Breakeven Analysis with proportions only

Question

Can someone help me solve the following breakeven analysis please:
Your client is a local beer company in South Africa who's considering sponsoring a Rugby team. Their gross margin on each liter of beer sold is 60%, their investment will be 5% of their current revenues, and fixed costs are 30% of revenues. By how much would their beer sales have to increase so this investment breaks even?

Answer 1

Hi there,

I would be happy to share my thoughts on your question:

First of all, with a 60% gross margin, every $1 of sales contributes $0.60 towards covering fixed and investment costs. The investment is 5% of current revenues, so if current revenues are R, the investment is 0.05R.
Moreover, to find out how much sales need to increase, set up the equation for the additional sales needed where additional sales times the gross margin equals the investment amount: additional sales × 0.60 = 0.05R.
Lastly, solve for the additional sales: additional sales = 0.05R ÷ 0.60 = 1/12R = 0.0833R, meaning sales must increase by 8.33% of current revenues to break even on this investment.

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Best,

Hagen

Answer 2

Hey this is a tricky one! My idea would be the following:

Understanding the Investment:
The company is planning to invest 5% of its current revenue to sponsor a rugby team. This means that if the company's total revenue is a certain amount, say 100 units (just as an example), the investment would be 5 units. Essentially, they’re spending 5% of what they currently earn in revenue.
Profit Margin:
The company's gross margin is 60%. This means that for every extra unit of beer they sell, 60% of the sales amount is kept as profit. The rest (40%) goes towards costs like production, distribution, etc.
What the Company Needs to Do:
To break even on this sponsorship, the company needs to sell more beer. The profit from these extra sales must be enough to cover the 5% of revenue they invested.
How Much Extra Sales Are Needed:
Since the company only keeps 60% of every extra dollar from beer sales, they need to sell more than just 5% extra to cover the 5% investment. To figure out how much extra sales are needed:
- Imagine for every 1 extra unit of sales, the company keeps 60% as profit.
- To make up for the 5% they invested, they need to sell enough extra beer to cover that investment, but because they’re only keeping 60% of each sale, they need more sales to reach the same amount.
Final Answer:
When you do the math, this comes out to 8.33%. This means that the company needs to increase its beer sales by 8.33% of its current revenue to cover the sponsorship cost and break even.

The idea is that with a 60% profit margin, they need to sell more than just 5% extra to make up for the cost. The 8.33% sales increase is the breakeven point where the additional profits from those extra sales would match the sponsorship investment.

Hope this helps a bit!

BR Alessa

Answer 3

5% / 60% = 8,33%

Fixed costs don't matter here.