1 answer

A man owns a hot dog stand. He sells 700 hot dogs per month at $3.25...

Question:

A man owns a hot dog stand. He sells 700 hot dogs per month at $3.25 each making the total revenue $2,275. Each hot dog, bun, and condiments costs the man $0.70 and he has fixed costs of $1,800, making his total costs $2,290. Therefore, he realizes a loss of $15 a month.

  1. What is his break-even point?
  2. At the current sales levels of 700 hot dogs, what price does the man need to charge in order to break even?
  3. If the man reduces his variable costs from $0.70 to $0.60 and all else stays constant (i.e. he still has fixed costs of $1,800 and charges $3.25 per hot dog), what is his new break even point?
  4. If the man reduces his fixed costs from $1,800 to $1,700 and all else stays constant (i.e. we still have variable costs of $0.70 each nd charge $3.25 per hot dog), what is his new break even point?
  5. Which of these two cost reductions lowers his break even point the most?

Answers

(1) Break even happens when Total Revenue = Total Manufacturing cost

To break even, let the number of hot dogs = x

Selling price per hot dog (for making) = $3.25

Therefore, Total Revenue = 3.25x

Manufacturing cost/Hot Dog (Variable cost) = $0.70

Manufacturing cost for x hot dogs = 0.7x

Fixed Cost = $1800

Total Manufacturing cost = 0.7x + 1800

Therefore 3.25x = 0.7x + 1800

Solving for x, we get 3.25x - 0.7x = 1800

x = 1800/2.55 = 705.88 \approx706 hot dogs

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(2) Keeping number of hot dogs made and sold = 700.

Let the selling price/hot dog = x

Total Revenue = 700x

Total Manufacturing cost = 700 * 0.7 + 1800 = 2290

Therefore, for break even, 700x = 2290

Solving for x, we get

x = 2290/700 = 3.2714

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(3) New break even pointy when variable cost becomes 0.6.

Therefore 3.25x = 0.6x + 1800

Solving for x, we get 3.25x - 0.6x = 1800

x = 1800/2.65 = 679.245 \approx680 hot dogs

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(4) New break even point when fixed cost is reduced to $1700.

Therefore 3.25x = 0.7x + 1700

Solving for x, we get 3.25x - 0.7x = 1700

x = 1700/2.55 = 666.67 \approx667 hot dogs

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(5) As seen above, when the fixed cost is reduced to $1700, the break even is reduced to 667 hot dogs which is lower than the break even point of 680 buns when the variable cost is reduced to $0.6/hot dog.

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