Present value: Difference between revisions
imported>Doug Williamson (Make 1.10 explicit so 10% is visible.) |
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'''Example 1''' | <span style="color:#4B0082">'''Example 1'''</span> | ||
If $110m is receivable one year from now, and the appropriate cost of capital for this level of risk (r) is 10% per year, | If $110m is receivable one year from now, and the appropriate cost of capital for this level of risk (r) is 10% per year, | ||
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'''Example 2''' | <span style="color:#4B0082">'''Example 2'''</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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'''Example 3''' | <span style="color:#4B0082">'''Example 3'''</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, leaving everything else the same as before. | ||
Revision as of 14:41, 13 November 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 1.10-1
= $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
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.
