How Risk, Return and Valuation Correlate

Corporate Finance

Valuation, risk and return are closely linked, from different perspectives. Primarily, risk determines, to some degree, the level of returns, while both need to be seriously considered when conduction a valuation. In many occasions, the analysts work with information from the present, creating forecasts about risk and return that allows them to give, with a reasonable probability, expectations about future events.

This paper aims to look into more details at aspects related to valuation, risk and return. It will look, in the beginning, at different valuation techniques, detailing each of them and presenting their advantages and disadvantages. It will then focus on the analysis of risk and return, as a fundamental component of the valuation process. The paper will conclude with an overview of the methods and techniques described and ideas on best practices.

Valuation techniques

Valuation is the process of putting value on something, of analyzing what something is worth. It is important to note that, while valuation is often associated to a business (analyzing what a business is worth), there are many other cases when valuations need to be undertaken, including asset and liability valuations or the valuation of a particular project (in order to determine its viability).

Valuation comes as a necessity in different situations, particularly when a company will be sold. The group that sells the company needs to know a fair value for the company, depending on which it can settle on an appropriate price for the organization. As theory discusses (Vault, 2005), in its basic form, the value of the company is given by the sum of its debt and equity. A future investor who purchases a company assumes both its equity and its debt.

The debt is easier to calculate than the equity, because it is, in fact, the accounting value for the debt. However, equity is more complicated to evaluate and there are different valuation techniques that are applied exactly so as to best value equity. The four major valuation techniques are the discounted cash flow (DCF) analysis, the multiples method, the market valuation method and the comparable transactions method. This paper will briefly look at each of these.

Discounted cash flow (DCF) analysis. This is considered the most thorough way to complete the valuation of a company (Vault, 2005). With this method, there are two techniques that can be implemented: the adjusted present value method and the weighted cost of capital method. The former focuses on the free cash flows that a company or project can generate over the next period of time. The latter looks at the market value of debt or equity. In its very simple form, as described by Penman (2011), the discounted cash flow analysis forecasts the future cash flows (or future rates of return), factors a growth rate into the equation and then discounts these cash flows to obtain their present-day value. The discount rate is usually the cost of capital, namely how much does it cost to borrow the funds that will finance this investment.

The multiples method. The multiples method takes into consideration the fact that, quite often, there is not enough information to complete the valuation process. With this method, the evaluator takes known indicators, such as EBITDA, and compares this to other indicators of relevant competitors in the market.

The market valuation method. This is considered the simplest of the four techniques, but is only applicable to companies that are publicly traded, at the stock exchange. The method implies multiplying the total number of shares by the price per share and the result is the market value of the equity. However, this is usually not the price that someone would pay if he were to acquire the company: the market value receives a discount or a premium, depending on the economic conditions, on supply and demand or on the way an acquisition is made (as a hostile takeover, for example).

The comparable transactions method. This method proposes a comparison with similar transactions that occurred on the market, under similar conditions, and uses discounts or multipliers to adjust the respective value. The method needs to analyze the way the previous valuation was completed, particularly as to what method was used and what the key valuation parameter was.

Strictly in terms of corporate valuation, professor Giddy (2006) proposes a different categorization approach that includes five general categories of methods. These include asset-based methods, comparables, free cash flow methods, option-based valuations and special applications. Since some of these have been previously described, the paragraphs below will focus only on those that have not yet been mentioned.

Asset-based methods are those methods that look at the book value of the company. Basically, this technique is an accounting approach that takes into consideration what the different assets of the companies are worth, according to their book value. This means adding up everything from cash to equipment and to inventory. From this, the existing debt of a company is subtracting, resulting an estimate value of the company.

There are at least two problems with this approach. On one hand, it appears rather static. Evaluating something from its book value may not take into consideration the fact that the respective asset may have devalued in time or, in fact, may have grown in value from the moment it was recorded in the books. This brings about the second problem: a true and correct evaluation of many of the company's assets is often complex. An important asset, for example, is the company's brand name or the company's reputation, but it is often difficult to put an immediate value on this.

In terms of special applications, Giddy looks at particular situations where the valuation may differ than one in a situation with no constraints. For example, he is referring to the valuation of a company in distress, which may result in results that are different than if the company were not in distress. Other special applications include the valuation of a company in a merger and acquisition context or the valuation of a company facing corporate financial restructuring (Giddy, 2006).

The options-based methods were left towards the end of this description because these methods link well with the risk and return discussion that will follow. As Giddy (2006) points out, one of the big challenges of executives is the way to properly include risk and uncertainty in the valuation process, particularly during investments or acquisitions. Many of the methods previously mentioned, including the adjusted present value, use several instruments in order to minimize this problem, but it is not always enough. Option-based methods take into consideration the fact that decisions are made in a way that leaves some alternatives on the table and that consider a more flexible environment.

Option-based methods use, as their fundamental assumption, the fact that the future value of an investment or a project is uncertain. Options allow the possibility of either investing in the project at a future time or stopping the project altogether. Depending on these scenarios, the valuation changes accordingly.

Risk and return

It is now a good time to introduce risk and return into the discussion. As mentioned, the first connection between risk, return and valuation is that the valuation of a company, of a security or of anything else is related to things that will happen in the future. The analyst is trying to determine how something will behave, from a financial and economic perspective, in the future. As such, he is trying to make assumptions and use them in models in order to have a prediction about the future. Risk plays an important role in making this prediction.

The work of Van Horne and Wachowicz (2011) are the best place to start in the process of understanding how the relationship between risk and return operates. They define the return as the difference between the initial investment and the price of the final sale, in the case of an asset. They mention that the rate of return is usually used, transforming the difference described above in a percentage by dividing it to the initial investment.

They argue that, with uncertainty being present, risk has an impact on the projected return. This also means that each return occurs with a certain degree of probability. They introduce the probability distribution as "a list of possible returns from investment together with the probability of each return" (Van Horne, Wachowicz, 2011). As such, some returns are more probable than others. In order to calculate the expected return of the investment, one connects the probability rates with the rates of return by weighting each return with the probability that it will occur and adding everything to give the expected return.

Again, one needs to emphasize that the existence of such things as probability distributions is related to uncertainty about the future: the investors cannot fully evaluate, given the instruments from the present, what the return is likely to be in the future. He is making educated guesses about these returns and these educated guesses are each given a probability rate that it would actually occur.

The probability distribution is often an object of study in risk valuation, thus having an important role in the risk-return relationship and in the overall valuation process. Instruments such as the standard deviation and variance measure how dispersed all these different probabilities, reflecting different scenarios, are. The degree of dispersion shows the risk of the investment. This is has a logical explanation: the more dispersed the probabilities are, the more there are different scenarios, which implies a greater degree of uncertainty, hence of risk.

Going back to the relationship between risk and return, there is the general understanding that "higher expected returns require taking higher risks" (Womack, Zhang, 2003). This type of accepted relationship comes from the logical assumption that, in order to accept a higher degree of risk, the investor needs a higher rate of return.

Perhaps one of the best ways to exemplify this is by thinking of the different types of securities. Securities such as U.S. T-Bills, guaranteed by the U.S. Government, have a low level of risk, primarily because there is little chance that the U.S. Government will fail to make a payment for them. At the same time, they also have a low rate of return, because it is a certain rate of return. The risk that the investor is assuming is very low and his pay for that risk is equally low.

On the other side of the spectrum, we have the junk bonds. The risk here is very high: it is often that junk bonds are related to failing companies, so the risk that the investor will lose his money is very high as well. At the same time, the rate of return for junk bonds is very high, because the investors is paid to accept a much higher level of risk than, for example, when he purchases T-bills.

One can thus understand the relationship between risk and return as a relationship of direct correlation: the two measures move together and this is logically explained by the fact that the investor needs to be paid in order to assume a certain level of risk, otherwise he would simply chose a lower risk investment, if it were to provide the same rate of return as the risky one, following the principle that at the same level of risk, it is logical to select the best paid investment.

The relationship between the risk-return pair and valuation becomes clearer now. When making an investment, as this paper has previously shown, the investor uses a valuation method in order to determine what the respective company or asset is worth. The investor may use one of the methods that implies using future cash flows to evaluate the present day value of that asset, investment or corporation. The problem is that these future cash flows have a probability of actually occurring. A proper valuation will attempt to have a result that is as close to the truth as possible, but, in the end, it remains an estimation and a forecast based on probabilities.