Corporate Finance & Portfolio Management

Abnormal Return

= Actual Return - Expected Return Expected Return can be calculated by using CAPM (re = RF +βi [E(RM)−RF]) or alpha/beta/benchmark return (re = α + β × r)

Purchases

= Ending Inventory + COGS - Beginning Inventory

Net Asset Value (NAV)

A Mutual Fund's value is determined by it's NAV which is calculated daily based on the closing price of the underlying securities.

Incremental Cash Flows

Additional cash flow realized from the of a decision to pursue a project. = cash flow with decision - cash flow without decision Interest costs are not included in incremental cash flows because those are captured in the Weighted Average Cost of Capital (WACC) that will be used to determine NPV of the project.

Calculating Beta

Beta = Cov Ra, Rmarket / market variance Beta = [(correlation a,b) (std dev a)] / std dev market

Accounts Receivable Aging Schedule

Classifies accounts receivable by the length of time that they have been outstanding. It is more useful to review this information in percentages (i.e. accounts receivable outstanding for 1 - 30 days divided by total accounts receivable)

Sunk Costs

Costs that cannot be recovered once they have been incurred and are IGNORED for capital budgeting purposes.

Dividend Payout Ratio

Dividend Payout Ratio = ((D₀)(# Shares Outstanding)) / NI (or earnings) If earnings is not given but EPS is, calculate earnings as EPS × # shares outstanding

Dividend Yield

Dividend Yield = Dividend per Share / Price per Share

Hedge Funds

Funds that look to generate absolute returns for investors (as compared to other funds that define a specific benchmark whose return they try to match or exceed) Hedge Funds vs. Mutual Funds: - Hedge funds charge a management and performance based fee - Hedge funds are exempt from many of the reporting requirements for public investment vehicles - Hedge funds require high minimum investment - Hedge funds usually have lock-ups (restrictions on withdrawals)

Comparing Investment Returns

Investment returns are all expressed as Bond Equivalent Yields (BEY) for comparison. Portfolio return is calculated as the weighted average of the BEYs of different assets in the portfolio. Asset weight is based on the proportion of the portfolio that is invested in that particular asset.

Risk-Return Trade Off

Over the long run, market prices reward higher risk with higher returns.

Price-to-Earnings (P/E)

P/E = Share Price / EPS P/E does not change after a stock dividend or stock split.

Discounted Payback Period

Similar to payback period but discounted cash flows are used in the calculations. Discounted payback period will always be LONGER than payback period.

Solvency Risk

Solvency risk is the risk relating to the cash position of an entity. (i.e. low cash reserves)

Number of Days of Inventory

The length of the period that inventory remains with the firm before being sold. # days of inventory = Inventory / (COGS/365) Want this ratio to be close to industry average.

Risk Free Rate

The risk free rate is equivalent to the cost of debt (rd) which is BEFORE TAX

Ex-Dividend Date

This is the first day that the shares trade without the dividend (stock price will go down by the amount of the dividend paid -- i.e. $100 stock declares a $2 dividend, on the ex-dividend date the stock price will open at $98)

Weighted Average Collection Period

Used to evaluate a firm's ability to collect its receivables. Measures how long it takes a company to collect cash from its customers irrespective of changes in sales and the level of sales. Weighted Avg. Collection Period = Collection period × weighted average collection period Ignores changes in sales and the level of sales.

Risk Culture

When effective risk management is truly integrated at all levels of management and into every step of the decision-making process. - results in lower probability of mgmt being surprised; faster responses to unfavorable events; fewer operational errors; strong levels of trust; better consideration of trade-offs and risk-return relationships

Expected Risk of Portfolio

σp = (1-wf)(σm) wf = weight of risk free asset(s) σp = standard deviation of returns of the market portfolio (risky assets)

Absolute Return Objective vs. Relative Return Objective

Absolute Return Objectives state the percentage return desired by the client on a real or nominal basis. Relative Return Objectives state the required return RELATIVE to a stated benchmark (i.e. S&P 500).

Separately Managed Accounts (SMAs)

Account managed exclusively for wealthy investor(s). Aims to meet needs of specific client. SMAs vs Mutual Funds: - SMA manager takes client's tax situation into consideration. - Investors in SMAs directly own the shares and have control over which assets are bought/sold and control over the timing of the transactions - Required minimum investment in an SMA is much higher than for a mutual fund. - Charges higher annual fees.

Independent Director

An independent director is a specific type of NON-EXECUTIVE DIRECTOR that does not have a material relationship with the company with regard to employment, ownership, or remuneration.

Annualized Return

Annualized return enables comparisons across investment instruments with different maturities. Rannual = (1 + Rperiod)∧(n/period) - 1 Rperiod = return on investment in period n = number of periods in a year (days = 365; months = 12) period = length of days/weeks/months that the investment return (Rperiod) is based on. The annualized return assumes that the returns earned over short investment horizons (less than one year) can be replicated, which is not always possible. Example: A portfolio with a return of 14.35% in 15 months has an annualized return of: Rannual = [(1 + .1435)∧(15/12)] - 1 = .1132 = 11.32%

Arithmetic or Mean Return

Arithmetic Return is biased upward because it assumes that the amount invested at the beginning of each period is the same. Arithmetic Return = ∑Ri ÷ T R = all returns T = number of returns Arithmetic Mean will be higher than Geometric Mean unless there is no variation in returns, in which case they will be equal.

Operating Breakeven Point (OBE)

At the Operating Breakeven Point (OBE) revenues will equal operating costs. PQobe = V × Q + F Q = F ÷ (P-V) P-V is also called "contribution margin", so Fixed Costs divided by Contribution Margin = Operating Breakeven Quantity. The Operating Breakeven Point ignores Fixed Financial Costs (C) (i.e. interest expense). It also ignores taxes.

Book Value of Equity and Book Value per Share

Book Value per Share = Book Value of Equity / # Shares Outstanding When market price per share > book value per share, then book value per share will decrease after a share repurchase. When market price per share < book value per share, then book value per share will increase after a share repurchase.

CAPM Assumptions

CAPM assumes that: - investors plan for the same single holding period - investors are risk-averse, rational, utility maximizing - markets are not affected by transaction costs or taxes - investors have homogenous beliefs - investors can invest as little or as much as they want in an asset - investors are price takers

Capital Market Theory

Capital market theory suggests that all investors will invest in some combination of the risk-free asset and the market portfolio (along the capital market line). Except for a 100% allocation to the market portfolio, which lies on the Markowitz efficient frontier, any point on the CML will lie above the Markowitz efficient frontier. Under the assumptions of capital market theory, an investor can borrow at the risk-free rate and invest more than 100% in the market portfolio.

Cost Structure of a Company

Companies incur two types of costs: 1) Variable costs - vary with the level of production and sales (e.g. raw materials costs; sales commissions) 2) Fixed costs - remain the same irrespective of the level of production and sales (e.g. depreciation and interest expense) The higher the fixed costs relative to the variable costs, the more levered a company is. Higher fixed costs (higher leverage) results in higher earnings volatility.

Credit Scoring Models

Companies will develop credit scoring models that they will use to determine what type of credit terms to offer a customer. The model will be affected by the customer's cash availability; organization type; and history of making payments on time.

Share Repurchase Method: Buy in Open Market

Company will designate a certain $ amount (total) that will be used to repurchase shares and they will repurchase from the open market when the stock is 'attractively' priced.

Conventional Cash Flow vs Nonconventional Cash Flow Streams

Conventional cash flow streams have one cash outlay followed by a series of inflows. Nonconventional cash flow streams experience more than one sign change (cash flows switch from negative to positive more than once)

Costs of Borrowing: Banker's Acceptance Cost

Cost of Banker's Acceptance (and other sources whose costs are stated as "all-inclusive"): = ((Interest) / (Loan - Interest)) × (12/# months) Interest = Loan Amount × Rate × Interest Weight (i.e. 1/12)

Costs of Borrowing: Commercial Paper

Cost of Commercial Paper (and sources with dealers' fees and backup fees which are quoted as all inclusive): = [(Interest + Dealer's commission + Backup costs) / (Loan amount - Interest)] × (12/# months)] Interest = Loan Amount × Rate × Interest Weight (i.e. 1/12) Dealer's commission = Loan Amount × Commission Rate × Interest Weight (i.e. 1/12) Backup Costs = = Loan Amount × Backup Rate × Interest Weight (i.e. 1/12)

Current Ratio

Current Ratio = Current Assets / Current Liabilities Current Ratio < 1 indicates negative working capital and means the company may not meet its financial obligations (i.e. liquidity crisis) HIGHER current ratio is better and indicates greater liquidity.

Degree of Total Leverage (DTL)

DTL examines the combined effect of DOL and DFL to determine the sensitivity of Net Income to changes in units produced and sold. DTL = % ∆ in net income ÷ % ∆ in number of units sold DTL = (Revenue - Variable Operating Costs) / Net Income DTL = DOL × DFL DTL = [Q × (P-V)] ÷ [Q × (P-V) - F - C] Q = number of units sold P = price per unit V = variable operating cost per unit F = fixed operating cost C = fixed financial cost

Payment Date

Date on which the company actually sends out/transfers the dividend payment to shareholders.

Dividend Dates

Declaration Date Ex-Dividend Date Holder-of-Record Date Payment Date

Evaluating Trade Discounts (Early Payment Discounts)

Early payment discounts should be availed if savings from paying early are greater than the returns that could have been earned by investing for a short period of time. Cost of trade credit (aka implicit rate) = (1 + (Discount / (1 - Discount)) ∧ (365 / days beyond discount period)) - 1 i.e. terms of "2/10 net 30" mean that a 2% discount is available if you pay within 10 days otherwise full amount is due within 30 days. Within the 'discount window' the cost of trade credit is zero (0%).

Internal vs External Risk Factors

Internal Risk Factors: shortfalls within the organization that would cause it to fail to meet objectives (i.e. liquidity issues) External (outside) Risk Factors: uncertain forces that the organization is exposed to (i.e. exchange rate fluctuations)

Portfolio Diversification Methods

Investors can diversify by: - Investing in a variety of asset classes (e.g., large cap stocks, small cap stocks, bonds, commodities, real estate, etc.) that are not highly correlated. - Using index funds that minimize the costs of diversification and grant exposure to specific asset classes. - Investing among countries that focus on different industries, are undergoing different stages of the business cycle, and have different currencies. - Choosing not to invest a significant portion of their wealth in employee stock plans, as their human capital is already entirely invested in their employing companies. - Only adding a security to the portfolio if its Sharpe ratio is greater than the Sharpe ratio of the portfolio times the correlation coefficient. - Only adding a security to the portfolio if the benefit (additional expected return, reduced portfolio risk) is greater than the associated costs (trading costs and costs of tracking a larger portfolio). - Adding insurance to the portfolio by purchasing put options or adding an asset class that has a negative correlation with the assets in the portfolio (e.g., commodities).

Pre-Tax & After-Tax Nominal Returns

It can safely be assumed that stated returns are given as Pre-Tax Nominal Returns. (Nominal meaning it does not factor in expenses or inflation). After-Tax Nominal Returns are calculated as: R after-tax = Net Return × (1-tax rate) i.e. if the net return on an investment/portfolio is 20%, and the tax rate is 25%, the after-tax return for the investor is: 20% × (1-25%) = 15%

Portfolio Performance Evaluation: Jensen's Alpha

Jensen's Alpha = Actual Portfolio Return % - Expected Portfolio Return % Where Expected Return (re) is calculated using CAPM: re = RF +βi [E(RM)−RF] Or calculated using alpha (α) and beta (β) against a benchmark return (r): re = α + β × r Jensen's alpha is represents the MAXIMUM that an investor should be willing to pay the portfolio manager. The higher the Jensen's Alpha for a portfolio, the better its risk-adjusted performance.

Liquidity Risk

Liquidity risk (aka Transaction Cost Risk) is a FINANCIAL RISK of substantial downward valuation adjustment when trying to sell an asset. risk that seller will have to reduce price of an asset below true market value in order to sell it quickly. Drivers of liquidity risk are changes in market conditions or the market for an individual asset and the size of the position (large positions are harder and more costly to sell) Transaction cost is the spread between the bid and ask price. Liquidity risk would arise if the spread widened as the asset was being sold.

Number of Days of Payables

Measures how long the company takes to pay its suppliers. # days payables = Accounts Payable / (Purchases / 365)

Number of Days of Receivables

Measures how many days it takes, on average, to collect receivables from customers. = Accounts Receivable / (Sales on Credit / 365) Too high a collection period: customers are slow to pay and too much capital is tied up in receivables Too low a collection period: company's credit policy may be too strict which could hurt sales

Portfolio Performance Evaluation: M²

M² = (RA - Rf) σm / σC - (Rm - Rf) M² is based on TOTAL RISK, not beta (systematic risk), and offers rankings that are identical to those provided by the Sharpe ratio. However, the M² rankings are easier to interpret as they are in percentage terms. A portfolio that matches the market's performance will have an M² of zero, while one that outperforms the market will have a positive M². The M² also enables us to tell which portfolios beat the market on a risk-adjusted basis.

One-Tier & Two-Tier Boards

One-Tier: United States; UK; India Two-Tier: Germany; China; Netherlands -- consist of both a Supervisory Board and a Management (Executive) Board Supervisory Board: Made up non-executive employee representatives - typically elected by the company's employees and could make up half of the supervisory board in large companies. Management Board: Made up of Executive Directors

Operational Risk

Operational risk is NON-FINANCIAL RISK that describes all internal risks arising from the people/processes/etc that work together in an organization to produce its outputs.

Positive Screening

Positive screening determines a theme that is best‐in‐class to invest in.

Risk Budgeting LOS 41e (describe risk budgeting and its role in risk governance)

Risk Budgeting: Focuses on how risk is taken by quantifying and allocating tolerable risk to various activities and/or investments based on their characteristics. Takes board level defined Risk Tolerance and brings it to a management decision/operational level. Risk budgets can be complex or simple; multi-dimensional or one-dimensional.

Risk Governance LOS 41c (define risk governance and describe elements of effective risk governance)

Risk Governance: the top-down process and guidance from the board that directs management activities to align with the goals of the overall entity. Risk Governance Steps: 1) Establish Risk Tolerance 2) Set Risk Budget 3) Identify Risk Exposure Enterprise Risk Management (ERM) - Determines organization's goals/priorities - Determines risk appetite and tolerance - Oversees risk management Effective Risk Governance: - Provides a sense of the worst loss that the organization can manage in various scenarios - Provides clear guidance - Leaves flexibility for mgmt to execute strategies - Focuses on ERM (not narrowly on biz divisions or departments) - Should establish risk mgmt committee - Should appoint Chief Risk Officer (CRO)

Risk Tolerance LOS 41d (explain how risk tolerance affects risk mgmt)

Risk Tolerance: identifies the extent to which the entity is willing to experience loss or fail to meet objectives. Board - defines risk appetite Management - executes strategies to keep risk at an acceptable level (as defined by board)

Risk Modification Options

Risk Transfer: process of passing on a risk to another party, usually in the form of an insurance policy. Risk Shifting: refers to actions that change the distribution of risk outcomes. Associated with derivative contracts. Risk Avoidance: Turning down projects Risk Acceptance: Self-Insurance (such as an established loss reserve); Diversification

Operating Risk

Risk associated with a company's operating cost structure (fixed vs. variable operating costs)

Risk Aversion

Risk averse investors aim to maximize returns for a given level of risk and minimize risk for a given level of return. Riskier investment will require a higher expected return.

Risk Seeker

Risk seeking investors get extra 'utility' (satisfaction) from the uncertainty associated with their investments.

Risk Tolerance

Risk tolerance refers to the LEVEL of risk that an investor is willing to accept in order to achieve investment goals. Lower risk tolerance = lower level of risk acceptable to investor Lower risk tolerance = higher risk aversion

Share Price after Stock Dividend

Share Price after Stock Dividend = old price / (1 + % stock dividend)

Share Repurchase

Share repurchases will INCREASE debt ratios if financed internally (with cash) because assets (cash) will decrease and equity will decrease. Repurchases can increase or decrease EPS depending on how and at what cost it is financed. *see 'Shares Repurchased Using Debt' Share repurchases can be authorized but not completed. They entail an outflow of cash from the company and do not have to be completed pro-rata across all of the shareholders. Share repurchases can be used to reduce the number of shares outstanding. They can send out a signal that the management believes the stock is undervalued.

Treasury Shares

Shares repurchased by the company are known as Treasury Shares. Treasury Shares, reported on the balance sheet, are not considered for dividends, voting, or calculating earnings per share

Surety Bonds Fidelity Bonds Indemnity Clauses and Hold Harmless Arrangements

Surety Bonds: an insurer promises to pay the insured a certain amount of money if a third party fails to fulfill its obligation. They are popular in commercial contracts where one party bears the risk of potentially suffering a huge cost if another party does not perform. Fidelity Bonds: cover against losses that result from employee dishonesty. Indemnity Clauses and Hold Harmless Arrangements: with indemnity clauses and hold harmless arrangements, one of the parties to a contract agrees to hold the other harmless and/or indemnify the other in the event of loss.

Cost of... Debt/Equity/Preferred Stock

The "Cost of Debt/Equity/Preferred Stock" is the return required by holders of the debt/equity/preferred stock. The Cost of Debt is calculated on a BEFORE-TAX and AFTER-TAX basis because the interest expense provides the company with a benefit -- the Tax Shield -- by way of reducing taxable income. Therefore, the before-tax cost of debt is higher than the after-tax cost of debt. Estimating Cost of Equity is more difficult than estimating Cost of Preferred Stock due to the uncertainty of future cash flows (both amount and timing) to common stock holders.

Pure Play Method (of estimating β)

The Pure-Play Method is used to estimate β of a project or company that is not publicly traded. Pure-Play Method of Estimating β: 1) Find a comparable company or project 2) Unlever the β of the comparable company or project to find 'asset beta' -- or beta that reflects business risk but does not include financial risk. βasset = βequity*[ 1 ÷ (1 + ((1-t*)×D/E*))] Use tax rate, D/E ratio, and βequity of *comparable company* 3) Adjust the calculated unlevered, 'asset beta', for the comparable level of financial risk (leverage) in the project or company under study. βproject = βasset[(1 + ((1-t**)×D/E**)] Use tax rate and D/E ratio of **subject company**

Risk Aversion Coefficient

The Risk Aversion Coefficient (A) is found in the Utility Function: example: U = E(R)-(1/2 × A σ2) "A" is positive and higher for investors who are more risk averse, as additional risk REDUCES the total utility they derive from their portfolios. "A" is negative for risk-seeking investors as additional risk increases total utility. "A" is zero for the risk-neutral investor as additional risk has no impact on utility.

Security Characteristic Line (SCL)

The Security Characteristic Line (SCL) plots the EXCESS returns of a security AGAINST the EXCESS returns on the market: Ri - Rf = αi + βi(Rm - Rf) Jensen's Alpha is the y-intercept Beta is the slope of the SCL

Capital Budgeting: Management

The capital budgeting process tells us two things about company management: 1) the extent to which management pursues the goal of shareholder wealth maximation 2) management's effectiveness in pursuit of this goal

Core-Satellite Approach

The core-satellite approach to constructing portfolios is defined as "investing the majority of the portfolio on a passive or low active risk basis while a minority of the assets is managed aggressively in smaller portfolios."

Declaration Date

The dividend is announced on this day (and div declared is reported under equity on the balance sheet)

Breakeven Number of Units

The number of units (Q) that must be sold at a given price (P) such that a company's revenue equals costs. Q = (F + C) ÷ (P - V)

Creditworthiness

The perceived ability of a company to satisfy the payment terms on borrowings in a timely manner.

LOS 40a: Portfolio Approach to Investing

The portfolio approach means evaluating individual investments on the basis of its contribution to the characteristics of the portfolio as a whole. An individual investment may be deemed 'too risky' on its own, but not when considered in combination with the other portfolio investments.

Profitability Index (PI) (aka Benefit Cost Ratio)

The ratio of discounted future cash flows to the initial investment. = (PV of future cash flows) ÷ Initial Investment = 1 + (NPV ÷ Initial Investment) If PI > 1 the company should ACCEPT the project and NPV will be positive. If PI < 1 the company should REJECT the project and NPV will be negative.

Business Risk

The risk associated with a company's operating earnings. Broken down into: 1) Sales Risk: the uncertainty associated with total revenue (affected by economic conditions, industry dynamics, gov regulations, demographics) HIGHER standard deviation of units sold and HIGHER standard deviation of selling price per unit will result in a wider (flatter) distribution of operating profit. *Greater earnings volatility depicts more sales risk.* 2) Operating Risk: the risk associated with a company's operating cost structure (i.e. proportion of fixed costs to variable costs). *Greater proportion of fixed costs equates to more operating risk. proporation FIXED COSTS > proportion VARIABLE COSTS = MORE RISK

Corporate Governance

The system of internal controls and procedures by which individual companies are managed. Corporate Governance systems are influenced by stakeholders (Stakeholder Theory) or shareholders (Shareholder Theory) as well as historical, cultural, legal, political, and other influences specific to a region

Opportunity Costs

The value of the next best alternative that is foregone in making the decision to pursue a particular project. These costs SHOULD be included in the capital budgeting process.

Core Satellite Investment Approach

Under the Core Satellite investment approach, investors invest most of their funds in passive investments and trade a small proportion of assets actively.

Beta (β)

β is calculated by regressing the company's stock's returns against market returns over a given period. β estimates are sensitive to: - length of estimation period - frequency of return intervals measured (i.e. monthly return vs. daily return -- daily return will result in a smaller standard error in the β estimate) - the choice of market index against which stocks are regressed - size of company (some say β should be adjusted upward if the company is small to reflect greater risk) - we assume MARKET BETA = 1* *Betas are believed to regress towards 1 over time which implies that the risk of an individual project or firm equals market risk over time.

Systematic (nondiversifiable) Risk

β is esposed to the following types of Systematic (nondiversifiable) Risk: a) business risk - reflects operating leverage and factors that affect sales (operating risk and operating risk) b) financial risk - uncertainty of profits and cash flows because of the use of fixed-cost financing sources such as debt and leases. Greater use of debt results in greater financial risk.

Portfolio Beta

βp = w₁β₁ + w₂β₂ + w₃β₃ ... The portfolio beta (βp) is used in the CAPM model to determine the expected return on a portfolio: E(Rp) = RF +βp [E(RM)−RF] E(Rp) --> expected return on portfolio RF --> risk free rate of return βp --> beta of portfolio (beta measures the sensitivity of the portfolio returns to changes in market returns) RM --> expected return on market

Capital Budgeting: Basic Principles

1) Decisions based on actual after-tax cash flows 2) Timing of cash flows is crucial 3) Cash flows are based on opportunity costs 4) Cash flows are analyzed on an after-tax basis 5) Financing costs are ignored from calculations of operating cash flows (financing costs are reflected in the required rate of return from an investment project) 6) Accounting net income is not used as cash flows for capital budgeting (because accounting cash flows are subject to non-cash charges (depreciation) and financing charges (interest expense)

Capital Budgeting: Process

1) Idea Generation (ideas can come from anywhere) 2) Analyzing Individual Proposals (collect info; forecast cash flows; evaluate feasibility) 3) Planning the Capital Budget 4) Monitoring and Post-Auditing (compare actual performance to forecasts and identify reasons for differences. This process can aid in indicating systematic errors, improve business operations, and provide concrete ideas for future investment opportunities.)

Capital Budgeting: Projects

1) Replacement Projects (maintain normal course of business; do not require very thorough analysis) 2) Expansion Projects (increase size of business; require careful consideration) 3) New Products/Services (requires very detailed analysis and more people) 4) Regulatory/Safety/Environmental Projects (usually mandated and do not generate revenue) 5) Other Projects (cannot typically be analyzed in a capital budgeting process; difficult to evaluate; risky)

Steps Toward Building a Portfolio

1) Risk Budgeting: process of subdividing the desired level of portfolio risk (determined in the IPS) across diff. sources of investment returns 2) Tactical Asset Allocation: deviation from strategic asset allocation for a short term 3) Security Selection 4) Portfolio Rebalancing: necessary when changes in security prices lead to changes in the weights of diff. asset classes in the portfolio.

Earnings Retention Rate

= (1 - (D÷EPS)) D --> current dividend EPS --> earnings per share EPS = NI/#shares outstanding The percentage of net income that is retained to grow the business, rather than being paid out as dividends.

Transforming D/E ratio to weight of debt (wd) and weight of equity (we)

= (D/E) ÷ (1 + (D/E)) = wd = D ÷ (D + E) 1 - wd = we wd --> proportion of debt used we --> proportion of equity used

Net Operating Cycle

= No. Days of Inventory + No. Days of Receivables - No. Days Payables = (365/Inventory Turnover) + (365/Receivables Turnover) - (365/Payables Turnover)

Tax Shield

= interest expense × tax rate Interest expense reduces profits before tax. Interest expense × (1 - tax rate) is the reduction to after-tax profits due to the tax shield of interest expense × tax rate.

Break Point (WACC Change)

A Break Point occurs when the WACC changes (increases) as additional capital is raised. The marginal cost of capital (MCC) is upward sloping because each additional dollar of capital raised (through debt or equity) adds more risk and will therefore charge a higher risk premium. Break Point = $$ at which a component's (debt or equity) cost of capital increases ÷ Proportion of new capital raised from the component WACC increases after each Break Point is reached.

Share Repurchase Method: Direct Negotiation

A company will negotiate directly with a shareholder to repurchase shares. This can occur when a large holder wants to see a large amount and the company wishes to limit the large sale from affecting the market and lowering share value, OR when the company wishes to prevent a shareholder from gaining too large a % of ownership or representation on the company's board.

Breakeven Point

A company's breakeven point (PQ) occurs at the number of units sold at which its net income = 0 (in other words, the point at which a company's revenues = its total costs) PQ = VQ + F + C P = price per unit Q = number of units produced and sold V = variable cost per unit F = fixed operating cost C = fixed financial cost

Growth Rate (g)

A company's sustainable growth rate (g) is calculated as follows: g = Earnings Retention Rate × ROE g = (1 - (D÷EPS)) × ROE (1 - (D÷EPS)) = earnings retention rate (D÷EPS) = dividend payout ratio D --> current dividend EPS --> earnings per share ROE --> Net Income / Avg. Total Equity

Levered Portfolio (Leveraged Portfolio)

A levered portfolio is one in which the investor is borrowing at the risk-free rate in order to invest more in risky assets. Return and risk for leveraged portfolios is higher than for unleveraged portfolios BUT, given that the investor's borrowing rate is higher than the risk free rate, for every additional unit of risk taken the investor gets a lower increase in expected return. (The capital market line is kinked (slope decreases) at the point where leverage is used). In a leveraged portfolio, investment in the risk-free asset(s) is NEGATIVE (wf < 0) and still needs to be included in the calculations of risk/return on the portfolio.

Inventory Turnover

A measure of how often inventory is created and sole over a period. = COGS / Avg. Inventory Too high: company may have too little stock on hand which may hurt sales Too low: company has too much liquidity tied up in inventory.

Return Generating Models LOS 43d (explain return generating models and their uses)

A return generating model is used to forecast the return on a security given certain parameters. Macroeconomic Factor Model: use economic factors (e.g. economic growth rates, interest rates, inflation rates) that correlate with a security to estimate returns. Fundamental Factor Models: relationships between security returns and underlying fundamentals (e.g. earnings, earnings growth, and cash flow growth) to estimate returns. Statistical Factor Models: use historical and cross sectional returns data to identify factors that explain returns and use an asset's sensitivity to those factors to project returns. (see Market Model card)

Working Capital Management

Short-term aspects of corporate finance activities. Managing current assets and current liabilities so that company has the liquidity it needs to handle operations and is making short-term investing decisions that are the most productive.

Share Repurchase Method: Buy Back a Fixed Number of Shares at a Fixed Price

Also known as a "fixed price tender offer" where the company offers to purchase a fixed number of shares at a fixed price (typically premium to current market price) on a fixed date in the future. Holders determine if they would like to sell for the price being offered. The company will then repurchase shares pro-rata from the holders that wish to sell.

Utility Function

An example of a utility function is: U = E(R) - (1/2)Aσ² U = the utility of the investment E(R) = the expected return σ² = variance of returns A = *additional return required by the investor to accept an additional unit of risk *A is known as the Risk Aversion Coefficient Given a list of returns (E(r), and standard deviations (σ) for various portfolios, the one that provides the highest utility (U) for a given investor will be selected.

Lending Portfolio

An investor who owns a lending portfolio is lending (investing) a portion of his net worth at the risk-free rate. Meaning he is invested in some risk-free assets and some risky assets but is not using debt to finance his position. Therefore, his portfolio will be located at a point along the capital market line (CML) below the location of the market portfolio.

Investment Opportunity Set (IOS)

An investors IOS consists of individual securities and portfolios that can be constructed by combining those individual securities. The investment opportunity set for an investor will lie within a minimum variance frontier curve. The curve, which forms around the investment opportunity set on a graph, represents the risk-return on all combinations of the investment opportunity set options.

DFL -- Important take away

At higher levels of fixed financing costs (higher DFL) the same percentage change in operating income will lead to a HIGHER percentage change in net income. Higher fixed financing costs INCREASE the sensitivity of net income to changes in operating income. Higher DFL = Higher Operating Risk = Higher Sensitivity = Higher Increase to Net Income when Operating Income Increases

Float Factor

Average number of days it takes a deposited check to clear. Float Factor = Average daily float* / average daily deposit** *float = amount of $$ in transit between payments made by customers and amount that can be used by the company (i.e. available balance) ** avg daily deposit = total amount of checks (deposits) / number of days

Estimating Beta (Beta of a stock)

Beta is a measure of the sensitivity of an asset's return to the market's return. It is computed as the ratio of the covariance of the stock's return and the market return to the variance of market returns. β = [Cov(Ri, Rm)] ÷ σ²m β = (correlation i,m) × [σi ÷ σm] σ²m = variance of market returns σi = standard deviation of asset, i σm = standard deviation of market, m

Cash Management Investment Policy

Basic structure: a) purpose - states reason for portfolio existence and general portfolio attributes (investment strategy) b) authorities - provides info about who supervises and what actions will be undertaken if investment policy isn't followed c) restrictions - types of allowable/unallowable investments and maximum proportion of each type of security that may be held (can also state minimum credit rating of portfolio securities)

Cost of Equity: Capital Asset Pricing Model (CAPM) Approach

CAPM (this formula is used for finding required individual asset returns, Re, and for required portfolio returns, Rp, and asset beta is replaced with portfolio beta) Re = RF +βi [E(RM)−RF] E(Re) --> cost of equity (aka required return on stock) RF --> risk free rate of return βi --> beta of stock (beta measures the sensitivity of the stock's returns to changes in market returns) RM --> expected return on market [E(RM)-RF] --> equity risk premium* *[E(RM)-RF], equity risk premium, can be estimated using a 'survey approach' where the average of the forecasts of financial experts is adjusted for the specific stock's systematic (nondiversifiable) risk.

Cost of Equity: CAPM w/ Country Risk Premium (CRP)

CAPM w/ Country Risk Premium (CRP) re = RF +βi [(E(RM)−RF) + CRP] The country risk premium (CRP) is added to the CAPM formula to capture the added risk in developing nations. CRP = Sovereign Yield Spread* × (Annualized Standard Deviation of Equity Index ÷ Annualized Standard Deviation of Sovereign Bond Market In Terms of the Developed Market Currency) *Sovereign Yield Spread = Yield on Bond in Developing Country - Yield on Bond in Developed Country (with similar maturity) i.e. To calculate the CRP of Malaysia you would need to know the following items: 1) the yield on a Malaysian bond 2) the yield on a US bond (with similar maturity) 3) the annualized standard deviation of the Malaysian stock market 4) the annualized standard deviation of Malaysia's US dollar denominated bond market.

Dividend Types

Cash Dividends - regular (consistent -- maybe quarterly) - extra or special (to distribute extra cash to shareholders in a good year) - liquidating dividend (to distribute assets when company is closing) *taxable; REDUCE a company's liquidity ratios; increase debt-to-assets ratio; increase debt-to-equity ratio) Stock Dividends (increase # shares and reduce share price) - issuance of additional shares in lieu of cash dividend - stock split *both a stock dividend and a stock split have no economic effect on the company and no effect on liquidity or solvency ratios - reverse split (reduce # shares and increase share price) ** stock dividends can help bring the company's stock price into optimal range. Company with a stock worth $100 ($60) might issue a stock dividend (reverse split) to increase(decrease) the number of shares and reduce(increase) per share price to a more desirable level (i.e. $80).

Compliance Risk (Regulatory, Accounting, and Tax Risk)

Compliance risks are NON-FINANCIAL RISKS that refer to the risk of an organization incurring significant unexpected costs (i.e. back taxes, financial restatements, penalties)

Costs of Borrowing: Line of Credit Cost

Cost of Line of Credit (and other sources that require a commitment fee): = ((Interest + Commitment Fee) / Loan Amount) × (12/# months) Interest = Loan Amount × Rate × Interest Weight (i.e. 1/12) Commitment Fee = Loan Amount × Fee Rate × Fee Weight

Investment Policy Statement (IPS): Purpose

Creating an IPS is a collaberative process between client and portfolio manager. Purpose: - acts as a guideline for investment decisions that will help the client reach his/her goals - establishes a standard against which the PMs performance can be measured

Credit Risk

Credit risk is a FINANCIAL RISK of loss is one party fails to pay an amount owed on an obligation (i.e. bond or derivative) Drivers of credit risk are fundamental weaknesses in the economy, industry, demand for a company's product.

Holder-of-Record Date

Date on which, if you hold the stock on or before, you will receive the dividend that has been declared.

Measures of Risk for Derivatives

Delta: measures the sensitivity of the value of a derivative to a small change in the underlying asset Gamma: captures the impact of relatively large changes in the underlying asset on the value of the derivative Vega: captures the impact of changes in the volatility of the underlying asset on the value of an option contract Rho: measure the sensitivity of the value of a derivative contract to changes in interest rates

Expected Return on Portfolio

E(Rp) = (wf)(Rf) + (1-wf)(E(Rm)) wf = weight of risk free asset(s) Rf = risk free rate of return E(Rm) = rate of return on the market portfolio (return on risky assets)

Earnings Yield

E/P = Earnings Yield = (1 / (P/E)) or = EPS/ stock price Earnings Yield < the cost of borrowing, then a share repurchase will be dilutive and EPS will DECREASE Earnings Yield > the cost of borrowing, then a share repurchase will be anti-dilutive and EPS will INCREASE Earnings Yield = the cost of borrowing, then a share repurchase will not change EPS

Degree of Operating Leverage (DOL)

ELASTICITY MEASURE. We use DOL to examine a company's SENSITIVITY of operating income to changes in unit sales. In other words, DOL tells us the percentage change we can expect in operating income for every 1% change in units sold. DOL = % ∆ in operating income ÷ % ∆ in units sold DOL = (Revenue - Variable Operating Costs) / (Revenues - Variable Operating Costs - Fixed Operating Costs) When operating income = 0, DOL is undefined DOL = (Q × (P-V)) ÷ (Q × (P-V) - F) Q = number of units sold P = price per unit V = variable operating cost per unit F = fixed operating cost Q × (P-V) = contribution margin (P-V) = contribution margin per unit DOL equals 1 when there are no fixed costs (aka no operating leverage) DOL is negative when the company makes operating losses. LOWER DOL implies LESS sensitivity to changes in units sold which could imply lower proportion of fixed costs in the company's cost structure (i.e. lower operating risk). The sensitivity of operating income to changes in the amount of units sold DECREASES at higher sales volumes.

Share Repurchase with Debt Financing

EPS after repurchase using debt financing: = [NI - (after-tax interest expense)] / Shares Outstanding After Repurchase If the after-tax cost of borrowing (rd × (1-t)) is GREATER THAN the earnings yield (EPS/ Stock Price), than EPS falls after the repurchase. If the after-tax cost of borrowing is LESS THAN the earnings yield, than EPS rises after the repurchase.

Exchange Traded Funds (ETFs)

ETFs issue shares in a portfolio of securities and are designed to track the performance of a specific index (using proportional investing). ETF vs Mutual Funds: - Similar to open‐end mutual funds in that they usually trade close to their NAV per share. -Similar to closed‐end mutual funds in that they trade in the secondary market. - Diff. from MFs in that shares are bought from other investors and shares can be bought/sold at premium or shorted - Diff. from MFs in that brokerage fees are incurred - Diff. from MFs in that they pay out dividends rather than reinvest, generally have a tax advantage over MFs and generally require a smaller investment ($$)

Risk Management Framework LOS 41b (describe features of Risk Management Framework)

Effective Risk Management Framework addresses the following areas: - Risk Governance (board of directors; top-down guidance that takes an enterprise-wide view rather than a business division or narrower risk view) - Risk Identification and Measurement (ongoing process that involves analyzing and identifying risk exposure, tracking changes in risk exposure, calculating risk metrics to gauge significance of risks) - Risk Infrastructure (people/systems/technology required to track risk exposure and conduct quantitative risk analysis) - Policies & Procedures (translate risk governance into day-to-day operations and decision making processes) - Risk Monitoring, Mitigation, and Management (the MOST DIFFICULT facet of risk mgmt framework; continually reviewing and reevaluating risk identifiers, policies and procedures, and changing risk exposures and drivers; recognizing when the entity's risk exposure is not aligned with predetermined risk tolerance and taking action to realign it) - Communication (continuous communication of risk tolerance/parameters/and constraints, across all levels of the organization; must be clear and timely)

Financial Risk and Non-Financial Risk

Financial Risk: risks that originate in financial markets (risk of loss due to third party defaulting, changes in ptranrices or interest rates) and are more external in nature. Non-Financial Risk: Emanate from a variety of forces and involve RELATIONSHIPS between the organization and peers, regulators, environment, suppliers, employees, customers. Non-Financial risks have some sort of 'internal' component.

Geometric Mean Return

Geometric Mean Return represents a "buy and hold" strategy and accounts for compounding of returns. It does not assume that the amount invested in each period is the same. R = {[(1+R₁) × (1+R₂) × ... (1+R_)]∧ (¹/ⁿ)} - 1 Geometric Mean is the compound holding period return raise to the power of 1 divided by the number of compounding periods minus 1. Geometric Mean will be lower than Arithmetic Mean unless there is no variation in returns, in which case they will be equal. Arithmetic Mean ADDS, Geometric Mean MULTIPLIES!

Gross and Net Returns

Gross Returns are calculated BEFORE deductions for mgmt expenses, custodial fees, taxes and other expenses that are NOT directly linked to the generation of returns. Trading expenses are accounted for in the gross return calculation because they are necessary to generate the return. Gross Return is an appropriate way to evaluate portfolio performance. GROSS RETURN > NET RETURN Net Returns deduct all managerial and administrative expenses that reduce an investors' return. This is the return that investors are most concerned with.

Evaluation of Inventory Management

High level of inventory: undesirable as it inflates storage costs and can result in inventory damage or obsolescence. Shortage of inventory: can hurt sales; lose customers Inventory management is evaluated by analyzing inventory turnover and # days of inventory.

Holding Period Return (HPR)

Holding Period Return measures the return earned on an investment over a single specified period of time. HPR = [(Pt - Pt-₁ + Dt) ÷ Pt-₁] -1 Pt = price at the end of the period Dt = dividend for the period Pt-₁ = price at the beginning of the period HPRs can be calculated for more than one period by compounding single period returns: R = [(1+R₁) × (1+R₂) ×.... (1+R_)] - 1

Distributional Characteristics (Return Distributions)

IF returns are NOT normally distributed (unable to be described completely by their mean and variance) the distribution may deviate from normality because of: SKEWNESS: asymmetry of returns - distributions concentrated to the left (more data to the left) is referred to as RIGHT or POSITIVELY skewed - distributions concentrated to the right (more data to the right) is referred to as LEFT or NEGATIVELY skewed KURTOSIS: fat tails or higher than normal probabilities for extreme returns which leads to an increased asset risk that is not captures by the mean/variance framework.

Investment Policy Statement (IPS): Components

IPS components: - intro and statement of purpose - Statement of Duties and Responsibilities (describes duties and responsibilities of client, investment manager, and asset custodian) - procedures - Investment Objectives of the Client - Investment Constraints of the Client - Investment Guidelines (map for how policy should be executed --leverage and derivatives used?-- and lists specific assets that should be excluded - Appendices (Strategic Asset Allocation and Rebalancing Policy)

Money Weighted Return (aka IRR)

IRR accounts for the amount of money invested in each period and provides information on the return earned on the actual amount invested. Use cash flow function on calc to determine IRR. Drawback of IRR is that it does not allow for return comparisons between diff individuals or diff investment opportunities. (i.e. two investors in the same mutual fund could have different IRRs if they invested varying amounts of $$ in different periods).

IRR of a Perpetuity

IRR of Perpetuity: = $$ Perpetuity Payment / $$ Initial Cash Outlay i.e. Project costs $270mm upfront, and will pay $30mm each year in perpetuity. Find IRR. IRR = 30/270 = 11.1%

Investment Evaluation Assumptions

In order to use MEAN and VARIANCE to evaluate an investment, we must assume: 1) that the investment's returns follow a normal distribution (which is fully described by its mean and variance), and 2) that markets are informationally and operationally efficient.

Independent vs. Mutually Exclusive Projects

Independent Projects: projects with unrelated cash flows. If a company has the resources, both project A and project B can BOTH be chosen. Mutually Exclusive Projects: projects that compete directly with each other for acceptance. Either project A OR project B may be accepted. Not both.

Indifference Curves

Indifference Curves represent the investor's utility function. Points on the indifference curve above the capital allocation line are desirable but unattainable with the given assets, points below the CAL do not maximize return for a given level of risk. Slope of Indifference Curves: - Risk‐neutral investors have perfectly horizontal indifference curves. - Risk‐seeking investors have downward‐sloping or negatively sloped indifference curves. The point where an investor's indifference curve is tangential to the CAL is the optimal portfolio for that investor.

LOS 40b: Types of Investors

Individuals: - Defined Contribution Plan (employee puts money away and is accepting the risk in the portfolio; needs to accumulate wealth to replace wages or plan for specific life events (i.e. college) Institutional: - Defined Benefit (employer has an obligation at a later date and is accepting the risk in the portfolio) - Endowments (perpetual, need income for short term spending needs and have long term capital preservation requirements) - Banks (must be relatively liquid and regulations may limit risk exposure) - Insurance companies - Investment companies - Sovereign wealth funds (SWF) (gov owned fund that reinvests revenues from resources, like oil, to benefit future generations

Inventory Management Approaches

Just-In-Time: the reorder point is determined by historical demand and this method reduces in-process inventory and carrying costs. Economic Order Quantity: minimizes total ordering/holding costs and relies on expected demand (need reliable demand forecasts)

Legal Risk

Legal risk is a NON-FINANCIAL RISK and can be risk of being sued or risk of contract terms not being upheld by a legal system.

Net Operating Cycle (aka Cash Conversion Cycle)

Length of the period from paying suppliers for materials to collecting cash from sales. Net Operating Cycle = # Days of Inventory + # Days of Receivables - # Days of Payables SHORTER cycles are desired. A long conversion cycle suggests that a company has too much $$ tied up in working capital.

Buyout and Venture Capital Funds

Leverage Buyout (LBO) funds raise money to take over companies and are usually financed with a large amount of debt. Venture Capital Funds invest in start-ups. Buyout & Venture Capital Funds vs Mutual Funds: - LBO and Venture Capital take an active role in the underlying companies - The eventual exit strategy is taken under consideration before potential investment is made. Similar to hedge funds in that they require high minimum investment, withdrawals are limited/not allowed, and performance fees may be charged.

Leverage Ratio (Investment)

Leverage Ratio = Total value of the position / Value of the equity portion of the investment

Leverage

Leverage refers to a company's use of fixed costs in conducting business. Those fixed costs are: a) Operating Costs (e.g. rent and depreciation) b) Financial Costs (e.g. interest expense) As leverage increases: - the volatility of a company's earnings and cash flows increases and, therefore, risk borne by investors increases - the more risky it is, therefore, a higher discount rate must be used to value the company - sensitivity to economic downturns increases Higher degree of leverage = steeper slope of net income (units sold on x-axis; net income on y-axis)

Leveraged Return

Leverage return is computed when an investor uses leverage (either by borrowing money or using derivative contracts) to invest in a security. Leverage enhances returns, but also magnifies losses.

Yields

MMY = ((Face - Price)/Price) × (360/days) MMY = (HPY) × (360/days) BEY = ((Face - Price)/Price) × (365/days) BEY = (HPY) × (360/days) Discount Basis Yield = ((Face - Price)/Face) × (360/days) Discount Basis Yield = % discount × (360/days) **Price = Face Value - (Face × Discount Rate × Days/360)

Risk-Adjusted Portfolio

Managers concerned with maximizing risk-adjusted returns should: - invest in a higher weight of securities with a higher value of Jensen's alpha - invest in a lower weight of securities with higher nonsystematic risk

Short Term Financing

Many bank/non-bank options exist that can be utilized by small to large companies depending on their creditworthiness. Examples on page 95-96 of Wiley Study Guide Vol. 4

Market Risk

Market risk is a FINANCIAL RISK that arises from changes in interest rates, stock prices, exchange rates and commodity prices. Drivers of market risk are fundamental economic conditions or events in the overall economy, the industry, or the company itself.

Market Characteristics

Markets are not always operationally efficient. Operational efficiency can be hindered by liquidity which effects the bid-ask spread. - illiquid stocks have a wider spread and suffer a greater price impact.

Payables Turnover

Measures how many times the company theoretically pays off creditors over a period. Payables Turnover = Purchases / Avg. trade payables High payables turnover: company is not making full use of credit facilities (paying vendors too quickly) Low payables turnover: company has trouble making payments on time.

Accounts Receivables Turnover

Measures how many times, on average, accounts receivable are created by credit sales and collected over a given period. Accts Receivables Turnover = Credit Sales / Avg. Receivables An Accts Receivables Turnover close to industry average is desired.

Operating Cycle

Measures time needed to convert raw materials into cash from sales. Operating Cycle = # Days of Inventory + # Days of Receivables

Model Risk

Model risk is the NON-FINANCIAL RISK of a valuation error from the use of an incorrectly specified model or improper use of a valid model. Tail-risk is a form of model risk that refers to events captured in the tail of a distribution occurring more frequently than expected by the model.

Pooled Investments: Types (LOS 40e: describe and compare pooled investment types to mutual funds)

Mutual Funds Exchange Traded Funds (ETFs) Separately Managed Accounts (SMAs) Hedge Funds Buyout & Venture Capital Funds

NPV vs IRR vs PI

NPV > 0; IRR > WACC; PI > 1 NPV = 0; IRR = WACC; PI = 1 NPV < 0; IRR < WACC; PI < 1 When projects are mutually exclusive the one with the HIGHER NPV is selected. When capital rationing is involved (i.e. limited budget) we use Profitability Index (PI) to determine which projects to choose based on highest PI.

Net Present Value (NPV)

NPV measures the amount of money that a project is expected to add to shareholder wealth. = (∑CFt ÷ ((1 + r)∧t) - outlay CF --> after-tax cash flow at time, t. r --> required rate of return for investment (this is the firm's cost of capital adjusted for the risk inherent in the project) Outlay --> investment cash at time t=0 A project SHOULD be undertaken if NPV > 0 When NPV and IRR give conflicting results, the project with the highest NPV should be selected. **NPV assumes that interim cash flows are reinvested at the company's required rate of return.

Negative Screening

Negative screening excludes companies that violate accepted standards.

Non-Systematic (Unsystematic) Risk Systematic Risk

Non-Systematic Risk (aka idiosyncratic risk; diversifiable risk) is company or industry specific hazard that does not affect the entire market system. It can be diversified away in a portfolio therefore investors are not compensated for taking on non-systematic risk. Systematic Risk affects the entire market segment, or entire market segments, and is both unpredictable and impossible to completely avoid. It cannot be mitigated through diversification. Investors are compensated for taking on systematic risk because it cannot be diversified away. It is therefore priced into the market. An example of a non-systematic risk would be a product recall that affects one company but not the entire market. An earthquake (unavoidable and affects more than one company/industry) would be an example of systematic risk.

Nonsystematic Variance

Nonsystematic Variance = σ²i - (βi² × σ²m) σ²i = variance of stock or portfolio βi² = beta of stock or portfolio (remember to square this) σ²m = variance of the market

Pull on Liquidity

Occurs when cash leaves the company too quickly. - Making payments early, reduced credit limits, limits on short-term lines of credit, low levels of liquidity

Drag on Liquidity

Occurs when there is a delay in cash coming into the company. - Uncollected receivables, obsolete inventory, tight credit.

Cash Management Strategies

Passive Strategy: very few rules; limited number of transactions Active Strategy: constant monitoring; wider array of investments; more evaluation/forecasts/involvement - Matching Strategy: match the timing of cash outflows with investment maturities - Mismatching Strategy: intentionally mismatching timing of cash outflows with investment maturities; generally involve use of liquid instruments and derivatives - Laddering Strategy: scheduling maturities of portfolio investments such that maturities are spread out equally over the term of the ladder

Evaluation of Accounts Payable Management

Pay too early = lose out on interest income Pay late = lose credibility and hurt reputation and/or pay penalties/interest charges A number of factors go into managing payables: - number of suppliers - trade credit and cost of borrowing or alternative costs - controlling disbursement float - inventory management - electronic payments (more valuable than checks unless disbursement float and interest rates are high) We evaluate the management of payables using # of days of payables ratio (number of days, on avg, a company takes to pay supplier): = Accounts Payable / (Purchases / 365) = 365 / Payables Turnover

Perpetuity Formula: Calculating the Cost of Noncallable, Nonconvertible Preferred Stock

Perpetuity formula can be used to calculate the cost of preferred stock when the preferred stock is noncallable, nonconvertible, has not maturity date, and pays dividends at a fixed rate. rp = Dp / Vp Vp --> current value (price) of preferred stock Dp --> preferred stock dividend per share rp --> cost of preferred stock Rearranged you can determine the current value (Vp) of the stock as follows: Vp = Dp / rp

LOS 40d: Steps in the Portfolio Management Process

Planning: Understanding client needs; preparing investment policy statement (IPS) (IPS is a written doc that describes objectives and constraints of the investor and may include a benchmark against which the portfolio managers performance will be measured) Execution: Determining a portfolios asset allocation (i.e. debt, equities, fixed income, alternative investments -- diff. asset allocations explain most differences between portfolio returns); analyze securities within asset classes defined; construct portfolio Feedback: Monitor and re-balance portfolio (i.e. when equities do well and their weight in the portfolio goes over the goal weight, the portfolio will need to be re-balanced); measure and report performance (ethics - Fair; Accurate; Complete)

Portfolio Return

Portfolio Return is calculating by finding the weighted average of the returns on the individual assets in the portfolio. Rp = w₁R₁ + w₂R₂ + w₃R₃... On the exam you will be asked to find the weights of a two asset portfolio given Rp: Rp = w₁R₁ + (1 - w₁)R₂ ← solve for w₁

Liquidity Sources

Primary Source of Liquidity: Readily available such as cash and short-term funds (e.g. trade credit; bank line of credit) Secondary Source of Liquidity: Provide liquidity at a higher cost than primary sources. (e.g. negotiating debt contracts, liquidating assets/inventory, filing for bankruptcy)

Risk Metrics: Single-Dimensional Risk Measures LOS 41g (methods for measuring and modifying risk exposures and factors to consider in choosing among the methods)

Probability: measure of relative frequency with which one would expect outcome(s) to occur Standard Deviation (σ): measures the range over which a certain percentage of the outcomes would be expected to occur. σ -- overstates risk because it captures systematic and non-systematic risk (non-systematic risk can be diversified away); σ is not an appropriate measure of risk for non-normal distributions and may not exist for distributions with 'fat tails' Beta (β): measure of security's systematic risk which is what investors are compensated for in the form of a higher expected return (beta measures the sensitivity of a security's returns to the returns on the market portfolio and captures the market risk that a particular asset contributes to a well-diversified portfolio. Value at Risk (VaR): see separate flashcard

Purchase Price of a Discount Instrument

Purchase Price of a Discount Instrument = Face Value - Time Weighted Discount ($$) i.e. a discount instrument with a face value of $1000, a 6% coupon, and 60 days to maturity has a purchase price of: = $1000 - (.06 × (60/360) × $1000) = $990

Quick Ratio

Quick Ratio = (Cash + ST Investments + Receivables) / Current Liabilities HIGHER quick ratio is better and indicates greater liquidity. TRENDS in the ratios and competitors' ratios must be analyzed in order to determine whether a company's liquidity ratios are good or bad.

Average Accounting Rate of Return (AAR)

Ratio of the project's average net income to its average book value. = avg. net income ÷ avg. book value avg. net income --> sum of all net income (i.e. revenue - depreciation) during the project (not discounted) divided by # of years avg. book value --> (beginning project book value + ending project book value*) ÷ 2 *ending book value could be zero or greater than zero (i.e. salvage value)

Cash Forecasting

Short Term Cash Forecasting: Daily/Weekly; very reliable and accurate; used for daily cash mgmt Medium Term Cash Forecasting: Monthly/One Year; reliable and moderately accurate; used to plan financial transactions Long Term Cash Forecasting: Yearly for 3-5 years; not as reliable; low accuracy; used for long-range financial planning

Real Rate of Return

Real Returns consist of the real risk-free rate plus a premium for risk and a premium for inflation. These returns are useful for comparisons (across time periods because inflation rates may vary over time; across countries because inflation rates will vary from place to place) Real after-tax returns are not generally calculated by investment managers because it is difficult to estimate a general tax rate that is applicable to all investors. If no tax rate is given the Real Return is calculated as: Real Return = [(1 + stated return) ÷ (1 + inflation)] - 1 If tax rate and inflation rate are given, the after-tax real return is calculated as: = [(1 + After-Tax Net Return) ÷ (1 + inflation rate)] - 1 where After-Tax Net Return = Net Return × (1 - tax rate)

Risk Management LOS 41a (Define Risk Management)

Refers to the decisions and actions that must be taken in order to achieve return/performance objectives while taking on an acceptable level of risk. Risk Management: - DEFINES the level of risk that should be taken - MEASURES the level of risk actually taken - AIMS (goal) to maximize portfolio value while ensuring that actual risk is consistent with defined acceptable risk Risk Management is NOT about minimizing risk or predicting risk -- it is about actively understanding risk and being prepared for the impact of unpredictable events.

Return and Risk Expectations

Return expectations can be developed from historical data, economic analysis, or valuation models, while risk expectations (standard deviation and correlation estimates) are primarily obtained from historical data.

Risk Capture

Risk capture (which is a part of risk infrastructure) is the process through which risk exposures are populated in the risk management system.

Sales Risk

Risk due to the uncertainty of the number of units produced and sold and the price at which units are sold

Risk Neutral

Risk neutral investors seek higher returns irrespective of the level of risk inherent in an investment. In other words, if forced to decide between two investments, a risk neutral investor will choose the investment with the higher return and ignore the level of risk in each option.

Risk Acceptance

Self-Insurance: retaining exposure to a risk that is undesirable but too costly to eliminate by external means (i.e. setting aside capital/loss reserves to cover losses) Diversification is the most efficient form of "risk acceptance" (risk is still present but the effect of the risk is mitigated by diversification). Diversification is key to eliminating non-systematic risk.

Herstatt Risk (aka Settlement Risk)

Settlement risk is a NON-FINANCIAL RISK that arises from the timing of the payment process, typically due to significant time zone differences. Example: Party A wires funds for shares and Party B files for bankruptcy before sending shares to Party A.

Short Term Investments & Discount Instruments

Short-term investments consist of bank and non-bank (i.e. commercial paper) options that have various levels of risk and maturities. Discount Instruments are purchased at less than face value and pay face value at maturity. Purchase Price of Discount Instrument: Purchase Price = Face Value - (Face × Discount Rate × Days/360)

Cash Forecasts

Short‐term forecasts are made using simple projections. Medium‐term forecasts are made using projection models and averages. Long‐term forecasts are made using statistical models.

Relative Risk Objective

Specifying a standard deviation of returns relative to that of a benchmark index is a relative risk objective.

Relative Return Objective

Specifying portfolio return relative to a benchmark is a relative return objective.

Systemic Risk

Systemic risk is seen when the stresses and failures in one sector transmit stresses and failures to other sectors ultimately impacting a wide array of businesses/industries/the economy. Example: financial crisis of 2008 -- stresses and failures of highly levered financial institutions infested the entire financial system and disrupted the economy as a whole.

Tactical Asset Allocation

Tactical asset allocation refers to an allocation where the manager deliberately deviates from the strategic asset allocation for the short term if she believes that another asset class will perform relatively better.

Target Capital Structure vs. Current Capital Structure

Target Capital Structure: The capital structure that the company aims to maintain. Current Capital Structure: When the target capital structure is not given we can use the current capital structure to determine WACC. We must use the MARKET VALUE of debt/equity/preferred shares when calculating WACC using the company's current capital structure.

Portfolio Risk in relation to Covariance and Correlation

The COVARIANCE among the assets in the portfolio accounts for the bulk of risk. Anytime a CORRELATION between two assets is less than 1, diversification benefits are achieved. In an example where two assets have the same standard deviation and a correlation less than 1, the standard deviation of the portfolio containing these two assets will fall. Portfolio standard deviation is minimized when the correlation between the two assets equals −1. When the correlation between two assets equals 1 portfolio risk is equal to the weighted average of the risk of the two assets in the portfolio. Portfolio Standard Deviation: Pσ = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov₁,₂) Pσ = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρ₁,₂σ₁σ₂) NOTE: Portfolio standard deviation has a maximum value that is equal to the higher of the individual assets' standard deviation.

Capital Allocation Line (CAL)

The Capital Allocation Line (CAL) is an upward sloping line that plots the expected return on a portfolio containing a risk-free and risky asset (CAL represents the risk-return combinations of the set of portfolios that the investor can invest in) (standard deviation on the x-axis; expected return on the y-axis). The CAL intercepts the y-axis at the risk-free rate and it's slope is calculated as: CAL Slope = [E(r) - RFR] ÷ σ The slope of the CAL represents the additional return required for each additional unit of risk (aka the "market price of risk")

Markowitz Efficient Frontier

The Markowitz Efficient Frontier is the TOP PORTION OF THE MVF curve. It has a starting point at the GMVP. All portfolios on the MVF above and to the right of the GMVP are superior to (more efficient than) all portfolios below the GMVP. The Markowitz Efficient Frontier only consists of portfolios of risky assets. It does not include risk free assets. The efficient frontier represents a set of portfolios that have the minimum expected risk for every given level of expected return. Alternatively, it represents the set of portfolios that have the maximum expected return for every given level of risk.

Minimum Variance Frontier

The Minimum Variance Frontier is an envelope curve (C-shaped curve) that plots the risk-return characteristics of portfolios with the lowest level of risk at each level of expected return. (see image) Portfolio risk (standard deviation) is on the x-axis and E(r) is on the y-axis. No risk-averse investor would invest in a portfolio to the right of the MVF line as it would entail a higher level of risk than a portfolio on the MVF for a given level of return. The Global Minimum Variance Portfolio (GMVP) lies on the MVF curve at the lowest level of risk (furthest left point on the curve). The GMVP is defined as the portfolio on the MVF that minimizes the investors risk for 'any' given level of expected return.

Security Market Line (SML)

The SML illustrates CAPM with a y-intercept equal to the risk free rate and a slope equal to the market risk premium (Rm - Rf) A security whose required rate of return is greater than the expected rate of return is considered overvalued and plots below the security market line. A security whose expected rate of return is greater than the required rate of return (positive alpha) is considered undervalued and plots above the security market line.

Portfolio Performance Evaluation: Sharpe Ratio

The Sharpe Ratio is used to compute excess return per unit of TOTAL risk. Sharpe Ratio* = (Rp - Rf) ÷ σp *this is also the slope of the capital allocation line (CAL) A portfolio with a higher Sharpe ratio is preferred because it means that, for every unit of additional risk, the additional return will be higher than the additional return earned on a portfolio with a lower Sharpe ratio. Drawbacks: - Sharpe ratio uses total risk, even though only systematic risk is priced - the ratio itself is not informative (it must be compared to other Sharpe ratios)

Portfolio Performance Evaluation: Treynor Ratio

The Treynor Ratio is the Sharpe ratio with total risk replace by systematic risk (beta): Treynor Ratio = (Rp - Rf) ÷ βp Both the numerator and the denominator must be positive in order for the Treynor Ratio to have meaningful results.

Cost of Debt Capital: Yield To Maturity (YTM) Approach

The YTM is the yield that equates the PV of the bond's expected future cash flows to its current market price (P₀). YTM is the BEFORE-TAX COST OF DEBT. P₀ = [∑PMT ÷ (1 + rd/2)∧t] ⁺ (FV ÷ (1 + rd/2)∧ⁿ P₀ --> current market price of bond PMT --> interest payment in period, t rd --> yield to maturity on a bond equivalent yield (BEY) basis (BEFORE TAX COST OF DEBT = rd) n --> number of periods remaining to maturity FV --> par (maturity) value of the bond Use financial calculator to enter N; FV (par); PV (current price); PMT ((coupon/# payments in a year) * par); and CPT I/Y I/Y × #of payments in a year = BEFORE TAX COST OF DEBT (rd) (rd)(1 - tax rate) = AFTER-TAX COST OF DEBT

Contribution Margin

The amount that units sold contribute to covering fixed costs is the Contribution Margin. Contribution Margin = Q × (P-V) Contribution Margin per Unit = (P-V)

Capital Market Line (CML)

The capital market line (CML) is a special case of the capital allocation line (CAL), where the risky portfolio is the market portfolio. The risk-free asset is a debt security with no default risk, no inflation risk, no liquidity risk, no interest rate risk, and no risk of any other kind Points above the CML are not achievable. Points below the CML are inferior. The point at which the CML is tangent to the Markowitz efficient frontier is the optimal combination of risky assets, on the basis of market prices and market capitalizations. The optimal combination of risky assets is known as the market portfolio. ** CAL and CML only apply to EFFICIENT PORTFOLIOS. Not to individual assets or inefficient portfolios.

Crossover Rate

The crossover rate is the rate at which the NPVs of two projects are the same. Crossover rate = IRR of the DIFFERENCE between the two projects cash flows.

Cost of Debt Capital: Debt-Rating Approach

The debt-rating approach is used to find cost of debt when a reliable current market price isn't available and YTM approach cannot be used. BEFORE-TAX COST OF DEBT can be estimated using the yield (rd) on a similarly rated bond that has similar terms to maturity as a company's existing debt. = (rd of similar debt)(1 - tax rate of company) EXAMPLE: Alextar Inc. has a capital structure that includes AAA-rated bonds with 10 years to maturity. The yield to maturity on a comparable AAA-rated bond with a similar term to maturity is 6%. Using a tax rate of 40%, calculate Alextar's after-tax cost of debt. Solution: Alextar's after-tax cost of debt = rd(1−t) = 0.06(1−0.4) = 3.6%

Internal Rate of Return (IRR)

The discount rate that makes the sum of present values of the future after-tax cash flows equal to the initial investment outlay. The discount rate that equates the sum of the present values of all after-tax cash flows for a project (inflows and outflows) to zero. In other words, IRR is the discount rate at which NPV = 0 ∑CFt ÷ ((1+IRR)∧t) = outlay (∑CFt ÷ ((1+IRR)∧t)) - outlay = 0 If IRR > required rate of return, then NPV will be positive; ACCEPT project If IRR < required rate of return, then NPV will be negative; REJECT project ** IRR assumes that interim cash flows received are reinvested at IRR <-- this is a rather inappropriate assumption sometimes.

Externalities

The effect of an investment decision on things other than the investment itself. Investment decisions can have positive (i.e. increased efficiencies in other areas) or negative (cannibalism) effect. SHOULD be considered when making an investment decision.

Flotation Costs

The fee charged by investment bankers to assist a company in raising new capital. Flotation Costs are added to the INITIAL CASH OUTLAY of the investment: Flotation Cost ($) = flotation Fee% × $$ of initial outlay × we we --> proportion of initial outlay from equity

NPV: Stock Price Increase

The increase in the price can be calculated simplistically as: = NPV ÷ # shares Shareholder wealth will increase by NPV

Market Model (Single-Index Return Generation Model)

The market model is a single-index return model that is used to estimate beta risk and to compute abnormal returns (alpha). Ri = αi + βi(Rm) + ei αi = the intercept βi = the slope coefficient Both α and β are estimated using historical asset and market returns. Those estimates are then used to predict future returns. ei = error term (this is ignored in LI but will be tested heavily in LII)

Slope of the CML

The slope of the CML for lending portfolios (where a portion of the investor's funds are invested in the risk‐free asset) is dictated by the difference between the risk‐free rate and the market portfolio. The slope of the CML for leveraged or borrowing portfolios (where the weight of the market portfolio of the investor's portfolio is greater than 100%) is dictated by the difference between the cost of borrowing and the market portfolio. The slope of the levered portfolio will be lower than the slope of the unlevered portfolio. This means that every unit increase of risk for a levered portfolio will result in less of an increase in return. The greater the difference between the risk‐free rate and the cost of borrowing, the greater the significance of the kink in the CML.

Payback Period

The time it takes for the initial investment in the project to be recovered through after-tax cash flows from the project. All other things being equal, the best investment is one with the shortest payback period. Payback period should be used along with NPV or IRR to evaluate a project 1) calculate cumulative cash flows through each year 2) for fraction of years, take the amount still to be recovered at the end of the year divided by the TOTAL after-tax cash inflow from the next year. (i.e. if -$150 is unrecovered at end of year 3 and $400 after-tax cash flow is expected in year 4, then the payback period is: 3 + (150/400) = 3.375)

Thematic Investing

Thematic investing uses one factor, such as energy efficiency or climate change, as the basis for choosing potential investments.

Investment Strategies

Thematic: An ESG (environmental and social factors combined with governance) implementation method that focuses on a specific economic or social trend. Thematic investing uses one factor, such as energy efficiency or climate change, as the basis for choosing potential investments. Best-In-Class: seeks to identify the most favorable company in an industry based on ESG considerations. Negative Screening: method that excludes certain sectors or companies. (top down -- start with full pool of options, then eliminate) Positive Screening: method that seeks to identify companies that embrace desired ESG-related principles. (bottom up -- search for select attributes)

Cost of Equity: Dividend Discount Model Approach (Gordon Growth Model)

This cost of equity estimation approach asserts that the value of a stock equals the PV of its expected future dividends. Gordon Growth Model: Dividends grow at a constant rate P₀ = D₁ ÷ (re - g) so, re = (D₁ ÷ P₀) + g P₀ --> current market value of the security D₁ --> next year's dividend re --> cost of equity (required rate of return on common equity) g --> the firm's expected constant growth rate of dividends** ** See the 'GROWTH RATE (g)' flashcard for growth rate calculation formula

Cost of Equity: Bond Yield Plus Risk Premium Approach (aka Build Up Method)

This method of calculating cost of equity (return on equity) is simply adding a risk premium to the before-tax cost of debt. re = rd + risk premium rd --> before-tax cost of debt

Shares Repurchased Using Debt

To determine if earnings per share (EPS) will increase or decrease after a debt financed shares repurchase: 1) calculate basic EPS (NI/#shares outstanding before repurchase) 2) calculate earnings yield (Basic EPS / price per share) 3) calculate the after-tax cost of debt (cost of debt pre-tax (1 - tax rate)) If the after-tax cost of debt is LESS than the earnings yield than EPS will go UP after the debt financed share repurchase. If the after-tax cost of debt is MORE than the earnings yield than EPS will go DOWN.

Financial Asset Returns LOS 42a (calc and interpret major return measures and describe their appropriate uses)

Types of Returns: - Periodic Income (e.g. dividends and interest) - Capital gains/(losses) resulting from changes in market price Return Measures: 1) Holding Period Return (HPR) 2) Arithmetic or Mean Return (biased upward) 3) Geometric Mean Return (accounts for compounding) 4) IRR or Money Weighted Return (accounts for amount of money invested in each period and provides info on the return earned on the actual amount invested) 5) Annualized Return 6) Portfolio Return 7) Others -- gross and net returns; pre-tax and after-tax nominal returns; real returns; leverage return

Share Repurchase Method: Dutch Auction

Under a Dutch Auction, the company will specify a range of acceptable prices that it would repurchase stock at. Shareholders willing to sell must offer up the price at which they would sell and the company then repurchases shares, starting with the cheapest, until it has bought back all of the shares it wished to.

Utility

Utility is a measure of the relative satisfaction that an investor derives from a particular portfolio. It is an 'intangible' item calculated with a 'utility function' Some general assumptions can be made about 'utility': - higher returns result in higher utility - utility is unbounded (can be highly positive or highly negative) - higher risk results in lower utility - a risk free asset (that has a variance (risk) of zero) will generate the same utility for all types of investors NOTE: U is not an absolute measure of satisfaction. A portfolio with U of 2.5 is not necessary twice as satisfying to an investor as a portfolio with U of 1.25. However, the portfolio with U of 2.5 would be preferred. HIGH UTILITY IS DESIRED.

Risk Metric: Value at Risk (VaR)

VaR: a MINIMUM extreme loss metric that measures the size of the tail of the distribution of profits on a portfolio/for an entity. Composed of (1) currency amount, (2) time period, (3) probability (Example: If a bank states that it's VaR if $4million at 3% for one day, it means that the bank expects to lose a minimum of $4 million in one day 3% of the time. CVaR: Conditional Value at Risk - calculated as the weighted avg of all loss outcomes in a statistical distribution that exceed the VaR loss Expected loss given default - used to measure credit risk; provides the avg expected loss if the underlying company defaults VaR measurements can provide highly diverse estimates and are subject to model risk. VaR can UNDERESTIMATE risk. Scenario Analysis and Stress Testing go hand-in-hand with VaR

Variance, Covariance, and Correlation of Returns

Variance (the average squared deviation of observed returns from their mean, or expected return) measures volatility. Higher variance = higher dispersion of returns. Variance of a portfolio of assets must take into account the covariance (and correlation) between assets in the portfolio. Standard Deviation (square root of variance): Measures risk of an asset or portfolio of assets. If given two stocks (A and B) and the return on each stock for a number of periods you can calculate the covariance and correlation: 1) calculate the expected return, mean, of stock A (µA) and stock B (µB) 2) calculate the Variance of stock A (σ²A) and stock B (σ²B): Variance = σ² = ∑[(r-µ)²] / n-1 3) calculate the Standard Deviation of stock A (σA) and stock B (σB): Standard Deviation = σ = √σ² 4) subtract the expected return from the actual return (given) for stock A (rA - µA) and stock B (rB - µB) 5) Find Covariance=Cov(A,B) = ∑[(rA - µA)(rB - µB)] / n-1 6) Find Correlation = Cov(A,B) / σAσB

Weighted Average Cost of Capital (WACC) (aka Marginal Cost of Capital (MCC))

WACC is the expected rate of return that investors demand for financing an average risk investment of the company. = (wd)(rd)(1−t)+(wp)(rp)+(we)(re) wd → porporation of debt* rd → before-tax marginal cost of debt t → company's marginal tax rate wp → proportion of preferred stock rp → marginal cost of preferred stock we → proportion of equity re → marginal cost of equity *REMEMBER that (wd) = (1 - we) Assumptions when using WACC as the discount rate to evaluate a project: 1) The project will have a constant capital structure throughout its life. 2) The project is an 'average risk' project

Degree of Financial Leverage (DFL)

We use DFL to measure the sensitivity of cash flows available to owners to changes in operating income. HIGHER fixed financial costs INCREASE the sensitivity of net income to changes in operating income. (i.e. more debt financing equates to greater sensitivity of net income to changes in operating income, which means higher financial risk) DFL = % ∆ in net income ÷ % ∆ in operating income DFL = (Revenue - Variable Operating Costs - Fixed Operating Costs) / (Revenue - Variable Operating Costs - Fixed Operating Costs - Fixed Financial Cost) DFL = [Q×(P-V) - F] ÷ [Q×(P-V) - F - C] Q = number of units sold P = price per unit V = variable operating cost per unit F = fixed operating cost C = fixed financial cost Q × (P-V) = contribution margin (P-V) = contribution margin per unit

Defining Asset Classes

When defining asset classes: - Each asset class should contain assets that carry a similar expected return and risk, and correlation among the assets within a class should be relatively high. - Each asset class should provide diversification benefits. The correlation of an asset class with other asset classes should be relatively low. - Asset classes should be mutually exclusive and should cover all investment alternatives.

NPV Profiles

Y-Axis (Vertical): NPV X-Axis (Horizontal): Discount Rate (%) The point at which NPV intersects the Y-Axis = the sum of the undiscounted cash flows from the project The point at which NPV intersects the X-Axis = the project's internal rate of return when the project's NPV equals zero.