This Reading introduces practical problems encountered when estimating and applying the cost of capital in a DCF valuation. It applies, but does not derive, key ideas from modern portfolio theory and is accessible to readers who have not yet studied portfolio theory. The reading begins by defining the cost of capital narrowly, as a discount rate (in a DCF valuation) that must equal the opportunity cost of funds, or equivalently, the sum of the time value of money and a risk premium. This intuitive explanation is followed by the CAPM equation, and practical discussions of systematic risk, beta, and the equity market risk premium. The Reading then introduces WACC as an alternative calculation for the cost of capital and shows, graphically and mathematically, the correspondence between CAPM and WACC in the absence of taxes. The Reading also explains that the "(1-t)" adjustment term in the formula for WACC with taxes compensates for missing interest tax shields in the standard calculation of Free Cash Flow. The next section is a step-by-step explanation of how to calculate WACC for a real company, including discussions of data and sources commonly used by practitioners to compute leverage ratios, the cost of debt, the tax rate, the risk-free rate, and so forth. Finally, the reading walks through an illustrative calculation of WACC for Coca-Cola, as of December 31, 2015, using data from Coca-Cola's SEC filings and the capital markets. The Supplemental Reading section examines some of the limitations of WACC as a discount rate as well as some common errors that practitioners make in computing and using WACC. It also covers two alternatives to WACC-based DCF, the APV and CCF methods.
This is the second in a set of two Readings on Modern Portfolio Theory. It presumes readers have already read "Risk and Return 1: Stock Returns and Diversification" (#5220). This Reading starts by examining the effect of diversification on portfolio volatility, graphically and mathematically, for different levels of correlation among portfolio assets. Next, it compares portfolios and defines the concepts of efficiency and the efficient frontier. It introduces a riskless asset and uses it to identify the tangency portfolio and to define the Sharpe Ratio as a way to compare excess returns to risk. The discussion demonstrates how borrowing and lending can create any portfolio along the line between the risk-free rate and a portfolio in mu-sigma space, and it presents the two-fund separation theorem. Finally, the Reading considers the problem of whether to add a small amount of a risky asset to an existing portfolio as a way to derive the Portfolio Improvement Rule, before concluding with general equilibrium and the Capital Asset Pricing Model (CAPM). Topics covered in the Supplemental Reading section include estimation of betas, the equity market risk premium, and real-world application of CAPM, and criticisms of CAPM, both theoretical and practical. The Reading contains six web-based interactive illustrations. The first shows the decline in the volatility of a portfolio's returns as the number of stocks in the portfolio increases from two to 30. The second is the same as the first but allows the reader to specify the correlation among the 30 stocks. The third shows the region in mu-sigma space that includes all possible portfolios for five risky assets, the "broken eggshell" shape. The fourth shows possible portfolios composed of two assets when one of the assets is risk-free. The fifth illustrates how the tangency portfolio and Sharpe ratio are determined. The sixth illustrates the Portfolio Improvement Rule.
This is the first in a set of two Readings on risk and return. It introduces the ideas of financial risk and return, at first intuitively, with a discussion of investor risk aversion and tradeoffs, and then formally, with a basic explanation of pertinent statistics. It introduces probability distributions and their parameters-mean and standard deviation-as measures of expected return and risk. Using sample statistics from historical returns as coordinate pairs, it plots asset classes in mu-sigma space to give a graphical representation of risk and return, and defines dominance. To cement understanding, the text steps through calculations of risk and return statistics from historical price data for Microsoft to mu-sigma space. The second half of the reading covers the co-movement of stock returns using sample covariance, beta, and correlation computed for pairs of risky assets. Scatter plots and linear regression are introduced to calculate beta. The Reading introduces essential portfolio math, with portfolio weights and correlation coefficients. It shows that a portfolio's risk is lower than the weighted average risk of its component assets if the assets are not perfectly positively correlated. This fundamental statistical property gives rise to the economics of diversification. The Reading contains 7 web-based Interactive Illustrations. The first demonstrates the Central Limit Theorem. The second ensures a solid understanding of how returns are calculated from prices and dividends. The third shows how to create a histogram.
This reading introduces the theory of capital structure. It explores the determinants of an optimal capital structure-first in the context of Modigliani and Miller's (M&M's) perfect market conditions, and then as M&M conditions are selectively relaxed. The reading begins with an overview and comparison of the distinctive characteristics of debt and equity securities and why the choice between them is relevant. The effects of leverage on measures of company financial performance and on the allocation of risk between debt and equity holders follow, laying the groundwork for a discussion of capital structure choice that is initially cast in terms of selecting a target leverage ratio. Next, the M&M propositions are introduced and readers learn why, under perfect market conditions, financing decisions are irrelevant to firm value. Numerical examples and an interactive illustration are used to illustrate the propositions. The M&M conditions are then relaxed to include taxes, financial distress, agency costs, asymmetric information, etc. Alternative theories of optimal capital structure-including the static tradeoff model and pecking order theory-are developed and compared. The Supplemental Reading covers the difficulties of resetting capital structure once firms are overleveraged and also provides some real-world context for how corporate managers make capital structure decisions.
This reading introduces the capital allocation process. It presents the valuation tools and financial metrics used by companies to evaluate investment opportunities. The reading begins with the relatively simple problem of evaluating a single investment proposal using net present value (NPV) and relates NPV to the concept of value maximization. It then considers alternative metrics and examines the pros and cons of each. Each metric is compared to NPV in execution and likely performance. The reading then proceeds to a more complicated problem commonly faced by managers: how to choose among multiple projects, often in the presence of budgetary or managerial constraints. Students are given a framework for comparing and ranking projects utilizing the various metrics. A brief detour links NPV to the capital markets and, specifically, to risk and expected returns. The reading concludes with an overview of real-world complications that can limit the reliability of the various financial metrics used throughout the reading, and considers ways to adapt metrics and methodologies accordingly. The reading contains seven web-based interactive illustrations. Five of these provide an application and visual representation of important tools and metrics covered in the reading, including NPV, internal rate of return, payback period, and the profitability index. Two additional interactives illustrate the complexity of making capital budgeting decisions in a complex operating environment with multiple investment opportunities. The first of these examines the implications of using a single hurdle rate to evaluate projects of varying degrees of riskiness; the latter illustrates the difficulties involved in selecting the value maximizing set of opportunities in the presence of a budget constraint and/or in situations where one or more projects monopolize the available budget.
This reading covers the basic elements of bonds and introduces some of the analytical techniques used to understand and compare them. It assumes the reader is familiar with the concept of the time value of money (see HBP 8299). The reading provides an economic analysis of simple risk-free bonds, including both zero-coupon and coupon bonds, and extends to bonds with credit risk. The material covers the relationships between prices, yields and maturity and introduces the concept of duration. The reader is introduced to the yield curve and the term structure of interest rates. Selected advanced topics (floating rate bonds, forward rates, evaluating default risk) are included in the Supplemental Reading. The reading concludes with a brief discussion of how the formulas in the reading relate to pre-programmed Excel functions. The reading includes nine interactive illustrations: "Bond Terminology" is a term sheet excerpted from an Apple, Inc. prospectus which familiarizes the reader with bond terminology. "Calculating the Price of a Coupon Bond" calculates the price (present value) of a bond's cash flows, based on reader inputs for maturity, coupon and yield to maturity (YTM). "Inverse Relationship Between Bond Price and Yield to Maturity" demonstrates the inverse relationship between prices and yields. "Historical Yield Curves" is an animated display of the U.S. Treasury yield curve from 1962 to 2015. "Bond Duration" calculates the duration of a bond based upon inputs for maturity, coupon and YTM. "Bond Duration and Maturity" demonstrates the relationship between duration and maturity over a 50-year horizon. "Calculating Bond Duration" is an animated demonstration of how duration is calculated. "Bond Price Sensitivity to Changes in Interest Rate" demonstrates the sensitivity of bond duration to changes in interest rates and maturity.
Given an interest rate, readers will learn to calculate the present value of a sum to be received in the future or, alternatively, the future value of a sum invested today. The reading covers compounding and discounting, the two types of calculations used to determine the future and present value of money. It concludes with more complicated calculations drawn from real-world examples, and a brief discussion of how the formulas in the reading relate to pre-programmed Excel functions. The reading includes eight interactive illustrations: "Time Value of $100 Cash" shows the value of $100 compounded or discounted over 1-, 2-, and 3-year periods; "Calculating the Present Value of Multiple Cash Flows" is an animated presentation of present value calculations involving multiple (equal) cash flows and multiple periods; "Present or Future Value of Multiple Cash Flows" covers multiple (equal) cash flows and multiple periods, and allows readers to choose whether to compute present values or future values and observe the results; "Time Value of $100 with Compounding Frequencies" allows the reader to observe the impact of varying the interest rate and compounding frequency on the present or future value of $100; "Effect of Compounding Frequency" visually illustrates the economic impact of compounding frequency on future value; "Mortgage as an Annuity" is a mortgage calculator which allows the reader to set the APR and mortgage term and see how each affects the monthly payment as well as the split between principal and interest over time; "Present Value of Perpetuities and Annuities by Term" illustrates the changing relationship between a perpetuity and annuities (which share the same annual payment stream but differ in their term lengths) as interest rates change; "Practice Questions for Time Value of Money" is a self-study tool which enables readers to check their comprehension.
Magna International, Inc., a Canadian-based automotive parts manufacturer, is considering whether and how to unwind its dual-class ownership structure. A family trust controlled by the founder owns a 0.65% economic interest in the company but has 66% of the votes via a super-voting class of shares. Officers of the company are considering how to fashion a transaction that will end the family's control and win the approval of both classes of shareholders. The Magna (A) case asks the students to weigh the costs and benefits of dual-class ownership and the best way to convert to single-class. The Magna (B) case describes the proposal that Magna's board put to a shareholder vote. Students are asked to evaluate it and decide whether they would approve it.
Magna International, Inc., a Canadian-based automotive parts manufacturer, is considering whether and how to unwind its dual-class ownership structure. A family trust controlled by the founder owns a 0.65% economic interest in the company but has 66% of the votes via a super-voting class of shares. Officers of the company are considering how to fashion a transaction that will end the family's control and win the approval of both classes of shareholders. The Magna (A) case asks the students to weigh the costs and benefits of dual-class ownership and the best way to convert to single-class. The Magna (B) case describes the proposal that Magna's board put to a shareholder vote. Students are asked to evaluate it and decide whether they would approve it.
Magna International, Inc., a Canadian-based automotive parts manufacturer, is considering whether and how to unwind its dual-class ownership structure. A family trust controlled by the founder owns a 0.65% economic interest in the company but has 66% of the votes via a super-voting class of shares. Officers of the company are considering how to fashion a transaction that will end the family's control and win the approval of both classes of shareholders. The Magna (A) case asks the students to weigh the costs and benefits of dual-class ownership and the best way to convert to single-class. The Magna (B) case describes the proposal that Magna's board put to a shareholder vote. Students are asked to evaluate it and decide whether they would approve it. Spreadsheet to (211044).
A manufacturer and retailer of specialty doll products must decide which of two projects to fund. The decision requires the student to compute cash flows for the 2 projects, discount values to the present and compare and contrast different project performance measures.
Groupe Ariel evaluates a proposal from its Mexican subsidiary to purchase and install cost-saving equipment at a manufacturing facility in Monterrey. The improvements will allow the plant to automate recycling and remanufacturing of toner and printer cartridges, an important part of Ariel's business in many markets. Ariel corporate policy requires a discounted cash flow (DCF) analysis and an estimate for the net present value (NPV) for capital expenditures in foreign markets. A major challenge for the analysis is deciding which currency to use, the Euro or the peso. The case introduces techniques of discounted cash flow valuation analysis in a multi-currency setting and can be used to teach basic international parity conditions related to the value of operating cash flows.
This case consists primarily of excerpts from term sheets and prospectuses for six securities offerings made by US companies during 2009-2010, just after the financial crisis and recession of 2008-09. There are three issues of senior unsecured notes, one floating rate note, one equity offering, and one convertible note. The issuers are Microsoft, Coca Cola Enterprises, Norfolk Southern, IBM, Ford Motor, and Cephalon.
This note is an introduction to the cost of capital as used in discounted cash flow valuation analyses. The note covers basic financial economic principles and practical problems encountered in calculating the cost of capital, especially WACC. It concludes with cautionary advice about computing and applying WACC. The note is suitable for undergraduates, MBAs and executives studying basic cases on business valuation and capital budgeting.