You may have seen in news, articles or blogs that a certain stock/company is undervalued or overvalued and that it is an outstanding opportunity to buy/sell that stock. If we stumble on an in depth analysis, we may read terms as intrinsic value of a company, value relative to this or that sector or even some thoughts about the behaviour of the value factor. Notice that the term value is everywhere, but in different forms or nuances.

When we talk about the under or over valuation of an asset we are implicitly saying that the market is inefficient, i.e. the market price of an asset is not reflecting the (fair) value that an asset should have under its current characteristics.

According to this thought, the valuation models try to give the asset the value we think it should have. Obviously, this value will be subjective and will depend on the perception of the observer; that is why we frequently find valuations more or less optimistic according to the expectations of the analyst or the methodology used.

## Intrinsic value

The intrinsic valuation of a company links the value of a company with its potential of cash flow generation and the risk/uncertainty of those cash flows. The key point of modelling the intrinsic value is being able to assess this cash flow generation power and its risk, which can be based on a myriad of data or analysis (fundamental, technical analysis, macroeconomic, risk premia, etc).

The most used model to obtain the intrinsic value is the **Discounted Cash Flow (DCF)** method, in which the value of an asset corresponds to the present value of the future expected cash flows of the asset. The information we will need to know/estimate is:

- cash flows during the existence of the asset
- discounted rate to apply to the cash flow to get the present value

If we had an estimation of n future annual cash flows of a company and afterwards we considered perpetual cash flows at a terminal rate g, we could express the DCF as:

You sure recognize the first terms of the formula, as it is just the value of a series of cash flows brought to present, ubiquitously used in valuing assets, projects, etc with a finite life time.

The final term may result novel: it represents the endless present value of infinite cash flows – considering that the asset always exists. This present value is the result of the sum of an infinite geometric progression with rate (1+g)/(1+r), with initial cash flow CFg and growth rate g. This term may seem insignificant, however it constitutes an important part of the formula, weighting in some cases more than 50% of the intrinsic values.

## Methods

With the DCF formula is possible to value a company decomposing the value between equity and debt or in terms of the total enterprise value.

- If we work separately with the
**expected equity cash flows**(CFe) – levered cash flows – and the**expected debt cash flows**(CFd) of the company, using respectively as discounted rates a**return of equity ke**and a**return of debt kd**required by an investor, we can obtain the present values of equity and debt:

2. If we are assessing the entire company based on the **unlevered free cash flows (FCF)** and the **weighted average cost of capital (WACC)**, we would have:

**WACC **is the rate at which the free cash flow have to be discounted so that the first and the second method give the same result. Knowing that:

where *AD* is the debt change,* I *is the interest paid by the company and *T* the tax rate.

WACC should fulfill:

Even though in equation [5] we define a different value of WACC each year, in many cases we just estimate a constant WACC for the entire life of the company.

## Example

Next we show an example of DCF calculation based on dummy values considering very simplified premises. We part from the assumption that we have estimated some **free cash flows along 6 years** and that our analysts forecast **10% WACC** and a **perpetual growth of 2%** after 2016. The **debt value** at the end of 2010 is **869 **(in the same currency and significant figures than FCF).

In the next table you can observe the **present value** of the free cash flows using the WACC according to the addends of the formula in method 2.

From 2017 on we assume that the FCF is the one of 2016 increased by the perpetual growth g; applying the discount formula to obtain the present terminal value:

*Aggregating the FCF present values and terminal value* we would obtain the 2010 intrinsic valuation of the example. Subtracting the Debt value we would finally return the intrinsic equity valuation.

As I mentioned before, the terminal value gather a large part of the value, which demonstrate its importance.

## Final ideas

Following the presented method we could calculate a range of intrinsic values more or less optimistic changing the WACC, what would give us a deeper picture of the company according to different future scenarios.

To improve the calculations we could calculate WACC for each year according to expected return of equities and return of debt. I leave this calculations for future posts.

Hope you liked the post! Do not hesitate to sending your thoughts about asset valuation.