# Present value

*Investment appraisal.*

(PV).

Present value is the current equivalent value - of cash available immediately - for a future payment or a stream of payments to be received at various times in the future.

The present value will vary with the discount (interest) factor applied to discount the future payments.

Present value is today’s fair value of the future cash flow or cash flows, calculated by discounting them 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.