IMP Finance

Improving Investors' Outcomes in Financial Markets Worldwide

Welcome to Our Investment Guide

We help investors minimize judgment-based mistakes, and make intelligent decisions to invest and preserve the power of their capital for accumulating wealth for themselves and their future generations.

Understanding Investment Value

Understanding the value of an asset and the factors that determine this value is essential for making informed investment decisions. Valuation is a crucial financial tool that offers a framework for determining the investment worth of assets, companies, and investment opportunities in corporate finance, mergers and acquisitions, and portfolio management.

The core idea of fundamental analysis is that a firm's true value comes from its financial characteristics, such as growth creation, endogenous and external risks, and sustainable cash flows. Deviations from true value show potential buyers whether a stock is undervalued or overvalued, which does not mean at this point it is a good investment. Institutional investors in contrast to actively managed funds are not concerned with and do not estimate the investment value because most are passive investors following and buying mutual or index funds.

The index investing approach involves assembling, and then holding, a broadly diversified portfolio of common stocks deliberately designed to mimic the behavior of a specific benchmark index.

When it comes to investing, emotions are very real, in the sense that they affect people’s behavior and thus ultimately affect market prices.

Often investors begin with an economic assumption and then select stocks that fit within this great design for no one can predict economic changes any more than they have stock market predictive powers. Selecting stocks that will benefit from a particular economic environment inevitably leads to frequent adjustments and speculation, as portfolios must be continuously adjusted to adapt to changing economic scenarios.

No law says we must include every major industry within our portfolio, nor do we have to include 40, or 50 stocks in our portfolio to achieve adequate diversification.

The danger of purchasing too many stocks makes it impossible to monitor so many stocks' performance. Buying shares in a company without taking the time to develop a thorough understanding of the business is riskier than having limited diversification. What may go wrong with conventional diversification is that it greatly increases the chances an investor will buy something they do not know enough about.

The valuation process reveals a lot about how a stock is priced but also provides valuable insights into the determinants of value and helps us answer some fundamental questions.

The notion of buying stocks without understanding the company’s operating decisions, its products and services, employees’ relations, raw material expenses, plant and equipment, capital reinvestment requirements, inventories, receivables, and needs for working capital is unreasonable.

Business Principles

Every discipline has primary principles that govern and guide everything within corporate finance which are the investment strategy, the financing principle, and the dividend policy.

The investment principle determines where businesses invest their resources, the financing principle governs the mix of funding used to finance these investments, and the dividend principle shows how much earnings should be reinvested back into the business and how much is distributed to the business owners.

To maximize the value of a business, investment decisions must be considered in assets that earn returns greater than the minimum targeted rate of return reflecting the risk of the investment and the debt and equity capital needed to fund it. That return should make sense to the magnitude of expected cash flows and their time delivered, soon enough to justify the current interest rate.

The choice of the valuation approach will depend on our time horizon, the rationale for doing the valuation in the first place, and our beliefs about market efficiency, and if not, what form the inefficiency takes. Valuing a company using discounted cash flow and relative valuation models can yield different results.

We can use both discounted cash flow and relative valuation to value a company. Finally, the goal is to buy companies that are undervalued and if using both approaches, we benefit from market corrections both across time (which is the way you make money in discounted cash flow valuation) and across companies.

Valuation focuses on estimating investment value through fundamental principles rather than predicting market prices and to determine what one should pay for a security, not what one must pay. Investors typically purchase bonds at prices aligned with their expectations of future purchasing power.

Responding to Value Uncertainty

Types of Uncertainty

The future seems very esoteric in nature because people must learn to perceive things they cannot understand or comprehend.

When valuing firms, uncertainties can arise from company-specific actions or a lack of reactions to broader macroeconomic developments.

The valuations range across the spectrum from mature to high-growth companies, from developed to emerging markets, and from periods of stability to periods of crisis for they all require estimates for the future, and all of these estimates are made through the perception of uncertainty.

Micro uncertainty can often be mitigated by getting adequate information about the business of our interest and improving models and is also much more easily eliminated in a portfolio, since for every company that performs badly than expected, there will be another that performs better than expected.

The risk and return models designed for the establishment of appropriate discount rates account for macroeconomic risk exposure, assuming diversified investors. When facing uncertainty, minimizing valuation inputs and focusing on crucial aspects can be more effective than adding detail.

Incorporating uncertainty into the discount rate can be problematic, especially for firm-specific or latent risks. Firm-specific risks may be already diversified away in a portfolio, thus pushing the discount rate up to incorporate the risk will reduce value needlessly, while latent risks, with potentially significant impacts for investors, are harder to adjust for in discount rates.

Investment Worth and Market Price

What determines the value of a stock? The challenge is to explain the current price of a stock and what the appropriate price should be if we intend to purchase it. Before questioning the price of a security, we must understand how the current price is formed.

This distinction between investment value and market price is crucial. Business conditions often move ahead of stock prices, driven by 'orders received' or bookings, which lead to all other business cycle series.

Orders are recorded by managers before goods are manufactured, indicating that orders move first, business volumes next, and interest rates last.

Stock prices follow this momentum. Consequently, business orders are a better forecaster of stock prices and lead all other series in the business cycle.

The Logical Theory of Market Prices and Changes

What would investors do if they were perfectly rational? They would not pay more than the present value of future cash flows and also would not pay less, assuming true price in perfect competition with all traders equally well-informed.

It would also mean that market pricing wouldn't distort the purchasing power of money, as prices would reflect true value, ensuring that money's worth remains stable and consistent over time.

New information enters the stock market for all participants, but not all have the same expertise to interpret it right and quickly. Because few understand the current reality, big stock price changes do not occur instantaneously, and a large volume of trading takes place during that time.

The stock market reflects opinion rather than fact, as investors can only estimate values without absolute certainty. Market participants are divided into investors and speculators, neither of whom solely determines stock prices; instead, the security holders set the price. Hence, marginal opinion dictates market prices.

Some investors think that the money supply determines the price of stocks, however, the quantity of money alone does not guarantee that stock prices will rise. The sentiment and perceived value does. If investors believe that a stock is overvalued or does not offer a good future gain relative to its risk, they will avoid it, regardless of how much money is circulating in the economy.

When we talk about loans on stocks issued by a bank, investors, or non-bank institutions to another investor that might increase stock prices through leverage, these loans are bank assets, while demand deposits and currency are bank liabilities. Because these loans do not create bank deposits, they do not directly increase the money supply in the economy. Instead, they represent a reallocation of existing funds from the lender to the borrower.

So, the debasement of money through increased goods, services, and commodities prices will indirectly affect the cost of production, pushing selling prices, wages, and expenses up, thus causing stocks to rise and cost more in terms of depreciated money. Thus, the present value of future cash flows must be adjusted for the expected changes in purchasing power of money.

Potential investors might accept or reject the market quote if it exceeds what expected cash flows (dividends and stock buybacks) justify, opting to wait for a price adjustment. The bid and ask quotations reflect the opinions of the most optimistic buyers and the least optimistic sellers

Technical analysis theorizes that past share prices are key to future prices, but predicting market movements remains speculative and unreliable.

Speculators who rely only on price changes because short-term traders do not receive dividends must be able to foresee those price changes that coincide with the changes in the opinions of other market participants.

The current opinion may change in both right and or wrong direction, where the market price and the value of a stock may diverge greatly. Since the opinion is formed through the news, the task of forecasting opinion is resolved through forecasting the news, thus the movement of prices.

Value investing, recognizing the impossibility of precise price forecasts, offers a prudent and consistent strategy across various market conditions.

Efficient Market Hypothesis

Multiple market hypotheses, such as efficient or inefficient markets, random walk, and momentum, coexist. Each reflects how market participants respond to external influences and the global economy. Stock prices often diverge from underlying value

due to short-term supply and demand forces, influenced by various motives of buyers and sellers. This divergence highlights the market's inefficiencies.

If we say markets are efficient, then we say participants in the markets do not make mistakes; they exactly perceive facts and interpret public as well as private information in a similar manner. It would be strange if all markets were permanently efficient to all investors regardless if they are speculators or long-term investors.

In fact, investors who beat the market through their investment strategies make the market efficient for the market adjusts to their returns.

Those who believe that markets are efficient may still assume that valuation could contribute, especially when they value the effect of a change in a firm's management or understand why market prices change over time. Other investors skeptical of market efficiency consider that markets make mistakes and invest on that basis must believe that eventually markets will fix them and recognize that finding these mistakes requires a combination of skill and luck.

Valuations are open for subjective judgments and the final value we obtain from these models through the inputs used brings a lot of bias in the process.

The Basics of Intrinsic Value and Investment Process

Psychology plays a crucial role in market dynamics. Given the uncontrollable and unique nature of the market's events, an investment philosophy should be intuitive and adaptable rather than rigid. Exceptional returns are found by diverging from market consensus and exploiting inefficiencies, imperfections, and mispricing.

The key to successfully investing and managing assets lies in understanding not only what the value is, but the sources of the value.

Even after the most careful and detailed valuation, there will be uncertainty about the final numbers, influenced by assumptions we create about the future of the company and the economy. It is unrealistic to expect or demand absolute certainty in valuation since cash flows and discount rates are estimated. This also means that investors and analysts have to allow for a reasonable margin of error.

The problems do not arise from the valuation models we use, but from the difficulties we face in making estimates for the future. However, some models are more complex, and the inputs required to value a business increase, which brings more potential for errors.

Valuation is inherently subjective. Any notions and biases an analyst brings to the process will influence the resulting value.

Separating the information that matters from the information that does not is almost as important as the understanding that models do not value companies; we do.

In discounted cash flow valuation, our goal is to estimate the intrinsic value of an asset based on its fundamentals. Many discount cash flow models exist and some claim they are better or more sophisticated than others, but we aim to estimate where those cash flows go, whether they are distributed just to shareholders in the firm or to all equity, bondholders, and preferred stockholders.

Are we valuing the entire business or just equity, the two ways we approach valuing a firm? When considering a company for a potential investment we have two choices to value the business.

The first approach is if we value the entire business, where we estimate cash flows to both debt and equity investors before considering the debt payments.

To find the present value of the expected cash flows, we discount them back at the cost of capital (equity and debt investments), the weighted average relative to the required returns of equity investors and bondholders.

The other way of valuation is estimating the value of equity, the cash flows only to equity investors after the debt payments of interest and principal are paid and discounting those cash flows at the cost of equity or the return the equity investors require to invest in the business.

The purpose of using free cash flow calculations is to understand the company's past performance of cash inflows and outflows in operating, investment, and financial activities. To estimate the expected free cash flows in the future, a key ingredient for intrinsic valuation we need a basis for our forecast, and the way we compute free cash flows may differ from the way we computed free cash flow for explaining the past.

The accounting statement of cash flow purpose is not to provide information on free cash flows to equity, or what the company can afford to pay out to shareholders. This can have different consequences for the firm's cash balance, whether it is below or above the free cash flow number.

Correcting accounting inconsistencies will make the book values of companies in sectors such as service, technology, and pharmaceuticals more realistic. However, this will not address the fact that accounting is not meant to estimate the value of future growth, nor should it attempt to do so.

Using free cash flows in valuation is different than just looking at the cash flows in the past since it has no relevance to the value today. Instead, we use it as a base year from where we build our forward-looking forecast. In this case, we will need to eliminate any unusual and extraordinary items, something that happened that year, but we do not expect to recur in the future.

For instance, the change in working capital item is a recurring but very volatile metric, and using last year's number might be a bad indication, therefore we can normalize it by computing working capital as a percentage of revenues.

The non cash working capital as a percent of revenues can also change from one year to the next, and the most appropriate approach would depend on whether the company's working capital is volatile and unpredictable and how we assume its expected revenue growth in the future, as well as, how efficiently the company manages and can reduce working capital as a source of positive cash flows not only in the near future but for a longer time.

In case of negative non-cash working capital, a firm can use supplier credit as a source of capital in the short term and can be seen as a cost-efficient strategy, but in the long term bears potential downsides, and is perceived as a sign of probable default risk.

The conventional definition of working capital is the difference between current assets and current liabilities. Cash and marketable securities represent a fair return on riskless investments and unlike inventory, accounts receivable, and other current assets (which earn a rate above the riskless rate), for valuation purposes should not be included in measures of working capital.

We will also back out all interest-bearing debt, the current short-term and the portion of long-term debt due now, from the current liabilities. This debt will be considered when computing the cost of capital and it would be problematic to count it twice.

Many companies and analysts treat stock-based compensation and acquisitions using the company's stock as currency as if they are not an expense for the firm or cash flows when adding them back. When a firm gives shares away instead of paying cash, the impact on equity investors will make their equity less valuable.

Whether the firm buys growth through acquisitions with stock or cash this is a reinvestment that will reduce expected free cash flows to shareholders. A normalized net capital expenditures estimate must consider long-term internal investments in capital goods and external investments in acquisitions. Ignoring the costs and the growth that comes from acquisitions and benefits will result in the misevaluation of a firm that has established a reputation for growing through acquisitions.

Free Cash Flows to Equity and Potential Dividends

The value of equity is determined by discounting the expected cash flows to equity, which are the remaining cash flows after covering all expenses, reinvestment needs, taxes, and interest and principal payments. This discounting is done at the cost of equity, which represents the rate of return that equity investors require from the firm.

The dividend discount model is based on the assumption that the only cashflows received by stockholders are dividends.

Purchasing shares of publicly traded companies is a direct measure of tangible cash flows, and estimating its intrinsic value is the actual dividends paid to equity investors if we use the dividend discount model as a special case of equity valuation.

When estimating cash flows, many people focus on cash flows after debt payments (free cash flows to equity), as they see themselves as business owners buying shares and consider interest and debt repayments as cash outflows.

However, some companies do not pay dividends; some return cash to shareholders through a share buyback mechanism, and others use both dividend policies.

As investors we want to estimate the collective free cash flows returned to shareholders in the form of dividends and stock buybacks.

Earnings are a means to an end, not the ultimate goal. Therefore, a stock derives its value from cash flows and its ability to translate earnings into sustainable cash flows.

If earnings are not paid out as dividends are successfully reinvested at compound interest for the benefit of shareholders, then these earnings should produce dividends later; if not, money is lost.

The question is what level of earnings is needed to generate a dollar of dividends? True value depends on the distribution rate of earnings (payout ratio), and that rate is determined by the reinvestment needs for running the business.

Dividends and buybacks, while both methods of returning value to shareholders have contrasting effects, particularly in terms of who benefits and how. A dysfunctional dividend policy, particularly one that prioritizes high dividend payouts over strategic investments, can have negative consequences for a company.

Dividends should be the final step in the business process as they represent residual cash flows or potential dividends the company can afford to pay after the reinvestments for future growth are made and calculated for the net effect of the debt payments and new debt issues, or retained as cash reserves.

A business's dividend policy depends on the company development stage and transition period from a young company to a fast-growing firm, eventually maturing into an established enterprise. As buybacks can only redistribute value, the push of share buybacks has been ignited by debt financing contributing to heavily leveraged companies to satisfy the demands of greedy, short-term shareholders.

Adding more debt will increase the firm's cost of capital and its exposure to default risk, conversely by using cash it will decrease its cash balance. In both cases the company may invest less in its operating businesses, thus affecting their value.

The implications are straightforward and based on common sense. While a buyback or dividend alone cannot affect a company's value, the funding method and the investments it substitutes can determine whether certain value is ultimately added or destroyed.

As investors we want to understand how the management acts in the interest of shareholders that ensures all shareholders benefit proportionally to their ownership stake in the company. However, through buybacks only shareholders who choose to sell their shares back to the company receive the predetermined buyback price. Who is the management valuing more, the shareholders who remain in the company or those who sell their shares back, and why do they separate them in this way?

When buying back stocks at a price much higher than its intrinsic value there is value redistribution from the shareholders in the company to those who sell their shares back. If the management is shareholders-centered, buying back shares below the intrinsic value protects the interests of and delivers value to their ongoing shareholders.

We may assume that all reinvestments of undistributed earnings are promptly reflected in the company's market value and this company would have paid most of its earnings in dividends to its stockholders and obtained the needed cash for expansion through the issuance of additional stock. A similar company in the same industry, with a similar dividend payout rate, pays out only a small portion of its earnings as dividends and uses the remaining earnings for expansion.

To estimate the free cash flow to equity we start with net income from the cash flow statement and subtract what the company is reinvesting into long-term assets including acquisitions, we net out depreciation and amortization from capital expenditures to find the net capex, and we also subtract the change in non-cash working capital or reinvestments into short-term assets captured in working capital.

All non-cash charges like amortization and depreciation as well as Goodwill impairment are added back to net income. We add them back in because we previously subtracted them to get to earnings but it was not a cash expense.

Unlike the retention ratio used to estimate the expected growth rate in dividends, we replace the retention ratio with the equity reinvestment rate, which measures the percent of net income invested back into the firm.

The reinvestment rate depends on whether the company is a matured business that relies more on existing assets or is a rapidly growing business with much higher reinvestment requirements to gain future growth. The more the company reinvests the less there will be left over to pay in dividends.

Finally, we add the new debt issued, which is a cash inflow into the company, and subtract the interest and principal payments as a cash outflow. We end up with cash available for equity or potential dividends the company could have paid to shareholders.

After subtracting the reinvestments from the net income, we get to the FCFE before the debt cash flows or the amount before calculating the debt raised by the firm and the debt repaid. This step gives us a preliminary measure of cash available to shareholders (FCFE). However, it doesn't yet consider the impact of debt.

If the firm has no new debt issued but the repaid debt is higher than the amount of FCFE before debt cash flows, the debt effect will have negative FCFE for the year. A negative FCFE due to high debt repayment can signal a lack of cash for dividends or buybacks in the short term. However, it's crucial to analyze the context. The company might be prioritizing long-term financial stability by aggressively paying down debt.

Companies with large positive FCFE have the financial flexibility to consider dividends, share buybacks, or other uses for the cash.

The specific actions depend on their long-term strategic goals and investment priorities. It is important to distinguish between ability and action. A large positive FCFE indicates the ability to pay dividends or buy back stock, companies don't necessarily have to do so.

While the dividend distribution rate tells us the portion of earnings paid out as dividends, the cash flow available for dividends and stock buybacks measures the total cash returned to stockholders as a proportion of the free cash flow to equity. This distinction helps us understand not only the earnings distributed as dividends but also the overall cash returned to shareholders, including stock buybacks.

By understanding both the dividend distribution rate and the equity reinvestment rate, we can get a complete view of how a company uses its net income—whether it reinvests in the business or returns cash to shareholders.

Some firms need to finance their dividend payments, either from existing cash reserves or by issuing new stock or debt, others pay less than they can.

Accounting Inconsistency

In intrinsic valuation, where the objective is to get the best estimates possible for the future, we have a great deal more flexibility and discretion in which items to include or ignore in computing free cash flows, and how we estimate item value.

To estimate cash flows, we usually begin with a measure of earnings from accounting statements, but accounting earnings for many firms show little or no resemblance to the true earnings of the firm.

The rule for estimating, both operating and net income used as a base for projections should reflect continuing operations. It should not include any items that are one-time or extraordinary.

The accounting measures of earnings can be misleading because operating, capital, and financial expenses are sometimes misclassified. For instance, accounting has miscategorized R&D and operating leases as operating expenses, when the former is a capital expenditure and the latter a financial expense. As a consequence, the balance sheets of firms with substantial R&D and operating lease expenses may fail to reflect the assets created by these expenses, and the book value will be understated.

For an operating expense to be capitalized, there should be solid evidence that the benefits from the expense accumulate over multiple periods.

When converting the R&D expenses we first have to determine their amortizable lifetime for the research investment that has been expensed to deliver the targeted income or payoff. If the research investment assumes to generate future growth and earnings is treated as a research asset that after calculating amortization, its value will augment assets, capital, and book value of equity once research expenditures are capitalized.

The R&D estimate as capital expenditure will have a serious effect on the firm's profitability, earnings, and return on capital. The capitalized R&D number, which is the difference between the current year R&D expense and amortized R&D expenses from previous years, will increase the operating and net income of the firm.

The sum of values of unamortized R&D expenses from prior years is the value of research assets that would be added to the book value of equity for computing return on equity and capital measures.

The higher value will also provide a larger leeway for the firm's reinvestment needs. The higher reinvestment rate adjusted for net capital expenditures and the capitalized R&D expense to adjusted after-tax operating income increases the expected growth rate for the firm and affects its return on capital.

We also calculate the effect on after-tax operating income by treating R&D expenses as capital expenditures. This adjustment reflects the tax benefit the firm gains because the revenue code permits the entire R&D expense to be deducted for tax purposes, unlike other capital expenditures.

The right treatment of R&D expenses as capital expenditures is vital for the assumptions we make about growth in terminal value estimates and being consistent with assumptions about reinvestment rates and returns on capital. If R&D is expensed the computed reinvestment rate will not incorporate the research and development investments.

The company's FCFE from the financial year accounting statement may look very different from the company's normalized FCFE estimated for valuation purposes.

Free Cash Flow to the Firm

The value of the firm is estimated by discounting the expected cash flows to the firm. These cash flows are the remaining amounts after covering all operating expenses, reinvestment needs, and taxes, but before making any payments to debt or equity holders. The discounting is done using the weighted average cost of capital, which reflects the cost of the different financing components used by the firm, weighted according to their market value proportions.

Valuing the entire business, we estimate the cash flows to equity and debt holders they receive from the company. To compute the FCFF we start with the operating income before interest expenses and act, adjust it as if taxes were paid on that operating income. The pre-tax operating income provides a standardized starting point for the calculation, regardless of a company's specific tax rate. To arrive at the total cash available to both equity and debt holders, we need to factor in this tax expense.

Then we subtract the same reinvestments we computed in the context of free cash flow to equity which gives us the cash available to all claim holders.

Consequently, it is a pre-debt cash flow but after taxes and reinvestments. However, the tax rate the firm pays each year might be different for each year because the firm can carry over taxes from previous years.

The FCFF, in this case, is a big positive number compared to the same-year calculation when we computed the FCFE and arrived at negative cash flow to the equity.

Since FCFF is a pre-debt cash flow we see a positive cash flow before debt payments and recognizing the difference is a starting point. Valuing the business's FCFE and FCFF for the previous years we collected data from the company's financial statements.

However, the investment value of the business has nothing to do with these numbers as it is about projecting them in the future and smoothing out variables like the effective tax rate. To address this, we may consider using the average tax rate over time and apply the same approach to other variables in our valuation process. Although the effective tax rate can be used to arrive at the after-tax operating income in the early years, the tax rate used should converge on the marginal tax rate in future years.

For businesses to generate future growth they have to reinvest back into the company and the reinvestment rate is the percentage of the after-tax operating income reflecting that growth. Subtracting the FCFF number from the after-tax operating income gives us the reinvestment value, which we divide by the after-tax operating income to get the firm's reinvestment rate for the year.

A higher reinvestment rate generally suggests that a company is prioritizing future growth, but a higher rate might be not justified if the investments are poor or unproductive, therefore we have to assess the risk rate associated with those cash flows expressed through a discount rate in our evaluation model.

Stable earnings are attractive but may not translate to safer investments. Firms can have an even bigger impact on the book value of equity when they take restructuring or one-time charges.

Companies with stable earnings can still be volatile investments and may offer little growth potential, thus creating a trade-off between stable earnings and high growth. News not related to earnings but about management changes, macroeconomic news, interest rates, and information released by competitors in the same business can all drive stock prices to move even when earnings do not.

Risks and Accounting Principles

The accounting measures of risk only provide disclosures about potential obligations or losses in values designed to warn potential or current investors of the possibility of a company's default or the financial ratios that measure profitability, risk, and leverage.

Some accounting measures can be easily manipulated by firms at the time of financial reporting to give the illusion of safety.

For instance, accounting statements provide extensive historical data about the company's past investments or assets in place but very little information about new investments or assets that will generate future growth.

The discount rates we use reflect the riskiness of the cash flows where the cost of debt includes the default spread and risk and the equity risk premium in the cost of equity. The company's default risk depends on its financial obligations including interest and principal payments and the potential to generate high cash flows from operations to cover those payments, therefore more stable businesses with predictable cash flows will have a lower default risk than cyclical companies with volatile cash flows.

Investment involves uncertainty and risk, making risk management essential. Risk encompasses potential events that may not occur. To manage risk, investors must understand risk, recognize when risk levels are high and control risk effectively.

While returns are important, limiting risk is crucial. Higher risk does not inherently lead to higher returns; instead, it often results in losses. Risk assessment involves analyzing the potential loss probability and magnitude, often summarized by beta.

Understanding the relationship between price and value is vital for managing risk. High-quality assets do not always equate to high-quality investments, as price is a critical factor.

Efficient markets may still offer high-return, low-risk opportunities, especially where information asymmetry exists, or investors trade for non-value-related reasons.

Overvaluation is common due to speculative behavior, making it difficult for market forces to correct. Brokers may also offer overpriced investments without legal obligation to ensure fair pricing.

It is a simple fact that the current market values of different types of securities reflect the collective opinions of a vast number of investors studying these conditions as to what the future holds in store. When the majority believe the outlook is improving, prices rise; conversely, when most believe the outlook is becoming more uncertain, prices fall.

Although it would be risky to base an investment program on the ability of even the most renowned forecasters to predict immediate movements in stock prices, commodity prices, and interest rates, we can still recognize a major depression in stocks or bonds if and when it occurs.

If we maintain a moderate portion of our funds in cash or equivalent assets until that time, we could then buy securities at significantly lower prices than those before the drop.

The investors' objective is to maintain and increase their relative wealth and purchasing power, but there are two obstacles to the achievement of this goal.

The fluctuating purchasing power of money and constant increase in standard of living. The first essential for sound judgment in investment management is unbiased knowledge of past experience. But if all our reasoning and insight into the future are based upon a faulty belief of past experience, our conclusions also are almost certain to be incorrect.

Equity Risk Premium and Estimation

The equity risk premium represents the return expected from investing in stocks over risk-free rate securities, serving as a key component in determining the cost of equity and capital.

Equity risk premiums measure the price of risk in the equity market, the price driven by risk and greed and are conventionally established through a long period of the company's history providing an estimate of how much investors would have earned on average above the average risk-free investment return.

As these expectations evolve, the implied ERP would also change. This historical risk premium is a backward-looking static measure. An alternative estimate of ERP is a forward-looking dynamic approach based on what price investors pay for stocks now and what expected cash flows are and where the company's operations are not where it is incorporated.

A company based in the US but generating a significant portion of its revenue from various geographic locations with different country-risk premiums than the US equity risk premium. The company's exposure to that risk must be incorporated into the equity risk premium estimate.

Many firms that do business globally derive revenues from multiple locations so we can break down the company's operations for each country it operates based on revenues and an estimate of the weighted average risk premium for those regions.

Any investor can invest in riskless securities and make risk-free returns for a specified period with certainty, regardless of their skills, knowledge, luck, or investment approach. Everything above that riskless rate is the actual performance in nominal terms of an investor relative to the risk incurred.

When performing discounted cash flow valuation, we have to approximately estimate the additional risk exposure above the riskless security rate and decide which risk premium to use in our valuation determined by both our market views and the valuation task.

Cost of Equity and Betas

The expected return for equity investors includes a premium for the equity risk, known as the cost of equity. Similarly, the expected return for lenders includes a premium for default risk, known as the cost of debt. When considering all financing raised by a firm, the overall cost would be a weighted average of the costs of equity and debt, termed the cost of capital.

The most common practice used by most beta estimation services is to estimate the betas of a company relative to the market index where the stocks are traded. While this practice may deliver a reasonable measure of risk for an investor diversified through specific regions, it may not be the best approach for the globally diversified investor, who would benefit more from a beta estimate relative to an international index.

When an index is dominated by one or a few companies, the betas estimated against that index are unlikely to be true measures of market risk. They are likely to be close to 1 for the large companies and wildly variable for all other companies.

The beta estimates from different services will be different for the same firm at the same point in time. It is backward-looking with large standard errors and assumes the past is a perfect predictor of the future. We use past data to understand a company's business model, historical performance, and current competitive position not to extrapolate it in the future.

Using historical data for firms under restructuring can give a misleading picture of the firm's value, future cash flows, and risks for the ongoing changes in their capital structure and dividend policy.

The market is a dynamic environment, and random events can significantly affect a company's performance as a historical beta might not reflect its risk if we are in the middle of an economic disaster.

The beta of a firm is determined by three variables which are the type of businesses the firm operates in, the degree of operating leverage of the firm, and the firm's financial leverage. Although we may use these determinants to find betas in the capital asset pricing model, the same analysis can be used to calculate the betas for the arbitrage pricing and the multifactor models as well.

Firms with competitive advantage have higher flexibility and potential to reduce their operating leverage than smaller firms with higher growth potential and fixed costs coming from higher investment needs to generate that growth.

Bottom-up beta, as a better solution as the name suggests, estimates a company's beta by considering the business fundamentals and the risk profiles of similar companies within the industry.

To estimate the bottom-up beta we consider the betas of all publicly traded companies in the sector thus calculating the average beta in addition to the market debt-to-equity ratio, the effective tax rate, and a measure of operating leverage.

Should the beta for a company operating in a specific sector in a developed market be comparable to that of a company operating in an emerging market within different market risks?

The unlevered beta of a firm is determined by its assets - products, services, and whether it is a cyclical business or a discretionary sale potential, and its operating leverage where the levered beta includes the amount of financial leverage risk.

It also allows adjusting the beta for the firm's debt-to-equity ratio into the final beta calculation. The unlevered beta is adjusted using the company's market debt and market equity and the marginal tax rate to arrive at a levered beta (reflecting both business and financial risk).

This approach is useful for companies that have undergone significant changes in their business mix or recently entered new markets that will reflect the beta. The sector beta is more precise than an individual regression beta because averaging across many betas results in averaging out our mistakes.

The beta over the period reflects this average financial leverage or debt-to-equity ratio, which may differ each year, thus providing a different measure of levered beta.

If a firm changes business activities through acquisitions or closes a portion of its operations and plans to change the debt-to-equity ratio, beta can be adjusted to show these changes.

Taking an average unlevered beta number through different D/E ratios captured from the debt-to-capital ratio where an increase in debt will increase the levered beta and the cost of equity. More debt load will cause an increase in default spread and a decrease in credit rating, thus increasing the pre-tax cost of debt and interest expenses.

Therefore firms have to find an optimal debt ratio, which is the point at which firm value is maximized and based on their current financial position and future investment planning for expansion to decide how rapidly or gradually they should move to its optimal level to get optimal operating income results, or to decrease the leverage and default risk if the current debt ratio is much higher than the optimal.

For instance, the change in equity value related to the dividends and stock buyback policy and the expected equity price appreciation will affect the debt ratio in conjunction with whether the value changes down or upward.

The risk premium used to estimate the cost of equity for the emerging market company will include a country risk premium in the estimate, whereas the cost of equity for the established market company will not. Thus, even if the betas used for the two companies are identical, the cost of equity for the former company will be much higher.

Once we have estimated the riskless rate, the risk premium(s) and the beta(s) we can now estimate the expected return from investing in equity at the firm.

Cost of Debt

The principle is that the cost of debt is the rate at which a company can borrow money today for long-term; short and long-term debt and effectively treating all debt as if it were long-term for our valuation today, and what would be the cost to buy a company at today's interest rates.

Therefore, we start with the risk-free rate, the government bond rate and then we add a default spread for the company reflecting its likelihood of not paying its debt obligations.

Some companies have a bond rating, although not always reliable, issued by rating agencies and we can use it as a proxy for default risk and estimate the default spread. The company's debt rating yields a default spread added to the risk-free rate to get the pre-tax cost of debt.

The rating rate used should be for the whole company issued by the agency, not the rating for an individual bond for even a risky company can structure and issue a safe bond, and estimating the cost of debt based on that bond's rating will underestimate the overall cost of debt.

If there is no available rating, we can examine the financial characteristics and ratios of rated companies starting with the interest coverage ratio, which is the operating income divided by the interest expense, thus we can estimate the synthetic rating and default spread of the company that we use in the cost of debt calculation. The default spreads are obtained from traded bonds. An emerging market firm may be unlikely to achieve the interest coverage ratios of companies in developed markets.

However, synthetic ratings and interest rates in emerging markets may differ from those in a mature market for instance the US and in such a case we add to the risk-free rate and default spread of the business the default spread of the country.

To be consistent with our valuation we also consider the other sources of financing for a firm, the cost of hybrid securities - preferred stock and convertible bonds. The costs of those securities can be calculated separately if special features are added to the issuance contract or we can estimate their debt and equity components independently and incorporate them into the WACC formula.

The straight bond component is treated as debt and has the same cost as the rest of the debt. The conversion option is treated as equity, with the same cost of equity as other equity issued by the firm.

Before determining the weights, we must define what constitutes debt and what to include and exclude in our debt calculation.

Not all liabilities like accounts payable and supplier credit are considered debt, as they are not interest-bearing obligations, therefore we will include only interest-bearing debt liabilities and both short-term and long-term borrowings.

We will also capitalize operating leases and treat them as conventional debt because a lease agreement with fixed annual payments has a similar commitment as an unsecured debt in equal annual installments.

Converting operating lease expenses into a debt equivalent by using the firm's current pretax cost of borrowing as a discount rate yields a good estimate of the value of operating leases. We discount these future operating lease commitments back at the firm’s current pre-tax cost of debt to arrive at the debt value of these commitments.

Consequently, if the lease commitments for previous years are converted into debt and capitalized, they must be recognized as an asset in the balance sheet and a liability for the lease payment each year. Thus, we add the present value of operating leases to the debt outstanding to arrive at a total market value for the firm's debt or the adjusted debt for the firm.

We add back to the reported operating income the operating lease expense in current year and subtract the depreciation of a leased asset to calculate the adjusted operating income.

Alternatively, we can approximate an adjusted operating income by multiplying the present value of operating leases by the pre-tax cost of debt and adding the number to the reported operating income.

The capital leases are treated like assets owned by the firm and the firm can claim depreciation on the asset and the annual lease payment is computed as an imputed interest expense assumed as a debt payment.

Therefore, if we estimate the capital leases for five years we have to consider the lease payment for each year, to compute the present value of lease commitments at the pre-tax cost of debt rate using a present value of annuity formula. The correct formula for the present value of an annuity takes into account the time value of money by appropriately discounting each lease payment to its present value, summed up over the entire period.

Based on the present value of lease obligations we estimate the annual lease expense multiplied by the pre-tax debt rate.

These expenses, the annual interest expenses, and depreciation would be recorded in the company's income statement as part of the financial implications of the capital lease. The interest expense will decrease over time as the principal is paid down, while the depreciation expense remains constant if using the straight-line method.

The conversion from operating to financial expenses will affect the operating income, invested capital, and the cost of capital through the increased debt component in the debt ratio, though the equity part remains unaffected. As capital increases by the present value of the operating lease, the operating income decreases but only by the asset's depreciation, thus affecting the return on capital.

Now that we have the present value of the lease commitments, we can use it in any subsequent financial analysis, such as adjusting operating income to reflect the lease obligations, calculating the reduction in lease liability, and the effect on taxes. The depreciation expense on the asset and imputed interest payment on the lease according to the company's jurisdiction, accounting standards, and tax laws will create a total tax deduction benefit for the firm.

To understand the actual impact of a conversion we can compare the return on capital with operating lease treatment to the return on capital after lease adjustment.

Once we have the costs of debt, equity, and hybrid securities, we have to estimate the weights that should be attached to each. The weights should be based on market value rather than book value because the cost of capital reflects the current cost of raising funds through issuing securities.

For instance, the market values in the cost of capital are the cost of acquiring the company in the marketplace today, where we will have to pay the existing market prices, and the intrinsic value is the judgment on what the shares are worth.

In our forecasts we allow debt ratios to change over time and thus changing weights on debt and equity will also mean that the costs of equity, debt, and capital will change too.

Using the market value of the debt or its book value will give us different debt-to-equity ratios and thus will harm the estimate of weights on each of these components in the cost of capital as they reflect their market value proportions and measure how the existing firm is being financed.

The cost of debt must be adjusted for the tax benefits at the marginal tax corporate rate, the higher the tax rate the larger the benefits. Why do we net out the tax effect, because interest expenses are tax deductible, thus the after-tax cost of debt, will be the rate we will use when calculating weights of debt ratio and cost of capital.

If there is insufficient information about the company's debt maturity we can convert the book value of interest-bearing debt into a market value of interest-bearing debt by estimating the present value of interest expenses treated as coupons in an annuity calculation and the present value of the book value of debt discounted back from the averaged maturity at the current market price on debt. By combining the two present values we can approximate the market value of the company's short and long-term interest-bearing debt obtained from the balance sheet.

Cost of Capital

Businesses raise financing from three sources: equity, debt, and preferred stock and the cost of capital is defined as the weighted average of each of these costs based on the market values of each component. The cost of capital gives us information on how equity investors sense the risk of investing in the business and lenders' awareness of its current default risk.

The distinction between debt and equity, from a corporate finance standpoint, comes down to the characteristics of the cash flow claims associated with each type of financing. With debt, cash flows are contractual claims set up at the onset, and failing to meet those obligations can lead to bankruptcy or a probable loss of control over specified assets or even worse.

The cost of capital will be the weighted average of preliminary estimated debt and equity ratios with the cost of debt and equity as inputs calculated by combining the cost of equity and the after-tax cost of debt, weighted by their proportions in the company's capital structure.

Analysts often add premiums, some based on history, some on emotions, and others forced by bias, but ultimately it must be estimated consistently and viewed as a dynamic factor running with the macro conditions and business change. Illiquidity is probably the least understood and the most confused aspect of valuation and corporate finance. It is not just how illiquid an asset is that matters but when it is illiquid.

Once computed, it yields a hurdle rate in corporate finance for the management considering investment risk in new projects and a discount rate for investors to use in the valuation of the business's risk and its investment worth. To calculate the cost of capital we first need to calculate the cost of equity using our estimate of the risk-free rate, the beta of the firm, multiplied by our equity risk premium rate. The currency we use to estimate the cost of capital has to be consistent with the currency of the cash flow forecast.

The risk-free rate is the starting point and the risk premium is the fundamental and critical component in valuation and portfolio management.

A risk-free investment requires a no-risk potential that the issuer of the security will default on their contractual commitments. A short-term risk-free rate will not be a risk-free measure if our time perspective is long-term, for the cash flows from that investment will need to be reinvested back at different uncertain rates for future growth.

Additionally, it should be determined whether the rate is real or nominal based on whether the cash flows are estimated in real or nominal terms.

The risk-free rate for calculating the cost of capital is the long-term government bond if the government that issues it is a risk-free entity.

The government bonds are riskless in the sense that they will certainly be paid off in legal tender because the government is in control of new money creation and can always meet its obligation in the sense that its credit rating does not depend on its taxing power, but only on its power to create fiat money.

What will be the purchasing power of these coupons and the principal and what interest rate should be used in discounting this purchasing power? When lenders expect a decrease in money purchasing power they need to demand a higher interest rate to compensate for the depreciated money.

If the issuer of the government bond is a latent default entity, the risk-free rate must be adjusted by netting out the default spread of the risk-free rate. This calculation is often used in the context of emerging markets or countries with higher perceived risk. It adjusts the government bond rate to reflect what the rate would be if there were no default risk, thus providing a more accurate measure of the risk-free rate.

The country's actual bond rating reflects the default spread for that rating. If we cannot find a government bond rate or do not trust the government rate, take the US dollar risk rate as a basis and add to it the estimate of the difference between the inflation rate in the local currency and the inflation rate in the US dollars, where the total will be our risk-free rate.

Growth Evaluation

The value of a firm is the value of its existing assets and the value of its future growth generated through those old investments and new assets. The higher expected growth for a firm can come from either excess returns from competitive advantage gained over time like a well-known brand or reduced production costs, as well as specific advantages like licenses or product patents.

For the entire business, this estimates operating income growth, while when valuing the equity part, it focuses on equity income growth (net income or earnings per share).

Young companies derive the bulk of their value from growth assets, whereas more mature firms get their value from assets in place.

The value effect of growth depends on the efficiency of the reinvestment generating that growth. Return on invested capital serves as an indicator of growth quality. As growth will require reinvestment, the value effect of growth will depend on whether and how efficiently that growth is generated. The same growth is more valuable with less reinvestment than with more.

The historical growth rates for the same company can vary, depending on computational choices of how far back to go, which measure of earnings (net income, earnings per share, or operating income) to use, and how to compute the average (arithmetic or geometric). Again, if we are focused back on the past growth rates and try to extrapolate them into the future, we assume that the business will grow at similar rates regardless of the business's development from a small to a large company and market changes.

Once we shift our focus to the company's fundamentals, we can tie growth to how much and how well the business reinvests, the reinvestment rate of the after-tax operating income to generate future growth in operating income. With equity earnings, we measure reinvestment as the portion of earnings not paid out as dividends (retention ratio the percentage of retained earnings) and use the return on equity to measure the quality of investment.

Growth in Equity

Growth is the key input in every valuation and the relationship of growth to fundamentals will depend on what growth rate we are estimating.

The net income expected growth is determined by the equity portion reinvested back into the business and the return on equity estimated based on its book value, which is affected by how much debt level the firm chooses to fund its projects. Generally, increasing debt can lead to a higher return on equity if the after-tax return on capital exceeds the after-tax interest rate paid on the book value of debt.

We can estimate the expected growth rate if the improvement in return on equity is only on existing assets, or if the growth comes from new investments where additional growth is generated.

The growth in net income and earnings per share growth can differ because firms can issue new equity money to fund new projects, therefore we need to capture that growth and measure the investment that goes beyond retained earnings.

We also can modify the expected growth rate in equity if we exclude the effect of interest income from cash and marketable securities in net income and cash and marketable securities from the book value of equity to calculate the non-cash return on equity.

When we estimate the expected growth, the growth rates will be different if we calculate it relative to changes in equity return over time and whether the valuation is on existing investments, growth assets, or both old and new investments.

If the company maintains its return on equity and retention ratio, the expected growth rate based on current net income and retention ratio metrics will differ from the growth rate based on normalized metrics, using averaged net income for the years of our estimate with normalized return on equity and retention ratio.

To estimate the growth rate in net income, we calculate the net income for the years to get the aggregate net income value. We also compute the aggregate book value of equity to find the average return on equity ratio.

As previously noticed, we have estimated the company's equity reinvestment net of debt changes for each year from its net income to determine the equity reinvestment rate. Consequently, we aggregate the equity reinvestments to get the average equity reinvestment rate, dividing it by the aggregate net income value, thus estimating the expected growth through the averaged values of the reinvestment rate and return on equity.

Return on Equity

A key distinction between return on equity and return on capital is that ROE does not exclude cash from the calculation. Interest income from cash is part of net income, and the book value of equity incorporates the firm's cash holdings. As a result, ROE represents a composite return on all of the company's assets, including cash and operating assets.

Since cash delivers lower, close to risk-free returns than operating assets, firms with substantial cash balances will likely experience a lower return on equity.

To obtain a more accurate measure of the return on equity for operating assets, we can modify the calculation by excluding the interest income generated from cash holdings and adjusting the book value of equity to remove the impact of cash. This adjustment gives a better view of the non-cash return on equity generated by the company's core business, separate from the lower-risk, lower-return cash assets.

We see that the net income growth and earnings per share growth are affected by the return on equity and that return is affected by the level of debt to finance projects or investments. We also know that returns are not sustainable for various reasons, but mainly for losing a competitive position and ability to use efficiently its existing assets accumulated over the years.

We should be concerned about whether a high debt-to-equity ratio, a low effective tax rate, or nonoperating income causes a high return on equity.

Therefore, we can break down and calculate the return on equity by taking on the return on capital and adding the debt ratio then multiplying by the return on capital minus after-tax cost of debt. This approach results in a return on equity that is different from the one estimated using the net income and the book value of equity. The advantage is that it allows us to see the leverage effect on growth.

Growth in Operating Income

For firms with a stable return on capital, the expected growth in operating income is a product of the reinvestment rate or the portion of after-tax operating income invested in net capital expenditures and non-cash working capital and the quality of these reinvestments, measured as the return on the capital invested. When the return on capital changes over time, the expected growth rate will increase if the return on capital increases and decrease the growth rate if the return on capital decreases.

Return on Capital

The return on capital measures the profitability of capital investments in both short-term and long-term assets, funded by equity investors and lenders. This includes investments in projects, capital goods and working capital, assessing how effectively the company is using these combined resources to generate returns.

These investments are categorized into assets that generate cash flows now from prior investments and expected future cash flows from investments in new assets. How much, for how long time, and how efficient are the investments to generate sustainable and more predictable cash flows over time is assessed through the return that exceeds the cost of equity and debt capital. Whether the firm creates or destroys value is determined by whether returns are higher than the firm's cost to use that capital or what they have to pay back to its equity and debt investors as dividends, interest payments, and principal repayment.

Therefore, the firm's value is derived from its investments in existing assets and new investments, and the present value of cash flows as excess returns delivered from each accumulated asset and new investments.

To generate value, businesses must create growth, and the expected growth is estimated on the expected return on investments and the proportion of capital, whether from earnings or operating income reinvested back into the business.

We can start evaluating the quality and efficiency of prior investments to estimate the returns earned on equity and capital and use them as a basis for forecasting returns on future investments.

Our judgment on whether existing assets still deliver excess returns and the expected growth and returns from reinvestments in capital goods or buying growth through acquiring equity in businesses will greatly impact the investment worth we assign to a company.

Therefore, the return measure is the key number in a valuation, critical that we get a reasonable estimate of the return earned on existing investments. Even if the current returns are computed correctly, there is no guarantee that these returns will continue. Value is ultimately determined by expected returns on future investments.

Revenue Growth

In general, revenue growth tends to be more persistent and predictable than earnings growth. While there are many measures of profitability, scaling profits to revenues to arrive at profit margins makes the most sense. Although growth rates can be computed using any metric, revenue growth is the metric that best reflects operating growth.

Reinvestment Rate

As noticed earlier a company has to reinvest consistently to maintain its competitive position or become big and that reinvestment can be tied to earnings as a retention ratio, a reinvestment rate, or linked to sales, as a sales to invested capital ratio.

The efficiency of reinvestments comes from the efficiency in applying capital assets over time, such as equipment, and technology creating higher sale prices and thus returns delivered by the measure of efficacy of each asset compared to the prime cost of a capital asset. The prices and efficiency created by investments in new assets will decline with time resulting in a decline in returns where at some point the present value of cash flows will be equal to the cost of capital assets.

The formation of capital for new investments in capital assets through the equity market is much different from the bond market where the price or cost of equity capital for the newly issued equity is determined independently. The investment is considered not because the company's current stock price is high or low, but because such a strategy will increase future earnings.

Essentially, borrowers create the supply by issuing securities, and lenders create the demand by investing their savings in those securities.

The bond market plays an important role in determining long-term interest rates where businesses compete to secure debt financing from investors and likewise, investors compete for opportunities to invest. The cost of capital is reached by the interplay of activities in the mortgage market and the market for short-term loans, reflecting the way they influence each other.

Free Cash Flows Projections

When valuing a company we consider the big drivers of the business; reinvestments, profitability, and growth, whether it is a growing company or a matured business that relies more on past investments than reinvestments in growing assets, as well as, whether the future growth is generated through costs cutting or acquisitions.

Based on those premises and the level of how optimistic or pessimistic we are about the revenue growth potential we can establish a company's expected growth rate for the period of our valuation that could get lower with time.

Assumptions about revenue growth and operating margins have to be internally consistent. In general, revenue growth tends to be more persistent and predictable than earnings growth. We must make several subjective judgments about the competition environment, the firm's ability to sustain revenue growth, and its sales and marketing power.

To align revenue growth with reinvestment needs, we calculate the revenue generated by each dollar of capital invested to estimate how much additional investment the firm has to make to produce the projected revenue growth and to subtract it from the after-tax operating income, thus to find the FCFF in that year.

Terminal Value

While there are several approaches used to estimate terminal value, the one that is most consistent with an intrinsic valuation or discounted cash flow view is a stable growth model.

At the end of our estimation period, we can estimate the value of the firm as a going concern entity, assuming the cash flows will grow at a constant rate forever. Our reinvestment rate will decline with the decreased rate of stable growth in perpetuity and the assumed lower return on capital for all those inputs adjusted to reflect that growth rate and the industry average levels.

The higher a company's growth potential, the greater the proportion of its value derived from its terminal value. If the return on capital is higher than the cost of capital in the stable growth period, increasing the stable growth rate will increase value.

This terminal value has to be discounted back to the present at the cost of capital considering the lower new growth rate to get the value today.

As a firm grows, it becomes more tricky to maintain high growth, and at some point, it will grow at a rate less than or equal to the growth rate of the economy in which it operates, but the question is how and when the business will transition from creating high growth rate into stable growth.

For established and growth firms reporting rapidly growing revenues, maintaining their momentum power matters to preserve future revenue growth and excess returns. The resourcefulness of a firm's competitive advantages lays out the length of the high growth period.

During this transformational process, they will become less exposed to market risk, may raise and use more debt at better rates, have lower excess returns, and reinvest less than the time the company was a growing business.

It is worth assuming that as the firm moves from high growth to stable growth, the relationship between capital spending and depreciation will change, thus capital expenditures will become much larger than depreciation.

Discounting Computation of FCFF to Present Value

The value of a business is the present value of the free cash flows to the firm and the present value of the terminal price where a large portion of the value comes from the terminal value. People love to receive cash now for present consumption rather than into the uncertain future where the debased purchasing power and value of the currency decreases in time. Thus, the currency we use in our evaluation process will reflect the inflation rate embedded in it.

The discount rate is not only what we would like to make on an investment, but it is the opportunity investment we can make on the market with equivalent risk.

All those features are incorporated into the discount rate where a higher discount rate will lead to a lower value in cash flows in the present, while through compounding the present cash flows are estimated for their future value. As time is a key component, an important understanding is not only how much cash flows we receive but when we receive it at each point in time. The frequency of compounding affects the future and present values of cash flows as the real interest rate may differ from the effective interest rate.

If we think that the cost of capital will change over time, we have to figure out the discount factor for the initial period of our estimate and when changes occur to calculate the accumulated cost of capital for the entire period.

Final Adjustments

After we estimate the present value of FCFF we have to close the valuation by adding back what we did not include in our valuation. To compute the FCFF, we started with the operating income, so anything that is not an operating income has not been added back yet.

For instance, a firm may have a big cash balance that I did not count because the interest income from cash is not part of the operating income, so we will add back the cash balance.

If we incorporate the capital gain from the sale of marketable securities in the income we use in our forecasts we are assuming that at any time in the future, we can sell those securities for a higher price. We have to ignore them unless we are valuing a firm that is in the business of selling and buying securities.

We have to adjust for minority holdings that were not included in cash flows. The income from those holdings shows up below the operating income line.

Next, we have to subtract any other potential liabilities and add them to the debt account, like unfunded pension or healthcare obligations, and lawsuits if any, that may cause large liabilities.

The expenses associated with stock-based compensation/management options should be treated like any other operating expense and net out from equity's value to get the value per share today.

Liquidity

It is better to treat our investment and intrinsic value separately from the liquidity or marketability of a stock. If we assume a stock is both undervalued and liquid, but it is cheap partly because it is liquid, then how much is it cheap due to liquidity and how much is it because of other factors?

In the end, as this is a publicly traded company in this example if the stock's price was trading at a higher price per share than the price per share in our evaluation, this may suggest that in our valuation we were conservative, we made a wrong assumption about future growth potential and riskiness, or that the market is right/wrong but we are wrong/right, but who is more wrong?

The Core of Value Determination

The determinants of a business's value are simple but often not so easy to estimate. For startups, emerging market firms, or commodity companies, expected cash flows are the drivers of the value. These cash flows must consider growth prospects and the associated risks that may prevent their realization. While discounted cash flow (DCF) valuation is a popular method to build fundamentals, it is not the sole way to intrinsic value. Overconfidence can lead to inflated cash flow projections, unrealistically high growth rates, and underestimated risks, resulting in value overvaluation.

Precision and Humility in Valuation

Seeking precision in valuation often leads to disappointment. Recognizing the limitations of valuation models and maintaining humility can help mitigate the pain of errors. Valuations are still valuable if they are less wrong than market estimates.

The inputs that we use in the valuation will reflect our optimistic or pessimistic sentiment; thus, you are more likely to use higher growth rates and see less risk in companies you are predisposed to like. While precision is a good measure of process in mathematics or physics, it is a poor measure of quality in valuation. Even if your information sources are impeccable, you have to convert raw information into forecasts, and any mistakes that you make at this stage will cause estimation errors.

CAPM provides a basic framework for understanding the relationship between risk and return.

It's understandable to think that CAPM isolates unsystematic risk. It doesn't isolate unsystematic risk, it ignores it. However, remember that isolation implies separating something and examining it. CAPM doesn't do that with unsystematic risk; it simply assumes it's gone through diversification.

Investors should be aware of these limitations and consider them when using CAPM in real-world investment decisions. By ignoring unsystematic risk, CAPM simplifies the model and allows it to concentrate on the impact of systematic risk, which is the risk that cannot be diversified away and directly affects the expected return an investor can demand for holding an asset.

Lessons for Investors

A firm is a legal entity separated from other entities which are equity holders and lenders. The firm pools capital from those independent entities, invests on their behalf, and pays them off contractual interest to lenders and dividends to equity holders. The firm works for those investors and its prime goal is to increase their wealth.

The quality of a good business is its resourcefulness to generate not just profits but also convert these profits into cash flows that investors can collect.

Not all firms reporting stable earnings are considered good investments, but whether the firm offers growth potential, earnings stability leads to price stability, and how the market is pricing these stocks are essential considerations. Investing in a stock with stable earnings, low or no growth, and high price volatility is not a bargain.

Some investors follow firms with consistent and stable earnings per share as safe and therefore good investments. However, both theoretical support and empirical evidence for this belief are weak.

Companies that spend significantly on risk management products or acquisitions to mitigate risks that investors could diversify away for free are not serving their shareholders well. While stable earnings might suggest a degree of safety, they should not lead to expectations of superior investment performance.

We have learned that as our imperfect financial mechanism operates, it often drives security prices materially above or below the levels of their intrinsic worth; that the market prices of securities are influenced not only by current interest rates but also by the trend of commodity prices as evidenced by the varying purchasing power of the dollar; that whereas a large supply of idle funds resulting in a lowered interest rate will tend to raise the price of both bonds and stocks.

Rising commodity prices result in a subtle transfer of wealth from those having fixed money incomes, such as bondholders to other members of society; values change slowly and prices fast, and sentiment or crowd psychology often exerts a temporary yet powerful influence on the course of security prices.

Investment narratives are perennial, often rebranded to appear innovative. Despite sophisticated strategies, unexpected events can disrupt them. Success depends on thorough research, recognizing the imperfection of any approach, and protecting against potential pitfalls.

Investors must balance growth, risk, and cash flows. Recognizing that even well-run companies can be bad investments if overpriced is crucial. Consistent attention to intrinsic value, market dynamics, and prudent risk management can guide better investment decisions, ensuring alignment with long-term objectives.

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The content provided is intended to help users become financially literate. It does not constitute tax or legal advice and should not be relied upon as a forecast, research, or investment advice. It is not a recommendation, offer, or solicitation to buy or sell any securities or to adopt any investment strategy. Tax, investment, and other financial decisions should be made only with guidance from a qualified professional. We make no representations or warranties of any kind, express or implied, regarding the data provided, its timeliness, the results obtained from its use, or any other matter. By using this information, you acknowledge that you understand and agree to these limitations.

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