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What is work in a physics context? How do we use integrals to calculate work, and what quantities/units does work incorporate?

Is the following identity true or false? If false, provide a counterexample.

You were able to obtain a 20-year mortgage from your financial institution at a nominal annual rate of 6%.  Your monthly payments will be made at the end of each month.  If your monthly payment is $1,791.07, what was the original amount borrowed?  

Assume that you are on the financial staff of Carlisle Corporation, and you have collected the following data:  (1) The yield to maturity on the company’s outstanding 10% annual coupon bonds is 8%, and its tax rate is 25%.  (2) The risk-free rate is 3.5%, the market risk premium (rM – rRF) is 5.5%, and the firm’s beta is 1.10.  (3) The firm’s capital structure consists of 45% debt and 55% equity.  What is Carlisle’s WACC?

You have been assigned the task of using the corporate, or free cash flow, model to estimate Matthias Corporation’s intrinsic value.  The firm’s WACC is 12%, its end-of-year free cash flow (FCF1) is expected to be $525 million, and the FCFs are expected to grow at an 18% rate for each of the next two years (t = 2 and 3).  After t = 3, the free cash flows are expected to grow forever at a constant rate of 5% per year.  The firm has $330 million of nonoperating assets.  The company has $317.71 million in long-term debt, no preferred stock, and it has 150 million shares of common stock outstanding.  What is the firm’s estimated intrinsic value per share of common stock?

You have $10,000,000 in a portfolio consisting of 4 stocks with $2,500,000 invested in each.  The portfolio’s beta is 1.50.  You plan to sell Stock A in your portfolio and use the proceeds to buy Stock B.  Stock A has a beta of 1.25, while Stock B’s beta is 0.75.  After this transaction, what will the portfolio’s new beta be? (Hint:  Make sure to carry out your calculation to 4 decimal places.)  

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