Nominal and Present value: Difference between pages
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(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. | |||
<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%, | |||
the Present value is: | |||
PV = $110m x 1.10<sup>-1</sup> | |||
= '''$100m'''. | |||
And more generally: | |||
PV = Future value x Discount factor (DF) | |||
Where: | |||
DF = (1 + r)<sup>-n</sup> | |||
:r = cost of capital per period; ''and'' | |||
:n = number of periods | |||
<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, | |||
the Present value is: | |||
PV = $10m x 1.06<sup>-1</sup> | |||
= '''$9.43m'''. | |||
<span style="color:#4B0082">'''Example 3: Two periods at 6%'''</span> | |||
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<sup>-2</sup> | |||
= '''$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 ($8.90m) for the two years maturity cash flow, compared with the higher Present value of $9.43m for the cash flow receivable after only one year's delay. | |||
Even though the money amounts receivable are exactly the same, $10m, in each case. | |||
== See also == | == See also == | ||
* [[ | * [[Adjusted present value]] | ||
* [[ | * [[Annuity factor]] | ||
* [[ | * [[Compounding factor]] | ||
* [[ | * [[Discount factor]] | ||
* [[ | * [[Discounted cash flow]] | ||
* [[ | * [[Economic value]] | ||
* [[ | * [[Future value]] | ||
* [[Internal rate of return]] | |||
* [[Intrinsic value]] | |||
* [[Net present value]] | |||
* [[Profitability index]] | |||
* [[Terminal value]] | |||
* [[Time value of money]] | |||
[[Category:Corporate_finance]] | |||
[[Category:Long_term_funding]] | |||
[[Category:Manage_risks]] | |||
[[Category:Trade_finance]] |
Revision as of 12:45, 3 March 2019
(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 ($8.90m) for the two years maturity cash flow, compared with the higher Present value of $9.43m for the cash flow receivable after only one year's delay.
Even though the money amounts receivable are exactly the same, $10m, in each case.