Matthew Hagen started his company, The Sign of Things to Come, three years ago after graduating from Upper State University. While earning his engineering degree, Matthew became intrigued by all of the neon signs he saw at bars and taverns around the university. Few of his friends were surprised to see him start a neon sign company after leaving school. Matthew is currently considering the introduction of a new custom neon sign that he believes will sell like hot cakes. In fact, he is estimating that the company will sell 700 of the signs. The new signs are expected to sell for $75 and require variable costs of $25. The new signs will require a $30,000 investment in new equipment.

Required:

How many new signs must be sold to break even?
How many new signs must be sold to earn a profit of $15,000 before taxes?
Consider requirements C. through F. as independent situations:
If 700 new signs are sold, how much pre-tax profit will they generate?
What would be the break-even point if the sales price decreased by 20 percent? Round your answer to the next-highest number.
What would be the break-even point if variable costs per sign decreased by 40 percent?
What would be the break-even point if the additional fixed costs were $50,000 rather than $30,000?