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PV (present value) - 🧠 ANSWER ✔✔FV/(1+r)^n and Present value is the
discounted value today of future cash flows, using an interest (discount)
rate.
Ideal Conditions - 🧠 ANSWER ✔✔Ideal conditions mean we know an
objective probability for every future cash flow. Certainty is the special case
where one outcome has probability 1. Under such conditions, the best
,measure of income is simply the change in present value of assets and
liabilities
Objective Possibility - 🧠 ANSWER ✔✔everybody agrees on the
probabilities.
Example: a fair coin → P(heads) = 0.5, P(tails) = 0.5.
In ideal world, for every future cash flow you know:
what amounts can happen,
and with what probabilities - and no one disagrees.
So there is no argument about the model. You and others all compute the
same present value
certainty - 🧠 ANSWER ✔✔only one possible outcome and its probability is
1.
, Example: you will receive exactly 150 next year, for sure.
Then there is no risk, only time value of money.
Definition of income under ideal certainty - 🧠 ANSWER ✔✔Under ideal
conditions of certainty, the firm's assets and liabilities are measured at the
present value of their future cash flows. Income for a period is simply the
change in this present value between the beginning and the end of the
period, adjusted for transactions with owners (such as new capital and
dividends).
Book value = present value - 🧠 ANSWER ✔✔In the P.V. Ltd example, the
asset is always recorded at the present value of its remaining cash flows,
so the net book value of the capital asset at any year-end equals its
present value. There is no gap between accounting value and economic
value.
Ex-ante vs ex-post income - 🧠 ANSWER ✔✔Because there is no
uncertainty, ex-ante (expected) income equals ex-post (realized) income. In
year 1, expected income is the accretion of discount
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