Question

Markland Manufacturing intends to increase capacity by overcoming a bottleneck operation by adding new equipment. Two vendors have presented proposals. The fixed costs for proposal A are $50,000 and for proposal B, $70,000. The variable cost for A is $12.00 and for B is $10.00 . The revenue generated by each unit is $20.00.

What is the break-even point in dollars for proposal A is you add $10,000 installation to the fixed cost?

What is the break-even point in dollars for proposal B is you add $10,000 installation to the fixed cost?

What volume (in units) of output would the 2 alternatives yield at the same profit?

Answer 1

First let us summarise the information given in the question this will help us solve the problem in concern

Fixed cost

Proposal A fixed cost is $ 50,000

Proposal B fixed cost is $ 70,000

Variable cost

Proposal A - $12

Proposal B - $10

Revenue generated

$ 20 ( Each vendor )

Let us assume the number of units to be any unknown say 'y'

In the captioned scenario the cost of both the proposals are similar thus we can form a equation from the captioned information, which is as under : -

= Fixed cost + y * variable cost of A = Fixed cost + y* variable cost B

Putting all the information summarised above the equation is as follows

= $ 50,000 + $ 12 y = $ 70,000 + $ 10 y

Solving the equation it comes as

= $ 2 y = $ 20,000

= y = 10,000 Units ( This is the answer to the captioned question )

Now at this point it will be pertinent to discuss the main formula for calculation of Break even point . This can easily enable to solve the sub parts no matter the information given in the question. The formula is as follows: -

Break even point = Fixed cost / ( Revenue generated - Variable cost )

Interpretation to Point A can simply be taken as given to the question is to add $ 10,000 to the fixed cost of A making it $ 60,000. Modified fixed cost is $ 50,000 + $ 10,000 ( installation )

= $ 60,000 / ($20 - $ 12)

= 7,500 units is the Break even point

Interpretation to Point B can simply be taken as given to the question is to add $ 10,000 to the fixed cost of B making it $ 80,000. Modified fixed cost is $ 70,000 + $ 10,000 ( installation )

= $ 80,000 / ($20 - $ 10)

= 8000 units is the Break even point of proposal B

For the Third part it will be necessary to assume a profit amount and then move to solve the question. Let us assume the profit is $ 10,000. Then output of proposal A & B would be

Proposal A = $ 70,000 ( FC $ 60,000 + $ 10,000 assumed profit ) / ($ 20 - $12) = 8750 units

Proposal B = $ 90,000 ( FC $ 80,000 + $ 10,000 assumed profit ) / ($ 20 - $10) = 9000 units

There for we can conclude that in same profit level the units of proposal B will be more than proposal A