Present value: Difference between revisions
imported>Doug Williamson (Generalise first example from years to periods.) |
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(PV). | (PV). | ||
Today’s fair value of a future cash flow, calculated by discounting | Today’s fair value of a future cash flow, calculated by discounting it appropriately. | ||
The appropriate rate to discount with is the appropriately risk-adjusted current market [[cost of capital]]. | |||
<span style="color:#4B0082">'''Example 1'''</span> | |||
==Calculation of present value== | |||
We can calculate present value for time lags of single or multiple periods. | |||
<span style="color:#4B0082">'''Example 1: One period at 10%'''</span> | |||
If $110m is receivable one period from now, and the appropriate periodic cost of capital (r) for this level of risk is 10%, | If $110m is receivable one period from now, and the appropriate periodic cost of capital (r) for this level of risk is 10%, | ||
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And more generally: | And more generally: | ||
PV = Future value x Discount factor(DF) | PV = Future value x Discount factor (DF) | ||
Where: | Where: | ||
DF = ( 1 + r )<sup>-n</sup> | DF = (1 + r)<sup>-n</sup> | ||
:r = cost of capital per period; ''and'' | :r = cost of capital per period; ''and'' | ||
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<span style="color:#4B0082">'''Example 2'''</span> | <span style="color:#4B0082">'''Example 2: One period at 6%'''</span> | ||
If $10m is receivable one year from now, and the cost of capital (r) is 6% per year, | If $10m is receivable one year from now, and the cost of capital (r) is 6% per year, | ||
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<span style="color:#4B0082">'''Example 3'''</span> | <span style="color:#4B0082">'''Example 3: Two periods at 6%'''</span> | ||
Now let's change the timing from Example 2, leaving everything else the same as before. | Now let's change the timing from Example 2, while leaving everything else the same as before. | ||
If exactly the same amount of $10m is receivable, but later, namely two years from now, | If exactly the same amount of $10m is receivable, but later, namely two years from now, | ||
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== See also == | == See also == | ||
* [[Adjusted present value]] | * [[Adjusted present value]] | ||
* [[Compounding factor]] | * [[Compounding factor]] | ||
* [[Discount factor]] | * [[Discount factor]] | ||
* [[Annuity factor]] | * [[Annuity factor]] | ||
* [[Discounted cash flow]] | * [[Discounted cash flow]] | ||
* [[Economic value]] | |||
* [[Future value]] | * [[Future value]] | ||
* [[Internal rate of return]] | * [[Internal rate of return]] | ||
Revision as of 14:10, 16 November 2016
(PV).
Today’s fair value of a future cash flow, calculated by discounting it appropriately.
The appropriate rate to discount with is the appropriately risk-adjusted current market cost of capital.
Calculation of present value
We can calculate present value for time lags of single or multiple periods.
Example 1: One period at 10%
If $110m is receivable one period from now, and the appropriate periodic cost of capital (r) for this level of risk is 10%,
the Present value is:
PV = $110m x 1.10-1
= $100m.
And more generally:
PV = Future value x Discount factor (DF)
Where:
DF = (1 + r)-n
- r = cost of capital per period; and
- n = number of periods
Example 2: One period at 6%
If $10m is receivable one year from now, and the cost of capital (r) is 6% per year,
the Present value is:
PV = $10m x 1.06-1
= $9.43m.
Example 3: Two periods at 6%
Now let's change the timing from Example 2, while leaving everything else the same as before.
If exactly the same amount of $10m is receivable, but later, namely two years from now,
and the cost of capital (r) is still 6% per year,
the Present value falls to:
PV = $10m x 1.06-2
= $8.90m.
The longer the time lag before we receive our money, the less valuable the promise is today.
This is reflected in the lower Present value for the two years maturity cash flow of $8.90m, compared with $9.43m Present value for the cash flow receivable after only one year's delay.
