Clarke Ltd produces a single product - Leaving Cert Accounting - Question 8 - 2017

The break-even point (BEP) can be calculated using the formula:

ext{BEP} = rac{ ext{Fixed Costs}}{ ext{Contribution per Unit}}

First, we need the contribution per unit. Contribution is calculated as:

• Selling Price per Unit - Variable Cost per Unit
• Selling Price (60,000 units) = €1,320,000 / 60,000 = €22
• Variable Costs = Direct Materials + Direct Labour + Variable Factory Overheads = €270,000 + €207,000 + (€3 * 60,000) = €270,000 + €207,000 + €180,000 = €657,000
• Thus, Variable Cost per unit = €657,000 / 60,000 = €10.95
• Contribution per unit = €22 - €10.95 = €11.05

Now substituting values into the BEP calculation:

Total Fixed Costs = Administration Expenses + Selling Expenses + Fixed Factory Overheads = €101,250 + €82,500 + €60,000 = €243,750.

Thus,

ightarrow 22,036 ext{ units (approx.)}$$ To find the Margin of Safety (MOS): $$ ext{MOS} = ext{Actual Output} - ext{BEP} = 60,000 - 22,036 = 37,964 ext{ units}$$.

Let the number of units to be sold be denoted as N.

The required sales revenue for a profit of 10% can be defined as:

$ext{Sales Revenue} = 25N$ And the desired profit is:

Profit = 0.10 × Sales Revenue = 0.10 × 25N = 2.5N.

Consider variable costs (excluding sales commission) with:

• Variable cost per unit (excluding sales commission): €10.95 + 5% sales commission of Sales (which is €1.25).

Therefore, we can represent Sales as:

Sales = Variable Costs + Fixed Costs + Profit

• $25N = 10.95N + 177,750 + 2.5N$

Rearranging gives us:

$N = 17,258 ext{ units}$.

Let the selling price be denoted as S. The fixed costs are expected to increase by 12%, making them:

• New Fixed Costs = 60,000 + (0.12 × 60,000) = €67,200.

To maintain the same volume and profit, we must ensure:

$ext{Sales} = ext{Variable Costs} + ext{New Fixed Costs} + ext{Profit}$ Given that the sales volume remains 60,000 units:

$60,000S = (60,000 imes 10.95) + 67,200 + 419,250$

Solving for S, we find:

S = rac{(657,000 + 67,200 + 419,250)}{60,000} = €22.37.

To: Manager of Clarke Ltd

Subject: Recommendations Based on Market Research

Dear Manager,

After analyzing the current financial position and potential options for improving profitability, here are my recommendations:

1. Option 1: Reducing the selling price by 10% and increasing sales volume by 20% could attract more customers. However, while this option may increase volume, it significantly reduces profitability per sale. The net profit is estimated to decrease.

2. Option 2: Investing €40,000 in a new packaging design will increase the variable cost per unit by €2, yet could sustain the current sales volume and achieve a net profit increase.

Given that Option 2 generates an additional profit of €141,080 over Option 1, I recommend pursuing this option to maintain current sales revenues while enhancing profitability.

Best Regards, [Your Name]

Sensitivity Analysis is a financial modeling tool used to predict how different variables affect a given outcome under a specific set of assumptions. It is often framed as a 'what if' analysis and involves changing one key variable at a time to assess its impact on project viability or profit margins. The primary variables that are commonly analyzed include:

1. Selling price
2. Sales volume
3. Fixed costs

This helps management understand potential risks and the level of uncertainty in financial forecasts.