Present value: Difference between revisions
imported>Doug Williamson (Label first example as Example 1.) |
imported>Doug Williamson (Standardise appearance of page) |
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Today’s fair value of a future cash flow, calculated by discounting the future cash flow at the appropriately risk adjusted current market [[cost of capital]]. | Today’s fair value of a future cash flow, calculated by discounting the future cash flow at the appropriately risk adjusted current market [[cost of capital]]. | ||
'''Example 1''' | |||
If $110m is receivable one year from now, and the appropriate cost of capital for this level of risk (r) is 10% per year, | |||
the Present value is: | |||
PV = $110m x 1.1<sup>-1</sup> | PV = $110m x 1.1<sup>-1</sup> | ||
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And more generally: | And more generally: | ||
PV = | 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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'''Example 2''' | |||
If $10m is receivable one year from now, and the cost of capital (r) is 6% per year, | |||
the Present value is: | the Present value is: | ||
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'''Example 3''' | |||
Now let's change the timing from Example 2, 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<sup>-2</sup> | PV = $10m x 1.06<sup>-2</sup> | ||
Revision as of 17:16, 16 March 2015
(PV).
Today’s fair value of a future cash flow, calculated by discounting the future cash flow at the appropriately risk adjusted current market cost of capital.
Example 1
If $110m is receivable one year from now, and the appropriate cost of capital for this level of risk (r) is 10% per year,
the Present value is:
PV = $110m x 1.1-1
= $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
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
Now let's change the timing from Example 2, 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.
