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Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem.
r is the interest rate or discount rate, which reflects the cost of tying up capital and may also allow for the risk that the payment may not be received in full; [6] n is the time in years before the future cash flow occurs. Where multiple cash flows in multiple time periods are discounted, it is necessary to sum them as follows:
[2] [6] The "discount rate" is the rate at which the "discount" must grow as the delay in payment is extended. [7] This fact is directly tied into the time value of money and its calculations. [1] The present value of $1,000, 100 years into the future. Curves representing constant discount rates of 2%, 3%, 5%, and 7%
A valuation multiple [1] is simply an expression of market value of an asset relative to a key statistic that is assumed to relate to that value. To be useful, that statistic – whether earnings, cash flow or some other measure – must bear a logical relationship to the market value observed; to be seen, in fact, as the driver of that market value.
The US government uses a variety of discount rates but something around 7% is what the US Office of Management and Budget (OMB) recommends for a pretax rate of return on private investments. [2] In the United Kingdom, HM Treasury fixes the social discount rate for the public sector at 3.5%. [3]
The discount rate is commonly used for U.S. Treasury bills and similar financial instruments. For example, consider a government bond that sells for $95 ('balance' in the bond at the start of period) and pays $100 ('balance' in the bond at the end of period) in a year's time. The discount rate is
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