Assuming a 12% annual interest rate, determine the present value of a five-period annual annuity of $5,000 under each of the following situations: 1. The first payment is received at the end of the first year, and interest is compounded annually.
2. The first payment is received at the beginning of the first year, and interest is compounded annually.
3. The first payment is received at the end of the first year, and interest is compounded quarterly.

You have just been hired as a financial analyst for barrington industries. unfortunately, company headquarters (where all of the firm's records are kept) has been destroyed by fire. so, your first job will be to recreate the firm's cash flow statement for the year just ended. the firm had $100,000 in the bank at the end of the prior year, and its working capital accounts except cash remained constant during the year. it earned $5 million in net income during the year but paid $800,000 in dividends to common shareholders. throughout the year, the firm purchased $5.5 million of machinery that was needed for a new project. you have just spoken to the firm's accountants and learned that annual depreciation expense for the year is $450,000; however, the purchase price for the machinery represents additions to property, plant, and equipment before depreciation. finally, you have determined that the only financing done by the firm was to issue long-term debt of $1 million at a 6% interest rate. what was the firm's end- of-year cash balance? recreate the firm's cash flow statement to arrive at your answer

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Aproduction line has three machines a, b, and c, with reliabilities of .96, .86, and .85, respectively. the machines are arranged so that if one breaks down, the others must shut down. engineers are weighing two alternative designs for increasing the line’s reliability. plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. in either case, three machines (a, b, and c) would be used with reliabilities equal to the original three. a. compute overall system reliability under plan 1. (round your intermediate calculations and final answer to 4 decimal places.) reliability b. compute overall system reliability under plan 2. (round your intermediate calculations and final answer to 4 decimal places.) reliability c. which plan will provide the higher reliability? plan2plan1