b. Break-even point in dollars:

Break-even point in dollars can be computed by multiplying break-even point in units by sales price per unit as shown below:

5,000 units × $180

=$900,000

(2) Income statements:

a. Income statement under current operations:

exercise-1-cvapr-img1

b. Income statement under proposed operations:

exercise-1-cvapr-img2

The proposal should not be accepted because it will reduce the contribution margin from $54 per unit to $36 per unit and net operating income from $162,000 to $90,000.

(3) Target profit analysis:

a. Equation method:

Sales = Variable expenses + Fixed expenses + Profit
$180Q = $126Q + 270,000 + $189,000
$180Q – $126Q = $459,000
$54Q = $459,000
Q = $459,000 / $54
Q = 8,500 Units

b. Contribution margin method:

(Fixed expenses + Target income)/Contribution margin per unit
= ($270,000+$189,000)/54
= 8,500 units

On the basis of original data, company needs to sell 8,500 rechargeable lights to earn a profit of $189,000.

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