Finance & Quantitative Modeling for Analysts Specialisation

This course is available on Coursera, and here is my own note about this course. Also, this course is made up of 4 mini courses: Fundamentals of Quantitative Modeling, Introduction to Spreadsheets and Models, Financial Acumen for Non-Financial Managers and Introduction to Corporate Finance.

Fundamentals of Quantitative Modeling

Module 1

What is a model?

• A formal description of a business process.
• It typically involves mathematical equations and random variables.
• It is almost always a simplification of a more complex structure.
• It typically relies upon a set of assumptions.
• It is usually implemented in a computer program or using a spreadsheet.

Examples of models

• The price of a diamond as a function of its weight.
• The spread of an epidemic over time.
• The relationship between demand for, and price of a product.
• The uptake of a new product in a market.

Diamonds and weight

Spread of an epidemic

Demand models

The uptake of a new product

Ways to use models in practice

• Prediction: Calculating a single output: What's the expected price of a diamond ring that weighs 0.2 carats?
• Forecasting (time series): How many people are expected to be infected in 6 weeks?
• Optimisation: What price maximises profit?
• Ranking and targeting: Given limited resources, which potential diamonds for sale should be targeted first for potential purchase?
• Exploring what-if scenarios: If the growth rate of the epidemic increased to 20% per week, then how many infections would we expect in the next 10 weeks?
• Interpreting coefficients in model: What do we learn from the coefficient -2.5 in the price/demand model?
• Assessing how sensitive the model is to key assumptions.

Benefits of modeling

• Identify gaps in current understanding
• Make assumptions explicit
• Have a well-defined description of the business process
• Create an institutional memory
• Used as a decision support tool
• Serendipitous insight generator

Modeling Process Workflow

What if the model doesn't always work

• When the observed outcome differs greatly from the model's predicition, then there is the possibility of learning from thies event if we can understand why the difference occurs.
• Modeling is a continuous and evolutionary process
• We identify the weaknesses and limitations and iterate the modeling process to overcome them.

Data driven vs. theory driven

• Theory: Given a set of assumptions and relations, then what are the logical consequences? E.g. If we assume that markets are efficient, then what should the price of a stock option be?
• Data: Given a set of observations, how can we approximate the underlying process that generated them? E.g. I've separated out my profitable customers from the unprofitable ones. Now, what features are able to differentiate them?

Deterministic vs. probabilistic/stochastic

• Deterministic: Given a fixed set of inputs, the model always gives the same output. E.g. Invest $1000 at 4% annual compound interest for 2 years. After 2 years the initial $1000 will always be worth $1081.60.
• Probabilistic: Evven with identical inputs, the model output can vary from instance to instance. E.g. A person spends $1000 on lottery tickets. After the lottery is drawn how much they are worth dependes on a random variable, whether or not they won the lottery.

Discrete vs. continuous variables

• Watches can be digital or analog
• Likewise models can involve discrete or continuous variables. Discrete: characterised by jumps and distinct values; Continuous: a smooth process with an infinite number of potential values in any fixed interval.

Static vs. dynamic

• Static: the model captures a single snapshot of the business process. E.g. Given a website's installed software base, what are the chances that it is compromised today?
• Dynamic: the evolution of the process itself is of interest. The model describes the movement from state to state. E.g. Given a person's participation in a job training program, how long will it take until he/she finds a job and then, if they find one, for how long will they keep it?

Linear function

• $y = mx + b$
• Essential characteristic: the slope is constant.

The power function for various powers of $x$

• $y = x^{m}$.
• Essential characteristic: A one percent (proportionate) change in $x$ corresponds to an approximate $m$ percent (proportionate) change in $y$.

The exponential function

• $y = e^{mx}$.
• Essential characteristic: the rate of change of $y$ is proportional to $y$ itself.

The log function

• $y = \log_{b}(x)$.
• $\log(xy) = \log(x)+\log(y)$.
• The log function is very useful for modeling processes that exhibit diminishing returns to scale.
• There are processes that increase but at a decreasing rate.
• Essential characteristic: A constant proportionate change in $x$ is associated with the same absolulte change in $y$.

Module 2

Deterministic models

• There are no random/uncertain components in these models.
• If the inputs to the model are the same then the outputs will always be the same.
• The downside of deterministic models: it is hard to assess uncertainty in the outputs.

A linear cost function

• Call the number of units produced $q$, and the total cost of producing $q$ units $C$.
• Define $$C = 100+30q.$$

Interpretation

• The two coefficients in the line are the intercept and slope: $b$ and $m$ in general, 100 and 30 in this particular instance.
• $b$: the total cost of producing 0 units. That part of total cost that doesn't depend on the quantity produced: the fixed cost.
• $m$: the slope of the line: the change in total cost for an incremental unit of production: the variable cost.

Example with a 'time-to-produce' function

• It takes 2 hours to set up a production run, and each incremental unit produced always takes an additional 15 minutes (0.25 hours); always here means constant slope.
• Call $T$ the time to produce $q$ unites, then $$T = 2+0.25q$$
• Interpretation: $b$ is the setup time; $m$ is the work rate (15 minutes per additional item).

Linear programming

• One of the key uses of linear models is in Linear Programming (LP), which is a techinique to solve certain optimisation problems.
• These models incorporate constraints to make them more realistic.
• Linear programming problems can be solved with add-ins for common spreadsheet programs.

Growth in discrete time

• Growth is a fundamental business concept: the number of customer at time $t$; the revenue in quarter $q$; the value of an investment at some time $t$ in the future.
• Sometimes a linear model may be appropraite for a growth process, but an alternative to a linear growth model is a proportionate one.
• Proportionate growth: a constant percent increase (decrease) from one period to the next.

Simple interest

• Start off with $100 (principal) and at the end of every year earn 10% of simple interest on the initial $100.
• Simple interest means that interest is only earned on the principal investment.
• Every year the investment grows by the same amount.

Compound interest

• Start off with $100 (principal) and at the end of every year earn 10% of compound interest on the initial $100.
• Compound interest means that the interest itself earns interest in subsequent years.
• Notice that the growth is no longer the same absolute amount each year, but it is the same proportionate amount (10%).

Comparison between two interest

Constant proportionate growth

• Denote the initial amount as $P_{0}$.
• Denote the constant proportionate growth factor by $\theta$.
• The growth progression is $$P_{0},P_{0}\theta,P_{0}\theta^{2},...,$$
• $\theta > 1$ means the process is growing.
• $\theta < 1$ means the progress is decaying.
• The type of progression is called geometric progression.

The constant multiplier

• For the catch to fall by 5% each year, means that the multiplier is $\theta = 0.95$.
• In general, if the process is changing by $R$% in each time period, then the multiplier is $$\theta = 1+\frac{R}{100}.$$

The sum of the geometric series

• If we denote the sum up to time $t$ as $S_{t}$, then $$S_{t} = P_{0}\frac{1-\theta^{t+1}}{1-\theta}.$$
• More efficient than spreadsheet.

Present and future value

• If there is no inflation and the prevailing interest rate is 4%, then which of the following options would you prefer?
• $1000 today or $1500 in ten years?
• Either look at how $1000 will be worth in ten years or calculate how much you would have to invest today to get $1500 ten years from now.
• The latter approach relies on the concept of present value.

The present value calculation

• We know that $P_{t} = P_{0}\theta^{t}$ and making $P_{0}$ the subject of the formula means that $P_{0} = P_{t}\theta^{-t}$.
• Therefore, 1500 dollars in ten years time in a 4% interest rate environment is worth $1500(1+0.04)^{-10}$ in today's money, which is $1013.346, which is more than $1000, so you should prefer the second investment of $1500 received in ten years.
• This straightforward proportionate increase model allows for a simple discounting formula.

Use of present value

• A primary use in discounting investments to the present time.
• An annuity is a schedule of fixed payments over a specified and finite time period.
• The present value of an annuity is the sum of the present values of each separate payment.
• Present value is also used in lifetime customer value calculations.

Continuous compounding

• The compounding period for an investment can be yearly, monthly, weekly, daily etc.
• As the compounding period gets shorter and shorter, in the limit, the process is said to be continuously compounded.
• If a principal amount $P_{0}$ is continuously compounded at a nominal annual interest rate of R%, then at year $t$, $$P_{t} = P_{0}e^{rt}$$ where $r = \frac{R}{100}$.

Modeling an epidemic

• The model $P_{t} = P_{0}e^{rt}$ doesn't just describe money growing, it is called exponential growth or decay depending on whether $r$ is positive or negative respectively.
• A continuous time model for the initial stages of an epidemic states that the number of cases at week $t$ is $15e^{0.15t}$, halfway through week 7, how many cases do you expect?

Calculating the expected number of cases

• Interpretation of the 0.15 coefficient: There is an approximate 15 weekly growth rate in cases.
• Continuous models allow calculations at any value of $t$, not just a set of discrete values.

Using a model for optimisation

• A common modeling objective is to perform a subsequent optimisation.
• The objective of the optimisation is to find the value of an input that maximises/minimises an output.

Demand model

• Consider the demand model: $$Q = 60000P^{-2.5}.$$
• If the price of production is constant at $C=2$ for each unit, then at what price is profit maximised?
• Profit = Revenue - Cost
• Revenue = $P\times Q$.
• Profit = $PQ-CQ = Q(P-C) =60000P^{-2.5}(P-2).$
• Goal: Choose $p$ to maximise this equation.

Brute force approach

Calculus approach

• Profit is maximised when the derivatie or profit with respect to price equals to 0.
• Through calculus one obtains the optimal value of price as $$p_{\text{opt}} = \frac{cb}{1+b}$$, where $c$ is the production cost and $b$ is the exponent in the power function.
• The value (-b) is known as the price elasticity of demand.

Visualising the calculus solution

Module 3

Probabilistic models

• These are models that incorporate random variables and probability distributions.
• Random variables represent the potential outcomes of an uncertain event.
• Probability distribution assign probabilities to the various potential outcomes.
• We use probabilistic models in practice because realistic decision making often necessitates recognising uncertainty in the intpus and outputs of a process.

Key features of a probabilistic model

• By incorporating uncertainty explicitly in the model we can measure the uncertainty associated with the outputs, for example by giving a range to a forecast, which is a more realistic goal.
• In a business setting incorprating uncertainty is synonymous with understanding and quantifying in the risk in a business process, and ideally leads to better management decisions.

Valuing a drug development company

• A company has 10 drugs in a development portfolio.
• Given a drug has been approved, you have predicted its revenue.
• But whether a drug is approved or not is an uncertain future event (a random variable). You have estimated the probability of approval.
• You only wish to invest in the company if the company's expected total revenue for the portfolio is over $10B in 5 years time.
• You need to calculate the probability distribution of the total revenue to understand the investment risk.

Some examples of probabilistic models

• Regression models
• Probability trees
• Monte Carlo simulation
• Markov models

Regression models

• $E(Price|Carats) = -259.6 + 3721\times Carats$.
• The gray band gives a prediction interval for the price of a diamond taken from this population.

• Regression models use data to estimate the relationship between the mean value of the outcome (Y) and a predictor variable (X).
• The intrinsic variation in the raw data is incorporated into forecasts from the regression model.
• The less noise in the underlying data the more precise the forecasts from the regression model will be.

Probability tress

• Probability tress allow you to propagate probabilities through a sequence of events.
• $P(\text{Stop infringing}) = 0.1+0.9\times 0.15+0.9\times 0.85\times 0.2 = 0.388.$

Monte Carlo simuation

• From the demand model $$Q = 60,000P^{-2.5}.$$
• The optimal price was $p_{opt} = \frac{cb}{1+b}$ where $b = -2.5$, $c$ is the cost, $c=2$ and $p_{opt}\approx 3.33$.
• What if $b$ is not known exactly?
• Monte Carlo simulation replaces the number -2.5 with a random variable, and recalculates $p_{opt}$ using different realisations of this random variable from some stated probability distribution.

Input and output from a MC simulation

• Input: $b$ from a uniform distribution between $-2.9$ and $-2.1$.
• Output: $p_{opt} = \frac{cb}{1+b}.$
• 100,000 replications
• Interval $= (3.1,3.7)$.

Markov chain models

• Dynamics models for discrete time state space transitions.
• Example: employment status (the state of the chain).
• Treat time in 6 month blocks.
• Model states: 1. Employed; 2. Unemployed and looking; 3. Unemployed and not looking.

Probability transition matrix

• Markov property: transition probabilities only depend on the current state, not on prior states. Given the present, the future does not depend on the past.

A continuous random variable

• For a continuous random variable probabilities are computed from areas under the probability density function.

Key summaries of probability distributions

• Mean $(\mu)$ measures centrality.
• Two measuares of spread: - Variance $(\sigma^{2})$ and -Standard deviation $(\sigma)$.

The Bernoulli distribution

• The random variable $X$ takes on one of the two values: -$P(X=1) = p$ and -$P(X=0) = 1-p$.
• Often viewed as an experiment that takes on two outcomes, success or failure. Sucess = 1 and failure = 0.
• $\mu = E(X) = 1\times p+0\times(1-p) = p$.
• $\sigma^{2} = E(X-\mu)^{2} = (1-p)^{2}p+(0-p)^{2}(1-p) = p(1-p)$.
• $\sigma = \sqrt{p(1-p)}$.
• For $p = 0.5$, $\mu = 0.5, \sigma^{2}= 0.25$ and $\sigma = 0.5$.

The Binomial Distribution

• A Binomial random variable is the number of success in $n$ independent Bernoulli trials.
• Independent means that $P(A,\text{and},B) = P(A)\times P(B)$.
• Independence means that knowing that $A$ has occurred provides no information about the occurrence of $B$.
• Independence is a common simplifying assumption in many probability models.
• Example: Toss a fair coin 10 times and count the number of heads (call this $X$).
• In general, $$P(X=x) = C_{n,x}p^{x}(1-p)^{n-x},$$ where $C_{n,x}$ is the binomial coefficient: $\frac{n!}{x!(n-x)!}$.
• $\mu = E(x) = np, \sigma^{2} = E(X-\mu)^{2} = np(1-p).$

The Normal Distribution

• The Normal distirbution, also known as the Bell Curve, is the most important modeling distribution.
• Many disparate processes can be well approximated by Normal distributions.
• There are the Central Limit Theorem taht tells us Normal distribution should be expected in many situations.
• A Normal distribution is characterised by its mean $\mu$ and standard deviation $\sigma$. It is symmetric about its mean.

Examples

• There is a universality to the Normal distribution
• Biological: heights and weights
• Financial: stock returns
• Educational: exam scores
• Manufacturing: the length of an automotive component

• It is a famous example of continuous distribution, compared to Bernoulli and Binomial being discrete.

The Empirical Rule

• The Empirical Rule is a rule for calculating probabilities of events when the underlying distribution or observed data is approximately Normally distributed.
• It states: 1. There is an approximate 68% chance that an observation falls within one standard deviation from the mean; 2. There is an approximate 95% chance that an observation falls within two* standard deviations from the mean; 3. There is an approximate 99.7% chance that an observation falls within three standard deviations from the mean.

Empirical Rule example

• Assume that the daily return on Apple's stock is approximately Normally distributed with $\mu = 0.13%$ and $\sigma = 2.34%$.
• What is the probability that tomorrow Apple's stock price increases by more than 2.47%?
• Technique: Count how many standard deviations 2.47% is away from the mean, 0.13%. Call this counter the z-score: $$Z=\frac{2.47-0.13}{2.34} = 1.$$
• So from the Empirical Rule the probability equals approximately 16%.

Module 4

Regression models

• A simple regression model uses a single predictor variable $X$ to estimate the mean of an outcome variable $Y$, as a function of $X$.

Example

• Using the diamonds data: the predictor variable is the diamond's weight in carats and the outcome variable is the price of the diamond.
• If the relationship is modeled with a straight line we call it a linear regression: $E(Y|X) = b_{0}+b_{1}X.$

Correlation

• Correlation is a measure of the strength of linear association between two variables.
• It is denoted by $r$, where $-1\leq r\leq 1$.
• Negative values of the correlation indicate negative association and positive values indicate positive association.
• A correlation of 0 means no linear association between the variables.

Questions that can be answered with a regression

• In a business setting regression is most often used as a prediction tool. It is a core predictive analytics methodology: Give me a Prediction Interval in which the price is likely to fall.
• Interpreting coefficients from the model: How much on average do you expect to pay for diamonds that weigh 0.3 carats vs. diamonds that weigh 0.2 carats?
• How much of the variability in price is accounted for by the weight of the diamond?

Fitting a model to data using least squares

• Fitting a model requires an optimality criteria.
• Most regression models are fit using least squares: Find the line that minimises the sum of the squares of the vertical distance from the points to the line.

Residuals and fitted values

• Key insight: The regression line decomposes the observed data into two components; 1. The fitted values (the predictions); 2. The residuals (the vertical distance from point to line)
• The fitted values are the forecasts.
• The residuals allow us to assess the quality of the fit. If a point has a large residual it is not well fit by the regression. If we can explain why, we have learnt something new.

Interpretation of regression coefficients.

• For example, $E(Y|X) = 182 + 0.22 X$.
• Equate units on each side.
• Intercept is measure in units of $Y$.
• Slope is measured in units of $Y/X$.
• Intercept = Setup time in minutes.
• Slope = Work rate in minutes per additional item.

$R^{2}$ and Root Mean Squared Error (RMSE)

• $R^{2}$ measures the proportion of variability in $Y$ explained by the regression model. It is the square of the correlation, $r$.
• RMSE measures the standard deviation of the residuals (the spread of the points about the fitted regression line).

Using Root Mean Squared Error

• Assumption: at a fixed value of $X$, the distribution of points about the true regression line follows a Normal distribution, centered on the regression line.
• These normal distributions all have the same standard deviation $\sigma$, which is estimated by RMSE.

An approximate 95% prediction interval for a new observation

• Using the Normality assumption and the Empirical Rule, (within the range of the observed data) an approximate 95% prediction interval for a new observation is given by $$\text{Forecast}\pm 2\times\text{RMSE}.$$

Residual diagonostics - checking the Normality assumption

• The histogram of residuals from the diamonds regression is approximately Nomrally distributed, providing no strong evidence against the Normality assumption.

Fitting curves to data

• Often relationships are non-linear.
• Demand for a pet food against average price. A line is a bad fit to the data.

On observing curvature, transform

• This is where the basic math functions discussed in module 1 come in very useful.
• Look at the pet food data after having taken the log transform.

The regression equation for the log-log model

• The regression equation is now $$E(\log(S)|P) = b_{0}+b_{1}\log(P).$$
• This process shows how we could actually estimate the demand model that was the subject of the optimisation in module 2.

Multiple regression

• Multiple regression models allow for the inclusion of many predictor variables: In the fuel economy dataset we might add the horsepower of a car as an additional predictor
• With two predictors, $X_{1}$ and $X_{2}$ the regression model becomes $$E(Y|X_{1},X_{2}) = b_{0}+b_{1}X_{1}+b_{2}X_{2}.$$

Weight and horsepower as predictors of fuel economy

• Fitting a multiple regression model of fuel economy as a function of weight and horsepower.
• The model is now a plane rather than a line.
• For this model, $R^{2} = 84%$ and $RMSE = 3.45$, an improvement over the simple regression model with only weight included.

Logistic regression

• Linear regression is most appropriate when the outcome variable $Y$ is continuous.
• In many business problems, the outcome variable is not continuous but rather, discrete; Purchase a product: Yes/No; Medical outcome: Live/Die; Website Activity: Sign up/Don't sign up.
• Theses outcomes can be viewed as Bernoulli random variables.
• Logistic regression is used to estimate the probability that a Bernoulli random variable is a success, as a function of predictor variables.

Logistic regression fit

• The logistic regression fit is more appropriate, always predicting probabilities between 0 and 1.

Introduction to Spreadsheets & Models

Module 1

Module1.pdf

Module-1-Examples.xlsx

Excel order of calculation

• PEMDAS
• Parentheses
• Exponents
• Multiplication/Division
• Addition/Subtraction

Using functions

• We can use =sumproduct(x1:x3,y1:y3), where it means $(x_{1}+x_{2}+x_{3})\times(y_{1}+y_{2}+y_{3}).$
• Average: =average
• Min/Max: =min/=max
• Standard Deviation: = STDEV.P(x1:x3)

Using conditional expressions in formulas

• IF function: =IF(X,Y,Z), where $X$ means the condition, $Y$ means the task when it meets $X$, and $Z$ is the task else.

Module 2

Module2.pdf

Module-2-examples.xlsx

Module 3

Module3.pdf

Modul-3-Examples.xlsx

Excel random variable and other functions

• = randbetween $(x,y)$, where $x$ and $y$ are an interval (range)
• = exp, exponential function
• = forecast $(x,a:b,c:d)$, where $x$ is the forcasting year, $a:b$ is number of inputs (y-values), and $c:d$ is the independent variable $'x'$.
• = growth $(a:b, c:d, x)$, where $a:b$ is the known y values, $c:d$ is the corresponding $x$ values and $x$ is the forcasting year.
• = Correl $(x,y)$

Module 4

Module4.pdf

Module-4-examples.xlsx

Financial Acumen for Non-Financial Managers

Module 1

Definition of Accounting

• Accounting is a systme for recording information about business transactions and events.
• To provide summary statements of a company's financial position and performance to users who require such information.
• Financial accounting: Standardised reports for external stakeholders.
• Tax accounting: IRS rules for computing taxes payable.
• Managerial accounting: Custom reports for internal decision making.

Financial Reporting Requirements

• Each country has its own financial reporting requirements
• In ths U.S., The Securities and Exchange Commission (SEC) requires periodic financial statement filings:
• (1) 10-K: Annual report (within 60 days for big firms)
• (2) 10-Q: Quarterly report (within 40 days for big firms)
• (3) 8-K: Current report (material events)
• (4) Proxy, registration and insider trading statements.
• In other countries, firm file semi-annual reports instead of quarterly reports.
• Firms supplement filings with voluntary disclosure: Conference calls, press releases, forecasts, presentations at brokerage conferences.

Who makes the Accounting Rules?

• Generally Accepted Accounting Prinicples (GAAP) are established by:
• (1) U.S. Congress, but they delegate to the SEC.
• (2) The SEC, but they delegate to Financial Accounting Standards Board (FASB).
• International Financial Reporting Standards (IFRS) are required in over 100 countries, including the EU.
• The two sets of rules are similar, but not the same.

Financial Statements Provide Information About Firms' Ecnomoic Activities

• Raise Capital From Investors -> Acquire Resources -> Produce goods and services -> Collect from customers -> Distribute Funds to Investors.

More Timely Information Requires More Estimation

• Accounting systems slice the firms' life into arbitrary periods (quarters and years).
• This allows for the generation of more timely information.
• But many activities and decisions made to date aren't done - they still have implications for future cash flows.

Annual Report Contents

• Discussion of Firm's strategy, products, competitive environment, Financial statistics, Management discussion and analysis (MD&A)
• Financial statements
• Footnotes: These explain the accounting procedures used by the firms and discuss various assumptions regarding how the numbers were calculated.

What are the Required Financial Statements?

• Balance Sheet: Financial position on a specific date; Assets = Liabilities + Stockholders' Equity.
• Income Statement: Result of operations over a period of time; Net income = Revenues - Expenses.
• Statement of Cash Flows.
• Statement of Stockholders' Equity.

Balance Sheet

• Balance Sheet is a statement of financial position.
• Key components: Assets, Liabilities, Shareholders' Equity.
• Describes the resources (assets)
• Describes claims on resources (liabities)

Balance Sheet Equation

• Assets = Liabilities + Shareholders' Equity
• Resources = Claims on Resources by Outsiders + Owners.
• Just because a balance sheet balances, does not mean financial position is okay.
• Every transaction or event that is recorded in the financial statements must preserve the balance sheet equation. This means each transaction must balance.
• If one account is impacted, at least one other must be as well.

Presentation Format

• The balance sheet equation must hold for firms using GAAP as well as for those using IFRS.

Equivalent View

• Shareholders' Equity = Assets - Liabilities: Sometimes will see the term "Net Worth" or "Net Assets".

Relationship Between Financial Statements

• The balance sheet shows the resources and claims on the resources AT A POINT OF TIME.
• The income statement and cash flow statement provides information about how the balance sheet changes OVER A PERIOD OF TIME: The cash flow statements tells you how the CASH account on the balance sheet changes over time.

Issues in Recording Assets and Liabilities

• Recognition: Should an asset or liability be recognised in the financial statements?
• Measurements: How should asset and liability values be initially measured? Do we adjust the values over time? What do we remove them?
• Historical Cost: How much did you pay to acquire the assets?
• Fair value: What is the asset worth today?

Assets

• An ASSET is a resource that is expected to provide future economic benefits (i.e. generate future cash inflows or reduce future cash outflows).
• An asset is recognised when it is acquired in a past transaction or exhcnage and the value of its future benefits can be measured with a reasonable degree of precision.

Liabilities

• A LIABILITY is a claim on assets by 'creditors' (non-owners) that represents an obligation to make future payment of cash, goods or services.
• Not all liabilities will show up on the balance sheet.
• Liabilities to be settled more than a year in advance are generally measured at their present value.

Shareholders' Equity

• SHAREHOLDERS' EQUITY is the residual claim on assets after settling claims of creditors (i.e. assets - liabilities).
• Types of Shareholders' Equity: Contributed capital (common stock and additianal paid-in-capital); Retained Earnings; Treasury Stock (Repurchase some of our Own Shares).

Capital Structure

• Capital Structure is the way the firm has financed its assets.

Differences Between Debt and Equity

• Contractual: Payments to debt-holders are usually contractually specified (interest and principal); Equity holders are 'hoping' to get something (dividends & capital gains).
• Voting: Equity holders get to vote.
• Priority of Claims: Debt holders get paid first but their return is capped; Equity holders get nothing if the firm does poorly but get all the upside if the firm does well.

Leverage

• The amount of debt vs. equity in the capital structure.

Goodwill

• When you make an acquisition, you assign the purchase price to all the individual assets and liabilities that you have acquired.
• Value them at what you think their current fair value is (not the amount they were listed on the other company's books).
• This also means assign a value to any intangibles you have acquired (brand names, patents, etc.)
• If the total purchase price exceeds the sum of the above individual fiar values (and it usualy does), the rest is allocated to Goodwill.

Common Sized Balance Sheet

• Very useful tool in analysing financial statements.
• Divide everything on the balance sheet by that year's total assets.
• Tells you the percent of your total assets in each category.
• Helps illuminate structure of your assets.
• Especially useful in comparing companies of different size.
• For Xsite: Goodwill is 40% of total assets; Other intangibles are 22%.

Income

• Income is a measure of the performance of the company during a period of time.
• The Incoem Statement help link Changes in Balance Sheets.
• Income feeds into the Retained Earnings Account on the balance sheet.
• Retained Earnings Represents the CUMULATIVE INCOME* of the firm (net of what has been paid out as a dividend). $$\text{Retained Earnings}_ {\text{end}} = \text{Retained Earnings}_ {\text{beg}} + \text{Income This Year} - \text{Dividends this Year}.$$

Accrual Accounting

• Income is not the same as cash flow
• Accrual Accounting - the recognition that revenues and expenses are tied to business activites, not necessarily to cash flow.
• Income measures the increase in economic value from a transaction or event.
• Cash flow measures the receipt of that value in the form of cash.
• The difference is one of TIMING.

Income Statement Format

• The Income Statement generally has the following format: $$\text{Revenue or Sales} - \text{Cost of Goods Sold} - \text{Operating Expense} - \text{Interest, Other Gains, and Losses} - \text{Income Tax Expense}.$$

Revenue

• Revenue is an increase in shareholders' equity from providing goods or services.
• Revenue is recognised when both: it is earned(i.e. goods or services are provided) and it is realised(i.e. payment for goods or services received in cahs or something that can be converted to a known amount of cash).

Expenses

• Expenses are the decreases in shareholders' equity (not necessarily cash) that arise in the process of generating revenues.
• Expenses are recognised when either: Related revenues are recognised(product costs) or incurred, if difficult to match with revenues (period costs and unusual events).
• The underlying recognition concepts are the: Matching principle (product vs. period costs); Conservatism principle: recognise anticipated losses immediately, recognise anticipated gains only when realised.

Adjusting Entries

• The way events for which there are no underlying transactions or where no cash has exchanged hands - are recorded.
• Often done at the end of the period to record.
• Tricky to keep track of because they generally don't involve a specific transaction or have any cash to point to: Done when the firm already knows how good a year (or a quarter) they've had.

Other Things Need to Record

• Depreciation: We don't charge the entire purchase price of an asset to the period in which it was bought if it will provided benefits beyond that.
• Straight-line Depreciation: Takes the purchase price of the asset and spreads it out evenly over the useful life. $$\text{Depreciation Expense} = (\text{Original Cost} - \text{Salvage Value})/\text{Useful Life}.$$ To calcuate, you need an estimate of what the salvage value is and how long the asset is going to live.

Adjusting Entries

• Allowance for Uncollectibles
• Allowance for Returns
• Income Tax Expense
• Mark to Market Adjustments
• Impairment Charges
• Accrued Interest Expense or Income

Recurring vs Non-Recurring Items

• Earnings reports things that happened, but not all of them are likely to recur.
• Recurring items are more important from a valuation. (looking ahead) perspective.
• Analysts try to separate recurring from non-recurring items.
• What is an Impairment Charge?: Review assets to re-evaluate and write them down to actual lower value; Writing them down means the asset and owner's equity moves down.

Margin Analysis

• Take the Income Statement and divide everything by that year's Sales Revenue.
• This gives each expense item as a percent of revenue.
• It helps reveal the structure of your costs.
• It tells you how each dollar of sales gets 'eaten up' by different kinds of costs and how much is left over for profits.