Breakeven Analysis with proportions only

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

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

1. 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.
2. 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.
3. 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.
4. 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.
5. 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

5% / 60% = 8,33%

Fixed costs don't matter here.