# Valuation and returns

# Valuation and returns

Do stock indexes show the prospects of the economy? Not really. Do they exhibit the forecast of companies’ profits? This is closer but not enough. Do they demonstrate the estimation of companies’ values? That should be the case but often it is not. More often they show the guess on the direction the companies’ trading values will move which is triggered by the previous.

First, let’s clarify that it concerns only listed companies and more specifically those used in the indexes which are a subset. If those that composed the indexes have done a good job, it should reflect the whole set. Still listed companies are usually big and a small percentage of all companies. In USA, publicly traded companies amount to less than 1% of all companies in the non-farm business sector but 1/3 of employment. This shows how big they are relatively to the rest 99+%.

A number of shares are out there for each company. The stock price is calculated by dividing the company’s equity value by the number of shares. Two different values exist, the estimated value and the market value. They are supposed to be equal but very often they are not. When market price is higher, the stock is overvalued. When it is lower, it is undervalued. Finding undervalued companies is a way of making big money because market values supposedly will eventually reach their real values which are higher in the case of undervaluation. In the case of overvaluation, money can be made by shorting. This is an investment technique that bets on prices falling.

The intrinsic or absolute value is calculated by using a sophisticated method called discounted cash flows. The company’s cash flows are calculated for many years. A cash flow is receipts minus payments. It could be negative or positive. Initial investment is included as well as a negative cashflow since it was paid. These cash flows are discounted by some discount rate that is derived by other means.

The formula for DCF is;

DCF = CF1/(1+r) + CF2/(1+r)^{2} +…+ CFn/(1+r)^{n}

In the Capital Asset Pricing Model (CAPM);

ERi = Rf + βi (ERm−Rf)

ERi = expected return of investment Rf = risk-free rate βi = beta of the investment (ERm−Rf) = market risk premium

There is no need to fully understand all these sophisticated methods but just to get a vague idea on how the intrinsic value is calculated and perceive the conclusion. The intrinsic price of a stock depends on the estimated future cashflows and the discount rate. Future cash flows depend among other thing on earnings. These two concepts are closely related but not the same. Earnings depend on economy’s projection among other things. It is possible to have a very positive projection for the economy and a big drop in stock prices. How would such a thing be possible? One example is, if a big tax is introduced for big companies.

Another factor that affects prices is discount rate. The CAPM it is based on risk free rate Rf. The yield of a three month Treasury bill is often used. It is possible to have changes in interest rates and the prices not to move at all. This is because the markets have already anticipated the changes and included them in their calculations. So, to answer the initial question, stock indexes are affected by many factors and an important one is the prospects of the economy.

The discounted cash flow model can be used for investments and real estate as well. IRR (Internal Rate of Return) is the rate that makes the net present value of an investment equal to zero. Although it is not so correct theoretically, in practice it is used more often than calculating Net Present Value (NPV) by discounting with a different discount rate. IRR can be perceived as the return on the investment. In a loan or a bond, interest rate is constant. In an investment the return fluctuates, it is not constant.

Return on investment = net income / investment

Another way to approach the return of an investment is by the geometric mean.

(1+R1) × (1+R2) × (1+R3)× …×(1+Rn) = (1+R) ^{n} and solve the equation for R

One more think is worth mentioning.

Assets - Liabilities = Equity

This is a different value than market value and intrinsic value. It is a static value that does not take into account future cash flows. It is the value of the moment, if the company or the investment would cease operations. Assets should be calculated in market and not accounting values. Another way to make money is to find companies with market values lower than (Assets - Liabilities), stop operations, liquidate assets, pay liabilities and keep the profit. There has been some controversy though whether such a thing is ethical.