Question

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 $200, the sales price would be set at 1.5 times the VC/unit, and fixed costs are estimated at $750,000. a. Find the break-even quantity b. The investors will put up the funds if the project is likely to have an operating income (profit) of $500,000 or more. What sales volume (quantity) would be required in order to meet the minimum profit goal?

Answer 1

Solution:

a.Calculation of break even quantity :

The formula for calculating the break even quantity is

Break even quantity = Fixed cost / Contribution margin per unit

= Fixed cost / ( Sales price per unit – Variable cost per unit )

As per the information given in the question we have

Variable cost per unit = $200 ;  

Sales price = 1.5 times the VC/unit = 1.5 * Variable cost per unit

= 1.5 * $ 200 = $ 300

Fixed costs = $750,000

Applying the above information in the formula we have

= $ 750,000 / ( $ 300 - $ 200 )

= $ 750,000 / $ 100

= 7,500 units

Thus the break even quantity = 7,500 units

b. Calculation of Sales volume (quantity) required in order to meet the minimum profit goal of $ 500,000

The formula for calculating the sales volume (quantity) required in order to meet the minimum profit goal is

= ( Fixed Cost + Minimum profit ) / Contribution per unit

= ( Fixed Cost + Minimum profit ) / ( Sales price per unit – Variable cost per unit )

As per the information given in the question we have

Variable cost per unit = $200 ;     Sales price per unit = $ 300

Fixed costs = $750,000 ; Minimum Profit = $ 500,000

Applying the above information in the formula we have

= ( $ 750,000 + $ 500,000 ) / ( $ 300 - $ 200 )

= $ 1,250,000 / $ 100

= 12,500

Thus the sales volume (quantity) required in order to meet the minimum profit goal is = 12,500 units