Present value
(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.
