# Present value

*Investment appraisal.*

(PV).

Present value is 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.