Discounted cash flow (DCF) analysis

What is a cash flow?

A cash flow is a movement of money that goes into or out of a business, investment project or financial product (like stocks).

It is not equal to the net earnings, because to calculate the net earning, we have taken into account things that are costs but not expenses (tipically, depreciation and changes in working capital). Is the real money that a activity or product needs or produces.

You can see more about how to calculate the cash flow from the income statement here.

What is the time value of the money?

One euro or dollar today is not the same that a euro or dollar after a year. Money now is more valuable than money later on. There are two different reasons:

1. Inflation: sustained increase in the general price level of goods and services in a economy over a period time. It can be measured throught the Price Consumer Index (PCI) or the the GPD deflactor. Typical values range from 1% to 6%. It means, that after a year you loss 1-6% of purchasing power. More information here.
2. Interest earned: instead of saving the money under your bed, you can run a business, invest in the stock market or put the money in the bank to earn interest. Therefore, there is something called opportunity cost (the opportunity cost is equal to the earning that you could have made by using your money instead of saving it under the bed).

As a rule, the interest earned are higher than inflation. In fact, we can talk about nominal interest rates (earning of an activity) and real interest rates (nominal rates discounted by inflation rate).

To move between the present value and the future value of the money we employ the discount rate, which is usually equal to the cost of opportunity. If r is equal to the annual cost of opportunity, and considering that we can reinvest after a year, we can calculate the amount of money that we will have after T years:

Future value after T years = Preset value * $ (1 + r)^T$

We can modify the equation from above to know the present value of a future gain:

Preset value = Future value after T years / $(1 + r)^T$

What means discounting cash flows?
It means calculating the present value of future cash flows. It is important because to evaluate a project we need to sum up money in the same units.

If $C_{1}, ..., C_{n}$ are the cash flows of a project at periods 1, ..., n, the total present value (PV) is equal to:

$$PV= \sum \limits_{i=1}^n\frac{C_{i}}{(1+r)^i} $$

What is the net present vale rule?
The net present value (NPV) is the amount of wealth created by doing a project. It is equal to the present value of all the future cash flows minus the initial investment. It is a powerful tool to determine either to do an investment or not.

$$NPV= -I_{0} + \sum \limits_{i=1}^n\frac{C_{i}}{(1+r)^i}$$

If we considerer the initial investment as a cash flow (negative):

$$NPV= \sum \limits_{i=0}^n\frac{C_{i}}{(1+r)^i} $$

To know more about the discounted cash flow analysis, please visit the following related posts:

Discounted cash flow analysis - Real Estate
How to evaluate fixed-income investments