problem: a small coffee - shop sells iced coffee at ₱120 per cup. the variable cost per cup (coffee, ice…

problem: a small coffee - shop sells iced coffee at ₱120 per cup. the variable cost per cup (coffee, ice, cup, straw) is ₱45, while monthly rent, utilities, and staff salaries total ₱75,000 fixed costs. the owner wants to earn ₱45,000 net profit per month, and the income is taxed at 25%. question: how many cups of iced coffee must the shop sell each month to meet the target after - tax profit?

problem: a small coffee - shop sells iced coffee at ₱120 per cup. the variable cost per cup (coffee, ice, cup, straw) is ₱45, while monthly rent, utilities, and staff salaries total ₱75,000 fixed costs. the owner wants to earn ₱45,000 net profit per month, and the income is taxed at 25%. question: how many cups of iced coffee must the shop sell each month to meet the target after - tax profit?

Answer

Explanation:

Step1: Calculate pre - tax profit

The after - tax profit is $45000$ and the tax rate is $25%$. Let the pre - tax profit be $x$. Then $(1 - 0.25)x=45000$. Solving for $x$, we get $x=\frac{45000}{1 - 0.25}=\frac{45000}{0.75}=60000$.

Step2: Calculate total contribution margin needed

The fixed costs are $75000$. The total contribution margin needed is the sum of the fixed costs and the pre - tax profit. So, the total contribution margin $C = 75000+60000 = 135000$.

Step3: Calculate contribution margin per cup

The selling price per cup is $120$ and the variable cost per cup is $45$. The contribution margin per cup $cm=120 - 45=75$.

Step4: Calculate number of cups

Let the number of cups be $n$. We know that $C = cm\times n$. So, $n=\frac{C}{cm}=\frac{135000}{75}=1800$.

Answer:

1800