Donkey Corporation has collected the following information after its first year

Question

Donkey Corporation has collected the following information after its first year of sales. Net sales were $1,000,000 on 50,000 units; selling expenses $200,000 (30% variable and 70% fixed); direct materials $300,000; direct labor $170,000; administrative expenses $250,000 (30% variable and 70% fixed); manufaturing overhead $240,000 (20% variable and 80% fixed). Top management has asked you to do a CVP analysis so that it can make plans for the coming year. It has projected that unit sales will increase by 20% next year.

a) Compute (1) the contribution margin for the current year and the projected year, and (2) the fixed costs for the current year.
b) Compute the break-even point in units and sales dollars for the current year.
c) The company has a target net income of $187,000. What is the required sales in dollars for the company to meet its target?
d) If the company meets its target net income number, by what percentage could its sales fall before it is operating at a loss? that is, what is its margin of safety ratio?

Explanation / Answer

First of all, we have to get the data worked out:

Sales and variable costs will be affected by the number of units sold. Fixed costs will not be. We need to see the variable costs on a "per unit" basis (this will matter later).

Current Year:

Sales: $1,000,000/50,000 units = $20/unit

Variable Costs:
Variable Selling Expenses ($200,000 x 30%): $60,000/50,000 units = $1.20/unit
Variable Administrative Expenses ($250,000 x 30%) = $75,000/50,000 units = $1.50/unit
Variable Mfg. Overhead ($240,000 x 20%) = $48,000/50,000 units = $0.96/unit
Direct Materials: $300,000/50,000 units = $6/unit
Direct Labor: $170,000/50,000 units = $3.40/unit

Total Variable Costs per Unit = $13.06/unit

Fixed Costs ("per unit" figures are irrelevant):
Fixed Selling Expenses ($200,000 x 70%): $140,000
Fixed Administrative Expenses ($250,000 x 70%): $175,000
Fixed Mfg. Overhead ($240,000 x 80%): $192,000

Total Fixed Costs = $507,000

Projected Year:

Unit sales increase by 20%: 50,000 units x 120% = 60,000 units

Sales: $20 x 60,000 units = $1,200,000

Variable Costs:
Variable Selling Expenses: $1.20 x 60,000 units = $72,000
Variable Admin. Expenses: $1.50 x 60,000 units = $90,000
Variable Mfg. Overhead: $0.96 x 60,000 units = $57,600
Direct Materials: $6.00 x 60,000 = $360,000
Direct Labor: $3.40 x 60,000 = $204,000

Fixed costs do not change with increased sales volume.

Now that we have the data, we can do the problem. I'll give you the formulas and let you plug in the appropriate numbers above yourself. All the numbers you need are already up there.

1.) Contribution Margin = Sales - Variable Costs(Selling + Admin + MOH + DM + DL)

a.)Current Year:
b.) Projected Year:

2.) CURRENT YEAR ONLY:

Break Even in Units = Total Fixed Costs/Contrbution Margin per Unit

(Contribution Margin per Unit = Sales/unit - Variable Costs/unit)

Break Even in Dollars = Total Fixed Costs/Contribution Margin Ratio

(Contribution Margin Ratio = Contribution Margin/Sales)

3.) I'm assuming this is for the current year. We will need to solve for the number of units. This can be solved algebraically.

Target Profit = (Sales per Unit x Units Sold) - (Total Variable Costs per Unit x Units Sold) - Total Fixed Costs

Assume units sold is symbolized by the letter Q.

Therefore:

$187,000 = ($20 x Q) - ($13.06 x Q) - $507,000

$187,000 = $6.94Q - $507,000

$694,000 = $6.94Q

Q = 100,000 units sold

Sales = $20 x 100,000 units = $2,000,000

So, in order to have $187,000 in profit, we must sell $2,000,000 worth of units.

4.) This last part is beyond my level of expertise, but I'll give you a formula for it:

Margin of Safety Ratio = (expected sales - breakeven sales) / breakeven sales.

I hope that helps get you started on this. Good luck.

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