# Break-Even Point

Student: Lillie Wallace

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Professor: Layla Hedayat

24-September-2007

Break-Even Point

1) Rent-A-Dent (RAD) has rental specials on compact cars:

a) Hondas rent for $25 per day and $.24 (24 cents) per mile.

b) Toyotas rent for $31 per day and $.19 (19 cents) per mile.

Ø Write a cost equation for each rental car

Let the miles is represented by x, the cost is represented by C and number of days is represented by N.

Cost equation for Hondas,

Cost equation for Toyotas,

If we assume that cars are rented for a single day than the above equation can be written as:

Cost equation for Hondas,

Cost equation for Toyotas,

Ø The distance from Monterey, Ca to San Francisco, Ca is about 110 miles - **Break-Even Point** introduction. Which car would be the better choice to rent for a one-way drive to San Francisco from Monterey?

Cost incurred by Honda for a one-way drive to San Francisco from Monterey assuming the journey is completed with-in one day,

Cost incurred by Toyota for a one-way drive to San Francisco from Monterey assuming the journey is completed with-in one day,

The cost for Honda is $ 51.4 and for Toyota is $51.9 for a one-way drive to San Francisco from Monterey assuming the journey is completed with-in one day. Therefore, the Honda could be better choice to rent for a one-way drive to San Francisco from Monterey

Ø Which car would be the better choice to rent for a round-trip drive from Monterey to San Francisco and back?

Cost incurred by Honda for a round-trip drive from Monterey to San Francisco and back assuming the journey is completed with-in one day,

Cost incurred by Toyota for a round-trip drive from Monterey to San Francisco and back assuming the journey is completed with-in one day,

The cost for Honda is $ 77.8 and for Toyota is $ 72.8 for a round-trip drive from Monterey to San Francisco and back assuming the journey is completed with-in one day. Therefore, the Toyota could be better choice to rent for a round-trip drive from Monterey to San Francisco and back.

Ø What is the break-even point for both rental cars, include the mileage and cost.

Figure 1: Break-Even-Point for Both Cars

At Break-Even-Point the cost for both cars will be equal, therefore

At Break-Even-Point the cost will be:

The break-even point for both rental cars is (120, 53.8) i.e. at 120 miles the cost is $ 53.8

2) Using your current employment status or future career objective, think of a situation that would require a cost analysis where the outcome would be based on a break-even point. Clearly explain the scenario and create the cost equations. Compute the break-even point and then make a management decision based on your calculations. Include any unforeseen “real-life” circumstances that may occur which could alter your decision.

Scenario: I am working in a production house which produces certain type of product for customer. The Fixed cost for the production of the product is $ 6000 and the variable cost for the production of a single unit of product is $ 2. Now suppose that a single unit of the product is sold to customer for $ 5. Now it is required to determine the break-even-point for the production of number of units of product i.e. the minimum number of unit of the product that can be produced for no-loss or no-profit.

Let x denotes the number of units of the product that is produced and sold to the customer. The cost will given by the equation,

C = 6000 + 2x

And the revenue will be given by the equation

R = 5x

Figure 2: Break-Even-Point for Product

From the figure 2 the break-even-point is the point at which the revenue and cost equation intersects i.e. (2000, 10000). Therefore, there should be at least 2000 units of product should be produced and sold so that cost and revenue are equal.

Now suppose there should be profit of at least $10000 is required from the sale of units of product. Therefore,

P = R – C

à P = 5x – 6000 – 2x

à P = 3x – 6000

à 10000 = 3x – 6000

à x = 16000/3

à x ≈ 5334

Therefore the production house should make at least 5334 units of product and sale so that at least a profit of $10000 can be made from the sale of the products.

Reference:

A. Angel, C. Abbott & D. Runde 2005. A Survey of Mathematics with Applications, 7th Ed, Pearson Education Inc

http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/BreakEven.htm accessed on September 22, 2007.