Consider Portfolio A: long 1 American put on a stock with strike price and expiration at T; short 1 American call on the same stock with the same strike and expiration date; and long 1 share of stock (a) If you are long portfolio A and the call is exercised, show that you will have at least K dollars plus the value of the put at time T, no matter when the call is exercised
(b) If you are long portfolio A, show that you are guaranteed a payoff of at least K at time T. Conclude that
Hint: Draw timeline from 0 to T. Plot the different cash flows under different scenarios. When adding up, don't forget TVM.

In its 2016 annual report, caterpillar inc. reported the following (in millions): 2016 2015 sales $38,537 $47,011 cost of goods sold 28,309 33,546 as a percentage of sales, did caterpillar's gross profit increase or decrease during 2016? select one: a. gross profit increased from 26.8% to 28.6% b. gross profit decreased from 28.6% to 26.5% c. gross profit increased from 71.4% to 73.2% d. gross profit decreased from 73.2% to 71.4% e. there is not enough information to answer the question.

When interest is compounded continuously, the amount of money increases at a rate proportional to the amount s present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) find the amount of money accrued at the end of 3 years when $4000 is deposited in a savings account drawing 5 3 4 % annual interest compounded continuously. (round your answer to the nearest cent.) $ (b) in how many years will the initial sum deposited have doubled? (round your answer to the nearest year.) years (c) use a calculator to compare the amount obtained in part (a) with the amount s = 4000 1 + 1 4 (0.0575) 3(4) that is accrued when interest is compounded quarterly. (round your answer to the nearest cent.) s = $

In each of the following cases, find the unknown variable. ignore taxes. (do not round intermediate calculations and round your answers to the nearest whole number, e. g., 32.) accounting unit price unit variable cost fixed costs depreciation break-even 20,500 $ 44 $ 24 $ 275,000 $ 133,500 44 4,400,000 940,000 8,000 75 320,000 80,000