Astock is trading at $50. you believe there is a 60% chance the price of the stock will increase by 10% over the next 3 months. you believe there is a 30% chance the stock will drop by 5%, and you think there is only a 10% chance of a major drop in price of 20%. at-the-money 3-month puts are available at a cost of $650 per contract. what is the expected dollar profit for a writer of a put at the end of 3 months? (hint: remember how we calculated the expected return (e(r)) for stocks? use the probabilities as the weights to calculate the weighted average profits in all scenarios.)

Assume today is december 31, 2013. barrington industries expects that its 2014 after-tax operating income [ebit(1 – t)] will be $400 million and its 2014 depreciation expense will be $70 million. barrington's 2014 gross capital expenditures are expected to be $120 million and the change in its net operating working capital for 2014 will be $25 million. the firm's free cash flow is expected to grow at a constant rate of 4.5% annually. assume that its free cash flow occurs at the end of each year. the firm's weighted average cost of capital is 8.6%; the market value of the company's debt is $2.15 billion; and the company has 180 million shares of common stock outstanding. the firm has no preferred stock on its balance sheet and has no plans to use it for future capital budgeting projects. using the corporate valuation model, what should be the company's stock price today (december 31, 2013)? round your answer to the nearest cent. do not round intermediate calculations.

Individual consumers belong to which step of choosing a target market? possible customers competition demographics communication

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x,y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.