pv prob - Present Value Measurements and...

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2_2SP04 January 11, 2008 1 Present Value Measurements and “Hicksian” Income Gaines Ville is considering purchasing a business venture on December 31, Year 0. If she does so, she will receive cash (gross) at the end of each year as follows: Year Amount 1 $14,000 2 16,000 3 12,000 4 10,000 $52,000 To receive the cash, however, it will be necessary for her to make gross cash payments for assets and/or services at the end of each year as follows: Year Amount 1 $ 3,000 2 4,000 3 9,000 4 2,000 $18,000 At the end of the four years this business will have no value. The short duration used here (rather than a going concern assumption), and the assumption that all payments are made at the end of the year are solely to simplify computations, i.e., they do not affect the basic idea with which we are concerned. After evaluating the risk of this business, Gaines is willing to pay a price that would secure her a 5% return on investment. This particular business requires no cash on hand (in general, cash is necessary/desirable because receipts and disbursements do not occur simultaneously and because of the uncertainty as to the amount and timing of the receipts and disbursements – however, neither situation exists here). As a result Gaines withdraws all excess (net) cash each year, either to consume herself, and/or to invest in another venture. Upon the purchase of the business, Gaines will be entitled to receive a total of $52,000, but she will be obligated to pay out $18,000. The net cash flow (NCF) will therefore be a net inflow of a total of $34,000. If the price of the business was $34,000, her income over the four years would be zero--and of course the rate of return on her investment would also be zero. Therefore, the price (now) has to be lower than $34,000 to yield her the 5% return.
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2_2SP04 January 11, 2008 2 The value of gross cash receipts (as opposed to NCF’s) at various points in time will be (assuming a 5% rate of return): (Present) Value of receipts end of year Receipts at end of year 0 1 2 3 4 1 $ 14,000 2 $ 16,000 3 $ 12,000 4 $ 10,000 Value before cash flow recd. Less:
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pv prob - Present Value Measurements and...

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