BUSFIN4221 – Investments (Fundamental Valuation Equation)

The Fundamental Valuation Equation

(BUSFIN 4221 – Investments)

Instructor:	Andrei S. Gonçalves
E-mail:	Andrei_Goncalves@kenan-flagler.unc.edu
Website:	andreigoncalves.com/BUSFIN4221

(to add on the main page). While each module describes a separate aspect of the investment world, they have several connections. One of the main links between them is the Fundamental Valuation Equation, which can be thought of as an equation to determine the price of any asset and represents the key principle of investment. To help build a connection between the different modules, here I provide some details on how they are all linked to the Fundamental Valuation Equation.

The Fundamental Valuation Equation is given by:

(1) $\begin{equation*} PV=\underset{h=1}{\overset{\infty}{\sum}}\frac{\widehat{CF}_{t+h}}{\left(1+dr\right)^{h}} \end{equation*}$

where:

* $PV$ is the present value of the investment (i.e., the current price)

* $\widehat{CF}_{t+h}$ is the estimate for the cash flow to be received at time $t + h$

* $dr$ is the discount rate investors apply to the future cash flows, $CF_{t+h}$

The valuation equation says that investors are willing to pay price $PV$ to receive (estimated) cash flows $\widehat{CF}_{t+h}$ in the future. What is the interest rate they receive in their investment? Well, in general, there is no interest rate since future cash flows are uncertain, but the discount rate works just like an interest rate. If $dr$ is high, then the price investors pay today, $PV$ , is low and their money grows fast as they receive the cash flows $CF$ . If $dr$ is low, then investors have to pay a high price today for these future cash flows and their money grows slowly as they receive $CF$ .

Everything we learn in this class can be traced back (directly or indirectly) to the fundamental valuation equation. As such, I want to keep this equation as the key piece of information that links all modules together. The following provides a description on how each module relates to the Fundamental Valuation Equation:

Module 1 – Introduction to Investments

In Module 1, we will learn about the supply and demand of capital. From the perspective of the valuation equation, the suppliers of capital are lending money in exchange for an “interest rate” $dr$ while the agents on the demand side (typically firms) are paying “interest” $dr$ to borrow money today. The borrowing and lending here are more general than the implicit borrowing/lending you have in your credit card (for instance, a firm selling stocks to the market is equivalent to borrowing capital from the market). However, the idea works the same way just as $dr$ works as an interest rate despite not actually being one.

This raises a lot of questions: how do investors decide on these discount rates? How can we estimate these implicit discount rates based on the data? Can we beat the market by choosing financial products with high discount rates (low prices)? Is that what Hedge Funds do?

Yes…investment is an exciting field! However, we need to take one step at a time. In Module 1, the objective is to learn about the demand and supply of capital in a more broad and conceptual way. We will answer questions such as (i) what financial products are out there?, (ii) Who issues them?, (iii) how does capital leave the pockets of investors and end up going to the demand side (to firms)?, and many other interesting questions. In later modules, we will dig deeper into the details of the valuation equation such as the implicit “discount rate”, $dr$ .

Module 2 – Portfolio Theory

In Module 2, we will learn about portfolio theory. How to build the best possible portfolio of risky assets and combine it with a risk-free asset? That is the key point of this module. How this relates back to the fundamental valuation equation? Well, it turns out that in order to find this “optimal” portfolio we need a measure of the “reward” investors receive when holding a given asset or portfolio. Such reward is the expected return the investor receives from holding the asset/portfolio. Guess what? The expected return of an investment is directly linked to the discount rate in the fundamental valuation equation, $dr$ .

This is intuitive. In Module 1, I argued that $dr$ works just like an interest rate. Well, the interest rate is precisely the reward one gets from lending money. Hence, $dr$ must be linked to the reward (expected return) one gets when making a risky investment. It indeed is. It turns out that the mathematical details for the link between $dr$ and expected returns are a bit more involved and, thus, I will only detail this result in Module 4 (when talking about Market Efficiency). However, the logic from the interest rate analogy should make it obvious that this must be the case.

In summary, the discount rate used in the Fundamental Valuation Equation is one of the main inputs to portfolio selection. The entire task of finding an optimal portfolio is really about trying to find a portfolio with the best risk-reward combination, with the reward being directly linked to discount rates.

Module 3 – Factor Models

In Module 3, we will learn about Factor Models. These are basically models to describe expected returns, $\mathbb{E}\left[r\right]$ . How this relates back to the fundamental valuation equation? As will be made more explicit in Module 4, the expected return of an investment is directly linked to the discount rate in the fundamental valuation equation, $dr$ .

Therefore, by describing expected returns as a function of systematic risk, this module provides a way for investors to select a “proper” discount rate based on the risk of their investment. As such, the use of the valuation equation coupled with factor models can help us price assets in financial markets.

Module 4 – Market Efficiency

In Module 4, we will learn about the Efficient Market Hypothesis (EMH). It says that as new relevant information arrives in financial markets it is correctly incorporated into prices immediately.

As argued before, the EMH can be translated into the statement $\mathbb{E}\left[r\right]=dr$ . Thus, the EMH tells us that we should use $\mathbb{E}[r]$ as our discount rate.

Module 5 – Debt Securities

Module 6 – Equity Securities

Module 7 – Derivative Securities