A typical Latino coffee farmer has fixed costs of $10,000 per year. Under the old distribution system, the farmer is paid $.40 per pound (U.S. weight measure) and the farmer’s variable cost per pound is $.30. What is the farmer’s breakeven point in units (pounds) under the old system? What is the farmer’s breakeven point in dollars?
Under the new distribution system, the farmer is paid $1.26 per pound, what is the farmer’s breakeven point in units (pounds) now? What is the farmer’s breakeven point in dollars?
FarmersProfit: income-costs
Netperlb*W - costperlb*W
So at breakeven, Profit is zero, so set the farmer's profit to zero, and solve for W.
To calculate the breakeven point, we need to determine the number of units (pounds) the farmer needs to sell to cover their fixed costs.
Under the old distribution system:
Breakeven point in units:
The difference between the selling price per pound and the variable cost per pound represents the contribution margin. In this case, the contribution margin is $0.40 - $0.30 = $0.10 per pound. To cover the fixed costs of $10,000, we need to divide the fixed costs by the contribution margin:
Breakeven point in units = Fixed costs / Contribution margin
Breakeven point in units = $10,000 / $0.10 = 100,000 pounds.
Breakeven point in dollars:
The breakeven point in dollars is calculated by multiplying the breakeven point in units by the selling price per pound:
Breakeven point in dollars = Breakeven point in units * Selling price per pound
Breakeven point in dollars = 100,000 pounds * $0.40 = $40,000.
Under the new distribution system:
Breakeven point in units:
Using the same calculation, considering the new selling price per pound of $1.26, and the same variable cost per pound of $0.30, the contribution margin is $1.26 - $0.30 = $0.96 per pound. Dividing the fixed costs by the contribution margin:
Breakeven point in units = Fixed costs / Contribution margin
Breakeven point in units = $10,000 / $0.96 = 10,416.67 pounds (rounded to the nearest pound).
Breakeven point in dollars:
Breakeven point in dollars = Breakeven point in units * Selling price per pound
Breakeven point in dollars = 10,416.67 pounds * $1.26 = $13,125.
To summarize:
Under the old system:
- Breakeven point in units (pounds): 100,000
- Breakeven point in dollars: $40,000
Under the new system:
- Breakeven point in units (pounds): 10,416.67 (rounded to the nearest pound)
- Breakeven point in dollars: $13,125