Question

In each of the following cases, calculate the accounting break even and the cash break even points. Ignore any tax effects in calculating the cash break-even.

Unit Variable
Case Unit Price Cost Fixed Costs Depreciation
1 $2,800 $2,295 $7,000,000 $1,250,000
2 51 43 65,000 160,000
3 12 4 1,800 700

Answer 1

To calculate the accounting and cash break-even points, fixed costs (with and without depreciation respectively) are divided by the contribution margin (unit price minus unit variable cost). The accounting break-even includes depreciation, while the cash break-even excludes it, focusing on cash flows.

Step-by-step explanation:

The subject of this question is to calculate the accounting break-even and cash break-even points. Both calculations determine the point at which a company neither makes a profit nor incurs a loss. For the accounting break-even point, fixed costs (including depreciation) are added to the variable costs and then divided by the difference between the unit price and the unit variable cost. However, the cash break-even point only considers the cash fixed costs (excluding depreciation) because it focuses on actual cash flows.

Let's calculate the break-even points for each case:

1. Accounting Break-Even Point (Case 1): (Fixed Costs + Depreciation) / (Unit Price - Unit Variable Cost) = ($7,000,000 + $1,250,000) / ($2,800 - $2,295) = $8,250,000 / $505 = 16,336 units (rounded to the nearest whole unit).
   Cash Break-Even Point (Case 1): Fixed Costs / (Unit Price - Unit Variable Cost) = $7,000,000 / $505 = 13,861 units (approx).
2. Accounting Break-Even Point (Case 2): (Fixed Costs + Depreciation) / (Unit Price - Unit Variable Cost) = ($65,000 + $160,000) / ($51 - $43) = $225,000 / $8 = 28,125 units (rounded to the nearest whole unit).
   Cash Break-Even Point (Case 2): Fixed Costs / (Unit Price - Unit Variable Cost) = $65,000 / $8 = 8,125 units (approx).
3. Accounting Break-Even Point (Case 3): (Fixed Costs + Depreciation) / (Unit Price - Unit Variable Cost) = ($1,800 + $700) / ($12 - $4) = $2,500 / $8 = 312.5 units (rounded to the nearest whole unit).
   Cash Break-Even Point (Case 3): Fixed Costs / (Unit Price - Unit Variable Cost) = $1,800 / $8 = 225 units (approx).

Answer 2

Case 1 Accounting break-even point = 13,861 units

Case 1 Cash break-even point = 11,286 units

Case 2 Accounting break-even point = 20,000 units

Case 2 Cash break-even point = 11,875 units

Case 3 Accounting break-even point = 225 units

Case 3 Cash break-even point = 138 units

Step-by-step explanation:

Break even point refers to the point or sales unit where total cost is equal to total revenue. That is, both total revenue and total cost at the point are even and there neither profit nor loss.

Break even point can be computed for accounting break even and the cash break even points. The difference between the two is that accounting break even point include depreciation in the fixed cost while the cash break even point deduct non cash expenses from the fixed cost. The formula for the are as follows:

Accounting break even point = Fixed cost / (Unit price - Unit cost)

Cash break even point = (Fixed cost - Depreciation) / (Unit price - Unit cost)

Using the two formula for this question, we have:

Case 1 Accounting break even point = $7,000,000 / ($2,800 - $2,295) = $7,000,000 / $505 = 13,861 units

Case 1 Cash break even point = ($7,000,000 - $1,250,000) / ($2,800 - $2,295) = $5,750,000 / $505 = 11,286 units

Case 2 Accounting break even point = $160,000 / (51 - 43) = $160,000 / $8 = 20,000 units

Case 2 Cash break even point = ($160,000 - $65,000) / (51 - 43) = $95,000 / $8 = 11,875 units

Case 3 Accounting break even point = $1,800 / (12 - 4) = $1,800 / $8 = 225 units

Case 3 Cash break even point = ($1,800 - $700) / (12 - 4) = $1,100 / $8 = 138 units