Question

Al Fagira Farm produces oranges and mangoes. The annual fixed costs are $40,000. The cost driver for variable costs is pints of fruit produced. The variable cost is $1.25 per pint of mango and 1.15 per pint of orange. Mangoes sell for $1.65 per pint, Oranges for 1.40 per pint. 3 pints of oranges are produced for every pint of mangoes.

Required:

1. Compute the number of pints of mangoes and oranges produced and sold at the break-even point.

2. What would be the BEP if the relationship is changed to 1:2 and other things remain the same (Two pints of oranges to one pint of mango).

3.What would be the BEQ if the management introduces new product of lime. The expected contribution margin per unit is .5. Under the new scenario, the farm is expecting to produce 6000 pints of orange,2000 of Mango and 1200 pints of lime. The introduction of product three will   increase the fixed cost of the farm by 20 percent. Other things remain the same.

Answer 1

Question 1

Number of Pints of Oranges and Mangies to be sold to reach Break Even = Total Fixed Costs / Weighted Average Contribution Margin per Pint

Fixed Costs = $ 40,000

Calculation of Weighted Average Contribution Margin per Pint

Particulars	Oranges	Mangoes
Selling Price per Pint	1.40	1.65
Less: Variable Costs per Pint	1.15	1.25
Contribution Margin per Pint	0.25	0.40

Contribution Margin on Sell of 3 Pints of Oranges = 3 Pints *$ 0.25 per Pint = $ 0.75

Contribution Margin on Sale of 1 Pint of Mangoes = $ 0.40

Total Contribution Margin on Sale of 4 Pints (3 Pints of Oranges and 1 Pint of Mangoes) = 0.75 + 0.40 = $ 1.15

Weighted Average Contribution Margin per Pint = Total Contribution Margin on Sale of 4 Pints / 4 Pints

= 1.15 / 4

= $ 0.2875 per Pint

Number of Pints in Total to be sold for Break Even = 40,000 / 0.2875

= 139,131 Pints

Ratio of Oranges to Mangoes = 3:1 whic means for every 4 Pints sold 3 Pints of Oranges are Sold and 1 Pints of Mangoes are Sold.

Then Pints of Oranges to be sold = 3/4 * 139,130 = 104,348 Pints

Pints of Managers to be produced and sold = 1/4 * 139,130= 34,783 Pints

Particulars	Orange	Mangoes
Number of Punts to be	104,348	34,783
Sodl to Reach Break Even	Pints	Pints

Question 2

Number of Pints of Oranges and Mangies to be sold to reach Break Even = Total Fixed Costs / Weighted Average Contribution Margin per Pint

Fixed Costs = $ 40,000

Calculation of Weighted Average Contribution Margin per Pint

Particulars	Oranges	Mangoes
Selling Price per Pint	1.40	1.65
Less: Variable Costs per Pint	1.15	1.25
Contribution Margin per Pint	0.25	0.40

Contribution Margin on Sell of 3 Pints of Oranges = 2 Pints *$ 0.25 per Pint = $ 0.50

Contribution Margin on Sale of 1 Pint of Mangoes = $ 0.90

Total Contribution Margin on Sale of 3 Pints (3/2 Pints of Oranges and 1 Pint of Mangoes) = 0.50 + 0.40 = $ 0.90

Weighted Average Contribution Margin per Pint = Total Contribution Margin on Sale of 3 Pints / 4/3 Pints

= 0.90 / 3

= $ 0.30 per Pint

Number of Pints in Total to be sold for Break Even = 40,000 / 0.30

= 133,333 Units

Ratio of Oranges to Mangoes = 2:1 which means for every 3 Pints sold 2 Pints of Oranges are Sold and 1 Pints of Mangoes are Sold.

Then Pints of Oranges to be sold = 2/3 * 133,333 = 88,889 Pints

Pints of Managers to be produced and sold = 1/3 * 133,333 = 44,444 Pints

Particulars	Orange	Mangoes
Number of Punts to be	88,889	44,444
Sodl to Reach Break Even	Pints	Pints

Question 3

Particulars	Oranges	Mangoes	Lime
Contribution Margin per Pint	0.25	0.40	0.50

Ratio = 6,000 Oranges : 2,000 Mangoes : 1,200 Limes

Ratio = 30 Oranges : 10 Mangoes : 6 Limes

For Every 46 Pints Sold 30 Pints of Orange are sold , 10 Mangoes are Sold and 6 Limes are Sold

Contribution Margin on Sale of 30 Pints of Orange = 30 * $ 0.25 = $ 7.50

Contribution Margin on Sale of 10 Pints of Mangoes = 10 Pints * $ 0.40 per Pint = $ 4

Contribution Margin on Sale of 6 Pints of Lime = 6 * $ 0.50 per Pint = 3

Then Total Contribution Margin on Sale of 46 Pints = 7.5 + 4 + 6

= $ 17.5

Weighted Average Contribution Margin per Unit = 17.5 / 46 = $ 0.3804 per Pint

Total Fixed Costs = 40,000 + 8,000 (Increase in Fixed Costs)

Fixed Costs = $ 8,000

Increase in Fixed Costs = 20% of $ 40,000 = $ 8,000

Break Even Point in Units = Total Fixed Costs / Weighted Average Contribution Margin per Unit

= 48,000 / 0.3804

Break Even Quantity = 126,172 Pints

Using Ratio = 30:10:6

Particulars	Orange	Mangoes	Lime
Units sold for Break Even Quantity	82,286 Pints	27,429 Pints	16,457 Pints

Special Point

All the answers were in multiple Decimal places but for convenience purpose answer has been rounded off to two decimal places so you can find a minor variations due to rounding off being done. For More precise answer you can redo the calculations part by using the figures provided for getting solutions.