Question

5. ). A cosmetic company has developed a new after-shave lotion. If the company goesinto small-scale production its annual fixed costs will be $200,000 and it can produce theproduct for a variable cost of $3 per unit. If the company goes into large-scale production itsannual fixed costs will be $400,000 and it can produce the product for a variable cost of$1.25 per unit.Assume that the selling price is $7 per unit.a) Determine the break-even points for small scale and large scale production.b) If the expected sales are for 500,000 units, which production process is more profitablesmall-scale or large-scale?c) Determine profits for both cases,d) Find the number of units for which one would be indifferent between small-scale andlarge-scale production

Answer 1

This is a simple question to solve.

First, we need to understand what is a break-even point.

Well, a break-even point is a point in sales where your company know it has covered all money they spent on fixed and variable costs but still don't have a profit. It means --> no loss but also no profit.

Letter A) To calculate a break-even point we can use the following equation:

`BEP=(C_(fixed))/(S_(price)-C_(variable))`

Where:

BEP = Break-even point;

Cfixed = Fixed Cost;

Sprice = Selling price; and

Cvariable = Variable cost.

So, for small-scale we have:

`\begin{gathered} BEP=(C_(fixed))/(S_(price)-C_(variable)) \\ BEP=\frac{200000_{}}{7_{}-3_{}} \\ BEP=50000 \end{gathered}`

And, for large-scale:

`\begin{gathered} BEP=(C_(fixed))/(S_(price)-C_(variable)) \\ BEP=\frac{400000_{}}{7_{}-1.25_{}} \\ BEP\cong69565.217 \end{gathered}`

Letter B:

We can see above the break-even point for small-scale(50000) is lower than large-scale(69565.217). That means for small-scale we need to sell fewer units to cover all our cost and start profit after that point, so if the expected sales are for 500000 units, the small production is more profitable.

Letter C:

The profits for small-scale starts after 50000 units sold and for large-scale starts after 69565 units sold approximately.

Letter D:

As we understand what is a break-even point, we know the number of units for each one would be indifferent between small-scale and large-scale is 50000 units and approximately 69565 respectively because at these points for both (small and large scale) we have neither a profit nor a loss.