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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:
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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 determines the importance of future rewards. A factor of 0 will make the agent "myopic" (or short-sighted) by only considering current rewards, i.e. (in the update rule above), while a factor approaching 1 will make it strive for a long-term high reward. If the discount factor meets or exceeds 1, the action values ...
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.
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 ]
Hyperbolic discounting is mathematically described as = + where g(D) is the discount factor that multiplies the value of the reward, D is the delay in the reward, and k is a parameter governing the degree of discounting (for example, the interest rate).
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.