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

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 the break-even point of PNG in both 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:

The equation to calculate break even point is:

SpQ = VeQ + Fe

Where;

• Sp = Sales price per unit.
• Q = Number (or quantity) of units to be manufactured and sold during the period.
• Ve = Variable expenses to manufacture and sell a single unit of product.
• Fe = Total fixed expenses for the period.

Let’s apply this equation to calculate the break even point of PNG.

SpQ = VeQ + Fe
\$180Q = \$126Q + 270,000
\$180Q – \$126Q = \$270,000
\$54Q = \$270,000
Q = \$270,000/\$54
Q = 5,000 units

PNG needs to sell 5,000 units to break even.

Alternatively, we can obtain the same answer by using the contribution margin method as follows:

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 simply multiplying the break even point in units by the sales price per unit as shown below:

Break even point in dollars = BEP in units × Sales price per unit
= 5,000 units × \$180
=\$900,000

### (2) Income statements:

#### b. Income statement under proposed operations:

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:

The equation to calculate the number of units to be sold to generate a target profit is:

SpQ = VeQ + Fe + Tp

Where;

Sp = Sales price per unit.
Q = Number (quantity) of units to be manufactured and sold during the period.
Ve = Variable expenses to manufacture and sell a single unit of product.
Fe = Total fixed expenses for the period.
Tp = Target profit for the period.

Let’s apply this equation to calculate the number of units to be sold to earn a profit of \$189,000.

SpQ = VeQ + Fe + Tp
\$180Q = \$126Q + 270,000 + \$189,000
\$180Q – \$126Q = \$459,000
\$54Q = \$459,000
Q = \$459,000/\$54
Q = 8,500 units

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

Alternatively, we can obtain the same answer by applying the contribution margin method as follows:

#### b. Contribution margin method:

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

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