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The utility of an event x occurring at future time t under utility function u, discounted back to the present (time 0) using discount factor β, is (). Since more distant events are less liked, 0 < β < 1.
The discount factor, DF(T), is the factor by which a future cash flow must be multiplied in order to obtain the present value. For a zero-rate (also called spot rate) r , taken from a yield curve , and a time to cash flow T (in years), the discount factor is:
The main models of discounting include exponential, hyperbolic, and quasi hyperbolic. The higher the time preference, the higher the discount placed on returns receivable or costs payable in the future. Several factors correlate with an individual’s time preference, including age, income, race, risk, and temptation.
The result quantifies the advantage of being the first to propose (and thus potentially avoiding the discount). The generalized result quantifies the advantage of being less pressed for time, i.e. of having a discount factor closer to 1 than that of the other party.
Therefore, the preferences at t = 1 is preserved at t = 2; thus, the exponential discount function demonstrates dynamically consistent preferences over time. For its simplicity, the exponential discounting assumption is the most commonly used in economics. However, alternatives like hyperbolic discounting have more empirical support.
The concept of the stochastic discount factor (SDF) is used in financial economics and mathematical finance. The name derives from the price of an asset being computable by "discounting" the future cash flow x ~ i {\displaystyle {\tilde {x}}_{i}} by the stochastic factor m ~ {\displaystyle {\tilde {m}}} , and then taking the expectation. [ 1 ]
Forward Discount Rate 60% 40% 30% 25% 20% Discount Factor 0.625 0.446 0.343 0.275 0.229 Discounted Cash Flow (22) (10) 3 28 42 This gives a total value of 41 for the first five years' cash flows. MedICT has chosen the perpetuity growth model to calculate the value of cash flows beyond the forecast period.
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