Pi

(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.

For example, if $110m is receivable one year from now, and the cost of capital (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

Examples

For example, 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.

Now changing the timing in this example, 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.

See also

• Adjusted present value
• Compounding factor
• Discount factor
• Annuity factor
• Discounted cash flow
• Future value
• Intrinsic value
• Net present value
• Profitability index
• Terminal value
• Time value of money