Fall 2015

Corporate Finance

"The best source of capital is to be highly profitable."
                        Tidjane Thiam, CEO of Credit Suisse

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Monday & Wednesday 8:35-9:50
Skinner 216
Office hours: MW 10-11AM

Satya J. Gabriel
Professor of Economics and Finance
e-mail: sgabrielatmtholyoke.edu
FAX: 413-538-2323

Course Description:

The course in corporate finance describes the corporation and its operating environment, the manner in which corporate boards and management evaluate investment opportunities/projects and arrange for financing such investments, create (or, alternatively, destroy) value for shareholders by planning and managing the transformation of a set of variable inputs (labor efforts, including the creative efforts required for innovations, raw materials, components and other forms of technology consumed in production processes) into a more highly valued set of outputs (embodying both the original investment value and any surplus value generated), and develop strategies for meeting the claims of financial market participants who are sought as financiers (and, therefore, residual claimants to net cash flows/surplus value) of such investments. It is understood that the shares of surplus value received by various claimants and retained by corporate boards of directors for investment and other uses results from complex social interactions, including, but certainly not limited to, transactions in various markets. Thus, the course provides students with a basic analytical framework for understanding how the various strategies for transforming variable inputs into more highly valued outputs, combined with struggles over corporate surplus value (in the form of cash flows) may be understood and resolved. In this context, the course is designed to provide students with analytical tools that allow them to determine the "intrinsic value" of a corporation (or any economic institution, including a state-owned enterprise that is to be privatized) and to assess the effectiveness of corporate management in maximizing that value, given specific competitive, regulatory, and market conditions.

Because the future surplus value/cash flows of any set of corporate investments are sensitive to constantly changing political, macroeconomic, competitive, and other conditions, students will be taught analytical techniques for taking into consideration alternative macroeconomic and competitive environments. After all, estimated value is a function of the particular model employed and each model is constructed around a specific stylized context (a model structure where elements are limited to a subset of possible phenomena). The model serves as a proxy for the real world: the overdetermined interactions of actual phenomena, whether identified/defined within the model in question or the vast expanse of other phenomena not defined within and therefore invisible to the model. This is important for anyone interested in predicting outcomes of corporate projects. In other words, it matters what type of model you use (and, therefore, what paradigms you employ in constructing models). Models constructed within the conceptual framework of specific paradigms (e.g. neoclassical, Marxian, Institutionalist, Post-Keynesian economics) provide alternative ways to predict the future (specific events in future time periods). Students are advised to read broadly (history, psychology, sociology, etc.) and to learn multiple paradigms with which to construct models for predicting future corporate cash flows, stock prices, index prices, option prices, housing prices, prices of commodities, paintings, and any number of other assets.

Financial models are designed to predict economic outcomes. How do you know if a model works? The model must provide results which allow reasonably accurate predictions of economic outcomes, such as the future revenue of General Electric. Your model does not have to be perfect. Indeed, it is impossible to be perfect. To succeed in the world of finance, you just have to be very good at building models (perhaps even excellent) in comparison to other people's models. In the case of financial models, we want to predict outcomes that would shape the results of financial statements, such as future cash flows, earnings, and various growth rates of variables that are measured within financial statements. Once you have chosen a particular model to test against empirical data, it is possible to use statistical analysis to verify that the model has utility (can achieve acceptable results). One of the more common forms of models are simulations. Simulations may be used to project alternative cash flow streams for firms under varying conditions of aggregate demand, inflation, tax rates, interest rates, and exchange rates, among other variables. While these techniques provide students with the tools for valuing enterprises under a wide range of conditions, one must also recognize that the short-term movements in equity valuations in the various stock markets are even more complexly determined.  Such stock price movements are not always determined strictly by intrinsic value, even when intrinsic value is estimated in the context of the aforementioned range of macroeconomic, competitive, and socio-political conditions.  As behavioral finance, and even earlier, John Maynard Keynes, has argued, investors in financial markets are capable of emotional buys and sells (in violation of consistently rational behavior dreamed of in neoclassical economic theory), panics, and herd behavior.  Thus, at any given moment, certain (and sometimes most) stocks can be and are mispriced, i.e. significantly divergent from any reasonable calculation of intrinsic value.  During bubbles and crashes this mispricing can reach extremes. The valuation techniques learned in this course provide students with a means for identifying such mispricing.  Mispricing is addressed by research in behavioral finance, an alternative paradigm to neoclassical economics and rejects the fictions of rationality and representative agents in favor of incorporating psychological research and empirical studies. This is a positive move by finance economists and may represent a tentative step towards more widespread adoption of the scientific method in economics, writ large.

If an economist is unable to use his or her theoretical tools to make predictions about future developments in financial markets or has no clue about whether an economy is likely to boom or bust, then it is best to spend very little time with that economist. It is one of the goals of this course to provide students with tools that improve their ability and confidence in using publicly available data and events for predicting changes in macroeconomic conditions, corporate share price growth or decline and the future direction of financial markets, more generally. In the spring of 1999, the corporate finance class discussed the coming end to the "speculative bubble" in internet stocks (which dramatically deflated in 2000).  In 2006 and 2007, we discussed the bubble in the housing market and predicted the bursting of that bubble, which had severe and still lingering consequences for global financial, labor, and goods markets. More recently, we discussed the manner in which the U.S. bond market was bolstered by decisions of the Chinese central bank (the People's Bank of China) to purchase billions of dollars worth of U.S. treasury bonds, accumulating approximately $1.5 trillion of U.S. dollars in U.S. treasury bonds, pushing up government bond prices and and pushing down the interest rates on those bonds (and putting downward pressure on all the related interest rates, including mortgage interest rates, that influence investment and housing construction in the U.S. economy). Our prediction that the bond market bubble would burst this summer has proven incorrect and we will further discuss the likely course of interest rates over the next three plus months (which still gives us time to be correct) and in 2016, examining which factors are likely to shape the Federal Reserve Board's decision. What factors might have short-sighted a bursting of the bond bubble and what are the identifiable factors that might be used in a model for predicting interest rate decisions? Among the factors that might be included in such a model are the future course of the unanticipated Ukraine crisis and the continued progress of ISIS/ISIL, as well as the extreme debt/insolvency crisis in Greece.

What lies ahead?  What will happen to stock prices? Bond prices? Housing prices? The U.S. dollar? As we develop our analytical skills, we shall also have occasion to discuss these questions and possibilities in the context of corporate finance.  This is fair warning then.  This is not a dry course where the professor comes to class and repeats what is in a textbook.  We'll learn a lot this semester --- the time value of money, the capital assets pricing model (CAPM), Arbitrage Pricing Theory (APT), the dividend valuation model (DVM), the advantages and disadvantages of restructuring, mergers and acquisitions --- but, in the spirit of a liberal arts education, we shall not restrict our learning to purely technical questions.  We will also discuss  relevant current topics and controversies.  Be prepared for this.

Some financial data sources can be accessed from the course's own corporate finance hotlinks page. If you notice dead links or mistakes on the hotlinks page, please bring them to the attention of Professor Gabriel.

Course Objectives:


Fall 2015

  • Text 
  • Primary Text: Aswath Damodaran, Investment Valuation, 3rd. edition, which is hereafter referred to as "The Text."
  • Secondary Text: Corporate Finance Compendium, which is hereafter referred to as "The Compendium."
  • Recommended but Not Required: George Soros, The Alchemy of Finance, 2004.
  • Recommended but Not Required: de Kluyver, Cornelis A., Corporate Governance v. 1.0, 2012, available on Flat World Knowledge website (can be read for free).
  • Recommended but Not Required: Micklethwait, John and Wooldrige, Adrian, The Company: A Short History of a Revolutionary Idea (Text optional)
  • Recommended but Not Required: Doug Henwood, 1997, Wall Street  This text is now available as a free download on the Internet (click here).
  • Web Case Studies & Essays (stay tuned) 
  • Grading policy 
  • Course grades will be based on the total accumulation of points from three sources: oral answers to questions during the normal course time (students should treat such questions as an oral examination), ten quizzes, and the final examination. 
  • In-class questions -- 10 percent of the final grade 
  • Weekly quizzes -- 70 percent of the final grade 
  • Final Examination -- 20 percent of the final grade 
  • Course calendar

    Sept. 9 Intro to Finance

    We begin with the long introduction to corporate structures and value creation. Read the following introductory questions on finance: Questions to Ponder. Also, read the following Intro to Finance. The questions and introduction will help us in our discussion of the role of finance in society. We will use a heuristic diagram of a firm and discuss various component parts of the overall social and technical processes that determine the success or failure of the firm: financing and access to tangible and intangible assets, nexus with labor markets and access to necessary skill-sets, the immediate process of production, transportation of products, marketing of products, final sales by which cash flows are generated, the receipt and distribution of the surplus value flows necessary to meet the demands of claimants. Click on "Intro to Finance?" above to read the introduction to the course. Read chapter one of text. Read the following short introductory essays on the cash flow cycle (click here) and cash flows, more generally, (click here).

    Pricing Stocks and the Volatility of Returns

    Why do stock prices demonstrate more volatility and non-normal (often non-linear) return distributions than would be consistent with neoclassical optimal pricing? If pricing diverges from intrinsic value, as given by the sum of future cash flows discounted by an appropriate expected discount rate associated with the security/asset being priced, then is it reasonable to asssume that stocks will eventually reach that intrinsic value? These are questions we will be discussing over coming weeks, but let's make sure that, even if the possible answers are not yet forthcoming, we understand the meaning and implications of these questions.

    Practice Short Answer Question:

    Damodaran discusses several general approaches to (philosophies of) portfolio management:
  • fundamental analysis
  • franchise buying
  • technical analysis (see chartists)
  • information trading
  • market timing
  • What is Damodaran's rationale for arguing that valuation can play a role in each of the above approaches?

    Practice Question:

    In the U.S., corporate senior management is expected to act
       A) so as to maximize their own utility.
       B) in the best interest of the employees.
       C) so as to maximize the gain to the community.
       D) in the best interest of the shareowners.

    Discussion Question:

    Explain the rationales for choosing sole proprietorship, partnership, or incorporation as the legal form of a start-up business.
    Discuss the agent-principal relationship. Agents are required to act in the interest of a principal. Corporate directors are elected by shareowners and have a fiduciary responsibility to act in the interest of shareowner value maximization (acting so as to generate dividends and/or capital gains for these shareowners). Senior managers, who are responsible to the board of directors, are also supposed to be acting in the interest of shareowners. In practice, these agents are likely to violate this responsibility to some extent. After all, pilfering paperclips is, technically, a violation but no one gets punished for pilfering paperclips. In fact, directors and senior managers may regularly engage in spending from corporate accounts that are not in the interest of value maximization for shareowners. After all, it is not just Chinese government officials who like taking "clients" out to banquet. Therefore, there are agency costs associated with directors and senior managers and, technically speaking, agency costs are a form of theft. The agent plays out of sight of the principal, spending lavishly on expense and travel accounts, taking home company notebook computers for the kids, getting excessively expensive compensation packages, proposing and approving acquisitions of businesses for more money than the businesses are worth, perhaps because the acquisition provides the agent with additional status, income, and/or a larger staff to order around. When directors and senior managers arrange these negative net present value acquisitions, they destroy shareowner value. In fact, corporate strategies and related capital spending that is done to protect the agent's position, status, or excess compensation (agency rents) at the expense of shareowners is as surely stealing as using the company car for personal (non-corporate) purposes. These and other agency costs, including costs associated with trying to minimize other agency problems, further erodes shareowner value.

    Sept. 14-16 Approaches to Valuation: The Text, chapters 1 & 2

    This week we will explore some of the concepts at the foundation of corporate finance, generally, and valuation, specifically. You will want to make certain that you understand the meaning of cash flow, present value and the related concepts of discounting, time value of money, and opportunity cost. Do not hesitate to ask lots of questions. These initial concepts are critical to understanding the more complex models in finance. If you choose a career in finance, you will be tested on these concepts in a professional setting and expected to understand them in communicating with colleagues, clients, and others, so learn them now.

    General Formula for Valuation:

    Value = Σ CFt * (1 + r)-t

    Future Value and Present Value Formulas:

    FVt = PV0 * (1 + r)t
    PV0 = FVt * (1 + r)-t

    FV and PV under Continuous Compounding

    FVt = PV0 * (ert)
    PV0 = FVt * (e-rt)

    Sept. 21-23 Perpetuities and Annuities : The Compendium, chapters 3 and 4

    Always remember that the value of assets is determined by future cash flows received by the asset owners (the timing of receipt of future cash and the probability that future cash will equal investors' expectations are key determinants of value). This value exists but is unknown, since future cash flows and the risk of not receiving 100% of expected cash flows depends on future and substantially unknown, events. Although actual intrinsic value of future cash flows are unknown, models may be constructed with which to predict such value. In other words, financial value is not a subjective phenomenon, but is, rather, a function of actual cash received and the opportunity cost and risk of receiving that cash in future.

    Perpetuity Formula:

    PV0 = CF/r,
    where CF is the CF paid each period and r is the required return.

    Growing Perpetuity Formula:

    PV0 = CF * (r-g)-1,
    where g is the periodic growth rate into perpetuity.

    Sept. 28-30 Valuation of Single Future Cash Receipts, Perpetuities, Annuities, and Non-constant Growth of Future Cash Flows
    The Text, Chapter 4

    Valuation of a Single Future Cash Flow:

    Simple Interest Future Valuation Formula:

               FVm = PV0 * [1 + (t * r)]

    Compound Interest Future Valuation Formula:

               FVm = PV0 * (1 + r)m

    Continuously Compounding Interest Future Valuation Formula:

               FVm = PV0 * er*t

    Zero Coupon Bond: Single Future Cash Flow Valuation Equation:

    PV0 = Par Value * (1 + r)-t,
    where t is the number of periods until maturity, when the par value of the zero coupon bond (usually $1,000) is received by the bondholder.

    Practice Problem: Zero Coupon Bond

    The par value on a zero coupon bond is $1,000. The bond expires in exactly 10 years. Assume that current traders/investors in these bonds require a return of 10%. What market price would you estimate for this zero coupon bond?
    October 5-7 Perpetuities, Annuities, and Non-constant Growth Continued

    One of the simplest valuation problems is the valuation of an asset that generates a single future cash payment at a time definite in future. This problem may be solved by using the present value formula for a single future cash flow. If you can estimate the value of a single future cash flow, then you have the basic tools for valuing assets that generate multiple future cash flows, although these more complex assets require some algebraic manipulation to obtain shortcut formulas that greatly simplify the generation of a valuation estimate.

    Bonds: The most popular annuity used in corporate finance.

    Executive Summary: Bonds are securities representing loans by the purchasers of the primary issue of bonds to the corporation or government entity that issues the bonds. The primary issue of bonds may be executed by merchant banks, who provide the proceeds minus a merchant (investment) banking discount and merchant banking fees. Bonds may be purchased by firms, institutions, and individuals. The Broader Bond Landscape:

    A bond is a financial contract. This contract stipulates that, in exchange for the purchase price of the bond, the holder has a right to receive specific cash payments. These cash payments are usually in the form of periodic coupon payments (aka interest payments) and the time definite repayment of principal. The dates for the periodic coupon payments and the repayment of principal at maturity are clearly stipulated in the contract (which is also called a bond indenture). In Europe, the coupon payments are sometimes annual. However, in the United States, these payments are typically made semi-annually (twice a year at six month intervals).

    Bonds are liabilities of the issuer. They are a securitized loan made to the issuer by the original purchasers of the bond issuance. A marketable bond can be sold by the original purchaser to other economic agents, who then possess the claim to the coupon payments and the repayment of the original principal. Bonds are assets of the purchaser (because they represent claims to positive cash flows in future). The purchase price of a marketable bond need not be equal to the original purchase price of the bond. Bond prices are determined by financial market transactions under ever changing political and economic conditions, including variable rates of inflation.

    Annuity Formula:

    PV0 = CF-r - [CF/(1 + r)m]-r
        where PV0 is the value of the annuity in t=0, CF is the continuing periodic cash flow, r is the required return on the annuity, and m is the maturity time period.

    Bond Formula:

    PVbond = CP1 * (1 + r)-1 + CP2 * (1 + r)-2 + ... + CPM * (1 + r)-M + Par Value * (1 + r)-M
               = Annuity of CPs + Discounted principal at maturity
                   where CPi is the first coupon payment and is equal to all other coupon payments. The last coupon payment CPm is paid at the same time as the principal is returned at the end of period m (the maturity period), and r is the required return or yield to maturity on the bond.

    Par value for most bonds issued in the U.S. is $1,000. This is the issuance price of the bond. If the bond is priced below this $1,000 in the security markets, then the bond is selling at a discount (to par value). If the bond is selling for $1,000 then it is selling at par value. If the bond is selling for more than $1,000 then it is said to be selling at a premium.


    A mortgage is an amortizing loan, meaning that we amortize the interest and principal payments over a specified time span (for housing mortgages this term is usually 15 or 30 years). Early in the life of the mortgage most of the payment is to cover interest due and a very small amount goes to reducing principal. However, over time the principal has been reduced and therefore the interest due on the remaining principal decreases for each payment period, with principal repayment amounts increasing to fill the gap. Typically, the person taking out the mortgage will make a down payment (perhaps 20%, which is common in the U.S.A.) plus fees (including closing costs) and then borrow the remainder. The mortgage formula is given by:

    Monthly Payment = A(B - C),
               where A = Loan Principal; B = (1 * r-1) and C = 1{[r * (1 + r)-m]}.
    Furthermore, r = mortgage interest rate and m = maturity month (360 in the case of a thirty year mortgage).

    NB: You will not be quizzed on the mortgage formula.

    Preferred stock is not an equity share. It is more properly described as a perpetual bond subsumed to all other credit obligations. In other words, preferred stock may last forever (theoretically) but is always inferior to other cash obligations. Preferred stock dividends are only paid if the firm has positive net cash flow (i.e. firm management has made all obligatory payments and has cash left over with which to pay the preferred shareholders).

    Valuation of a Preferred Stock:

              PV0 = Div1 * (rpref)-1
    where PV0 is the current value of the preferred stock (which should be approximately equal to the current stock price, since the value of preferred stock is unambiguously linked to the constant stream of dividends management of the issuing firm is required to pay if the firm has this money available after meeting all other cash obligations;

    rpref is the required return on the preferred issue. It can always be derived from the perpetuity formula, given that dividend payments (Div) are fairly predictable and the current price (P) is an observable. Thus, it is reasonable to assume that P = PV0.

    Div1 is the forward dividend for valuing the preferred stock at t=0.
    Oct. 5-7 Financial Statements and Cash Flow Estimation: The Text, chapter 3

    Cash flow represents the receipt (positive) and distribution (negative) of money. In a highly monetized economy, value is mostly in the form of received money and, as such, provides access to commodities and assets. Corporations live and grow on positive net cash inflow. However, to generate positive net cash inflows requires investments (negative cash flows) in assets, the purchase of variable inputs (negative cash flows), including the hiring of workers and staff (paid in wages and salaries, measured in cash), as well as benefits (which may also be measured in cash terms). Investment in new projects and the continuation of existing projects requires the expenditure of money. Workers, whose productivity potential is the basis for corporate value creation, must be paid in cash. Other variable inputs must be obtained in order for worker/staff productivity potential to be realized and these inputs typically require cash outflows. In other words, before a corporation can generate cash inflows, it needs to have the cash to obtain the prerequisites for value creation. In addition, cash is required to satisfy a wide range of economic agents whose cooperation is required for the corporation to receive future cash inflows, including various agencies of the national and local governments, landlords and other owners of land and buildings (rental or leasing payments are denominated in cash units), the government often requires taxes and fees (in cash) in exchange for its cooperation (including providing the legal basis for the corporation to exist, have exclusive ownership rights to property, and to act as a "legal person"), managers (including the inhabitants of the executive suites) supervise a wide range of workers/staff and expect to be well compensated in cash for their stellar management skills, and bankers and other creditors want cash for providing capital (in the form of money) to the corporation. In other words, corporations exist, in part, because of the cash flows received and distributed by corporate management, securing in the name of the corporation a wide range of cooperative behavior from other corporate managements, governments, and a wide range of individuals.

    Back to the Future: Estimating Future Cash Flows:

    NB: The discussion of cash flows (and the relationship between cash flows and income statement earnings will be further discussed in November when we read chapters 9 and 10 of The Text.

    Let's Talk Financial Statements:

    Describe the typical line items in the income statement, balance sheet, and statement of cash flows.

    Book Value (BV) vs Market Value (MV):
    Accountants are, essentially, financial historians. Generally accepted accounting principles (GAAP) sets the parameters for proper accounting and show a clear preference for historical data as inputs in financial statements. Adjustments (depreciation, amortization, etc.) to historical data are carried out in accordance with GAAP and used in financial statements. These historically-based calculations of asset value are contrasted to market determined, current prices for similar assets. While historically-based measures of asset value are favored in accounting, book value for financial institutions are a bit different, with a greater use (particularly since 2008) of market value (where assets are periodically repriced in accordance with recent market prices). If you would like to discuss why mark to market asset valuation became more popular in post-2008 accounting, then please feel free to ask about it in class.

    Oct. 19-21

    Risk, Return, and Opportunity Cost of Capital:
    The Compendium, chapter 5

    What determines the required return of bondholders, shareowners, or preferred stockholders? The present value rule requires that future cash receipts generated by corporate projects and/or non-operational assets be discounted back to the present and then summed to obtain present value. However, to carry out this discounting process to estimate present value necessitates a required return for the various contributors of capital (equity holders, long-term debt holders, and preferred stockholders). Firms with existing bonds outstanding and/or preferred stock can surmise the current required returns on those instruments by referencing market prices. The current yield to maturity on bonds (adjusted for flotation costs) provides a good estimate of the cost of debt capital and the preferred stock dividend yield provides a good estimate of the cost of raising funds via preferred stock (again, adjusted for flotation costs) If firm management has not issued bonds or preferred stock, then the required return of equity holders (shareowners) is still needed to discount corporate projects and by aggregating them determine the value of the corporation.

    How do we estimate these required returns?

    What is the difference between systemic and unsystemic risk? How does diversification affect these risks?

    Can you solve the problem below? What is the relationship between your answer and the concept of required returns?

    If you paid $100 for XYZ, Inc. in t=0 and receive a dividend of $.25 in t=1, and then sell the stock for $125 in t=1, what is your return?

    Back to the Future: Estimating Future Cash Flows:

    Scenario, Sensitivity, and Simulation Analysis

    Expected Value Function:
    Expected Value of a single cash flow in the next period (t=1) under the assumption that this nominal value is determined by one of three alternative scenarios (a, b, and c). Each scenario has an associated probability in a period 1. The current (t=0) expected value of the CF in period 1 is given by the formula:

    E(CF1) = Ρa*CFab*CFb + Ρc*CFc,

       where E(CF1) is expected nominal value of the cash flow realized in period 1; Ρa is the probability of scenario a occurring, CFa is the cash flow expected under scenario a, Ρb is the probability of scenario b, CFb is the cash flow expected under scenario b, Ρc is the probability of scenario c, and CFc is the cash flow expected under scenario c. We assume that these are the only three scenarios faced by the corporation in the upcoming period.

    Practice Expected Value Problem:

    Estimate APPL stock price a year from now (t=0 to t=1) if the stock price is treated as a cash flow:
    Ρa = 40%; CFa = $150;
    Ρb = 30%; CFb = $100;
    Ρc = 30%; CFc = $225

    Oct. 26-28 Human Behavior, Financial Risk, and Estimating Required Returns:
    The Text, chapter 4.

    We are Not Spock

    Most public financial models are based on neoclassical utility theory. Neoclassical utility theory makes a number of untenable assumptions -- untenable because these assumptions are not only unrealistic (when compared to real world behavior) but, more importantly, when incorporated into a financial model result in unreliable and mostly false predictions about the value of important variables, such as future cash flows, in future periods. Since finance is ultimately about predicting the future based on ex-ante real world data, then the reliance upon neoclassical theory in financial models leads to poor decisions and poor decisions lead to value destruction. Check out Joe Cohen's discussion of rational decision-making.

    Daniel Kahnemann and Amos Tversky received the Nobel Prize in Economics for developing one of the more prominent alternatives (to neoclassical economics) theories of decision making, prospect theory. We will explore prospect theory in November but, in the meantime, have a look at this lecture by another Nobel Prize winner, Robert Schiller: Click here for Prof. Schiller's lecture on prospect theory

    Capital Asset Pricing Model (CAPM)

    Capital Asset Pricing Model Formula:

    rxyz = rf + βxyz * [rm - rf],

      where rxyz is the required return, as estimated by CAPM, βxyz is the derivative of xyz returns with respect to a unit change in the market return (usually proxied with the S&P 500), rm is the estimated return on the market (S&P 500), and rf is the estimated risk free rate (usually proxied with the 91-day t-bill rate).

    William Sharpe received the Nobel Prize for Economics in 1990 for developing CAPM. In CAPM, Sharpe assumed that portfolio managers, including individuals managing their personal portfolio, are Spock-like beings, capable of evaluating the entire universe of potential securities (for long and short positions), the expected returns and probability distribution of these returns, and the correlations between all securities. Of course, these Spock-like beings are none other than the neoclassical homo economicae. Homo economicus, the epitomy of neoclassical rationality, is able to select (from the universe of possible portfolios) the optimal portfolio.

    These (professional and amateur) portfolio managers are assumed, at a minimum, to dominate the market with their optimally chosen portfolios. They select optimal portfolios comprised of risk free assets and risky assets, longs and shorts, in an institutional environment with minimal friction (low or no fees, no liquidity problems). This portfolio is constructed in such a manner as to eliminate company-specific risks by diversification. Given that these rational portfolio managers follow a set pattern of logical buys and sales of various weakly correlated securities under conditions of rational expectations where the price of equity shares of company XYZ are equal to the intrinsic value of XYZ. This portfolio of relatively uncorrelated, but correctly priced securities generates optimal returns Rational portfolio managers are assumed to earn a portfolio return that is perfectly (or near perfectly, if we allow for some market drift around normally distributed returns) related to expected portfolio returns. Because the return distributions are assumed to be normal, it is never anticipated that actual returns will dramatically diverge from expected returns (in other words, booms and busts in the market are precluded).

    What is the evidence for or against CAPM? Empirical research in finance has clearly demonstrated the inadequacy of CAPM. Research has shown that CAPM results in bad estimates of intrinsic value (which means bad estimated security prices leading to bad trades and sub-optimal portfolio returns). The realization of CAPM's failings led to the construction of alternative models and further empirical testing (leading to further improvements in the models). The discovery of previously hidden (from the general investing public) determinants of required returns has led to growing acceptance of such relatively more (than CAPM) complex models.

    Capital Asset Pricing calculator

    Stock Valuation with Dividend Valuation and CAPM Method

    Arbitrage Pricing Theory (APT)

    rxyz = α + βxyz1 * f1 + βxyz2 * f2 + ... + βxyzK * fK + ε,
       where rxyz is the predicted return on XYZ stock given the statistical correlations with factors 1 thru k (as estimated in the multiple regression), β 1 is the partial derivative that gives the contribution to rxyz for each unit increase in factor1. The logic works the same for the other partial derivatives (indicated by appropriate βs). The overdetermined nature of the real world means that a multiple regression must necessarily leave out relevant data, which is partial explanation for the error term, ε.

    Debt/Equity Risk Premium Model

    Corporations with outstanding debt in the form of long term bonds already have a measure of credit (or default) risk in the form of the yield to maturity of these bonds. It seems rational to assume a strong correlation between the yield to maturity of a corporation's long-term bonds and the required return of equity shares. This relationship was tested statistically over time and it was, indeed, evidence for such strong correlation. Further study of this correlation resulted in the debt/equity risk premium approach to estimating equity returns:
    r is estimated to be a number in the following region: (YTMxyz +.03) ≤ rxyz≤ (YTMxyz + .06)

    Political Risk:

    All stocks face some degree of political risk. However, sometimes political risk dominates all other forms of risk. This is the case for most Russian and Greek stocks. The conflict between NATO and Russia has had serious effects on a wide range of Russian stocks. Similarly, the Greek debt crisis and the inflexibility of the German government has sent shock waves through the Athens Stock Exchange, with Greek stocks down as much as 90%.
    Nov. 2-4 Market Efficiency, Nonconstant Growth, and Behavioral Finance:
    The Text, chapter 6

    Expected Utility Theory:

    Risk Adjusted Abnormal Returns (seeking alpha):

    RAARi = ri0 - αi + β * MRP;
         where RAAR is the risk adjusted abnormal return;
    ri0 = the observed return on stock i;
    α is the alpha intercept of a linear regression of stock i returns against market returns. If β = 1, then the stock return for stock i is perfectly correlated (in the linear regression) with market returns;
    MRP is the market risk premium, which is estimated based on past divergences between market returns and the returns on 91-day t-bills.

    Note that when α is significantly greater than zero the result contradicts efficient market trading in stock i. Hedge fund managers are always seeking alpha. This is the mission of most hedge fund managers and models that identify stocks with alpha are greatly prized.

    Prospect Theory:

    Modern Portfolio Theory:
    Modern portfolio theory (MPT) argues, in a nutshell, that you can avoid being exposed to significant company-specific risk by building a diversified (relatively uncorrelated securities) portfolio. It is possible to minimize exposure to unique (company-specific) risk without lowering your expected portfolio return. The mathematical algorithm for selecting this portfolio is determined based, in part, on statistics, including identifiable correlations between variables. It is also, however, dependent (on diving deeper into the theory) upon certain faulty assumptions (based on an expanding body of observations and experiments) about the underlying decision-making of traders in securities and the meaning of posited relationships that do not come directly out of statistical work, e.g. expected utility theory and the capital asset pricing model. In other words, MPT combines some elegant and empirically verified relationships (such as the ability to reduce risks unique to particular securities without damaging portfolio returns) with fantasy relationships (such as the idea that investors have the omniscience and mathematical ability to construct optimal portfolios by combining long and short positions without encountering frictional costs and context driven changes in risk), resulting in strategies that, in the macro (diversification), can have very positive benefits for investors while in the micro (individual decision-making rules) leading investors into mistakes in valuing individual securities. We will discuss this paradox in more detail this week.

    Nov. 9-11 Capital Budgeting & Capital Financing:
    The Compendium, chapter 6

    Investment/Merchant Banking Fees

    Senior management must submit project proposals that are estimated to generate sufficient cash flow to satisfy the required returns of the suppliers of firm (or specifically project-related) capital (equity or long-term debt). The cost of financing begins with these required returns but management must incorporate any and all additional costs of raising capital. Most corporations raise capital through the good services of investment (or merchant) banks. Investment banking services include consulting with the corporation issuing the securities, arranging dog and pony shows where firm management is able to pitch their securities, with the help of the i-bankers, to high net-worth individuals and buy-side financial corporations (such as mutual fund companies, pensions, and sovereign wealth funds), identifying which of these potential buyers is serious, how much they are willing to pay for the securities, and the possible allocation of a portion of the issuance to these potential buyers, and then pricing the securities in line with the price expectations of these potential investors, writing the prospectus for the security issuance, and filing all necessary legal documents. The price of these good services are, typically, a discounted purchase of the securities to be issued (the cost of underwriting) and fees. The i-banking cost of issuing these securities (also called flotation costs) is usually between 3 and 7% of the retail price of the securities. The discount and fees, therefore, reduce the amount of capital provided by the securities issuance and raise the corporation's cost of capital.

    An alternative to issuing equity shares through the i-banking process is to use retained earnings to finance capital budgeting projects. Retained earnings do not require flotation costs and are therefore cheaper sources of equity financing than new share issues through an i-bank. Indeed, most project financing is with retained earnings.

    Weighted Average Cost of Capital (WACC):

    wacci = ωid * rd + ωie + re
    wacci is the weighted average cost of capital for firm i;
    rd = YTM * (1-ti)
        with YTM defined as the yield to maturity for firm i bonds
    and ti is the effective tax rate for firm i;
    re is the required return on firm i common stock;
    ωid is the weight (percentage) of debt in total capital of firm i = Di * (Di + Ei)-1
    ωie is the weight of equity in total capital for firm i = Ei * (Di + Ei)-1.
    Di is total long term debt for firm i;
    Ei is equity for firm i;

    Return on equity (ROE):

    ROE = Net Income * BV-1
    where ROE is return on equity, BV ≡ Book Value = Total Assets - Total Liabilities.

    Practice questions, problems, and essays

    Nov. 16-18

    From Earnings to Cash Flows:
    The Text, chapters 9 & 10

    Key Concepts:

  • Revenue recognition
  • The Matching Principle
  • Mark to Market
  • Depreciation, Depletion, & Amortization
  • Foreign exchange translation
  • Pro forma income statement
  • Nov. 23-25

    Estimating Growth and Terminal Value:
    The Text, chapters 11 and 12

    Nonconstant Growth Stock Valuation Model:

    PAPPL0 = Σ[FCFt * (1 + r)-t] + PAPPLT * (1 + r)T
          where PAPPL0 is the estimated current price of Apple equity shares;
    Σ[FCFt * (1 + r)-t] is the sum of free cash flows (FCF) in periods 1 through T (where T is the year when the nonconstant growth period ends) discounted back to the present (t=0) at the discount rate (1+r)-t;
    PAPPLT * (1 + r)-T is the estimated future price (in period T) of Apple after the nonconstant growth period ends. This value is calculated as a growing perpetuity with a constant growth rate into perpetuity. This constant growth rate is difficult to predict but must be constrained by the growth rates of the markets within which Apple generates sales and related cash flow growth.

    Why are Apple, Google (now Alphabet), and Facebook good candidates for valuation with the nonconstant growth model?

    Nov. 30 & Dec. 2

    Dividend Discount Models & Free Cash Flow to Equity Models:
    The Text, chapters 13 & 14

    Boards of directors approve cash payments to shareowners in the form of dividend payments. These dividend payments are announced after approval, including specifying the date when a shareowner must own the stock to be eligible for the dividend payment (ex-dividend date).
    Dec. 7 Mergers, Acquisitions, and Corporate Control: Reading to be determined.
    Dec. 9 Review Session

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