Initially, three firms a, b, and c share the market for a certain commodity. firm a has 30% of the market, firm b has 45%, and c has 25%. each year, the following changes occur:

• a keeps 75% of its customers, while losing 15% to b and 10% to c.
• b keeps 60% of its customers, while losing 5% to a and 35% to c.
• c keeps 65% of its customers, while losing 15% to a and 20% to b.

(a) what is the current market share vector (ordered for a, b, and c)?
(b) find the transition matrix for this scenario.
(c) find the share of the market that each company has after two years.

Shrieves casting company is considering adding a new line to its product mix, and the capital budgeting analysis is being conducted by sidney johnson, a recently graduated mba. the production line would be set up in unused space in the main plant. the machinery’s invoice price would be approximately $200,000, another $10,000 in shipping charges would be required, and it would cost an additional $30,000 to install the equipment. the machinery has an economic life of 4 years, and shrieves has obtained a special tax ruling that places the equipment in the macrs 3-year class. the machinery is expected to have a salvage value of $25,000 after 4 years of use. the new line would generate incremental sales of 1,250 units per year for 4 years at an incremental cost of $100 per unit in the first year, excluding depreciation. each unit can be sold for $200 in the first year. the sales price and cost are both expected to increase by 3% per year due to inflation. further, to handle the new line, the firm’s net working capital would have to increase by an amount equal to 12% of sales revenues. the firm’s tax rate is 40%, and its overall weighted average cost of capital, which is the risk-adjusted cost of capital for an average project (r), is 10%. define “incremental cash flow.” (1) should you subtract interest expense or dividends when calculating project cash flow?

Now ray has had the tires for two months and he notices that the tread has started to pull away from the tire. he has already contacted the place who sold the tires and calmly and accurately explained the problem. they didn’t him because they no longer carry that tire. so he talked with the manager and he still did not get the tire replaced. his consumer rights are being violated. pretend you are ray and write a letter to the company’s headquarters. here are some points to keep in mind when writing the letter: include your name, address, and account number, if appropriate. describe your purchase (name of product, serial numbers, date and location of purchase). state the problem and give the history of how you tried to resolve the problem. ask for a specific action. include how you can be reached.

Peppy knows a lot about marketing, but not much about the legal or financial aspects of starting a new business. he wants to consult with a lawyer and accountant, but his budget is tight with all of the expenses involved in getting peppy's pizzazzeria up and running. peppy should: trust his basic instincts and try to put it together without the advice of lawyers and accountants. delay talking with a lawyer and accountant until the business has established a positive cash flow for at least one year. immediately hire full-time lawyers and accountants for his staff. consult with a lawyer and accountant even though the budget is tight.