A group of venture investors is considering putting money into Lemma Books, which wants to produce a new reader for electronic books. The variable cost per unit is estimated at $250, the sales price would be set at twice the VC/unit, or $500, and fixed costs are estimated at $350,000. The investors will put up the funds if the project is likely to have an operating income of $500,000 or more. What sales volume would be required in order to meet the minimum profit goal

3400 units

Explanation:

Profit is the difference between the sales revenue and the total costs. It is calculated as:

Sales Revenue - Total Costs

Total costs include both fixed costs and variable costs. Fixed costs do not change with the level of output whereas variable costs do change with the level of output. However, as more units get produced, the total fixed cost per unit does change as they get spread over a larger unit of output.

In order to calculate the minimum quantity, we can make use of the break-even point. This is the point at which the business makes neither profits nor losses and the TR is equal to TC. At this point, all fixed costs have been covered and any additional unit sold provides a profit of the amount Selling price per unit - Variable cost per unit (contribution margin). The break-even point is calculated as:

Fixed costs / (Sales price per unit - Variable cost per unit)

350000 / (500 - 250) = 1,400 units to cover all costs.

After this point, the profit per unit would be selling price - variable cost per unit i.e. $250. Hence, to obtain $500,000 operating income or profit, it has to sell $500000 / 250 = $2000 units after breaking even.

Hence, total number of units to sell to make $500,000 operating profit = 2000 units + 1400 units = 3400 units

This can be checked as follows:

Sales - [(VC x Q) + FC] = Profit

(3400 x $500) - [(3400 x $250) + 350000] = Operating Income

Operating Income = $1,700,000 - $1,200,000

Operating Income = $500,000