CFA L1 Flashcards
Add on yield Formula v Discount yield Formula
Add on Yield: (P1-P0/P0)-1
Discount Yield: (P1-P0/P1)-1
Cyclical v Defensive Stocks
Cyclical: Market goes up, stocks go up - high correlation. Eg: Real Estate
Defensive: Market and stock have comparatively less correlation - stocks not sensitive to market Eg: Pharmaceuticals
Front Running
An Asset manager buying stocks personally prior to making investments through his fund - as bigger investments make the price go up, he will benefit personally. This is illegal.
Joint Probability
= Intersection value / Grand Total
Conditional Probability (Probability of A | B)
= A Intersection B / A Intersection B + A’ Intersection B
= Joint Probability / Total Probability of B
Probability
= Favourable outcomes / Total Outcomes
0 <= P(x) <=1
where P = 0 is an impossible event
P = 1 guaranteed event
Sum of all P(x) = 1
Expected Value of x
E(x) = P(x)
Expected Return of Portfolio
E(Rp) = Sum of wiE(Ri) = w1E(R1) + w2E(R2) + … + wnE(Rn)
Covariance of Expected Returns of two variables
Cov(Ri,Rj) = E[(Ri-E(Ri)*(Rj-E(Rj)]
There is no n as sum of P =1
Covar(Ri,Ri) = Var(Ri)
Sample Covariance of Returns
Sum of [(R1 - R1bar)*(R2 - R2bar) / n-1
Portfolio Variance ie Var(Rp)
Sum of wiwjCov(Ri, Rj)
= W^2Var(Ra) + 2WaWbCov(a,b) + Wb^2*Var(Rb)
- Keeps on adding for every asset added - Number of elements of Cov part = NC2 where N = number of stocks
Roys Safety First Criterion
= | Rp - RL | / SDp
- RL is the threshold level
- Higher the ratio, better as lower shortfall risk
- Shortfall % - z value
Rp - RL | / SDp
Sharpe Ratio
- When RL = Rf
= | Rp - Rf | / SDp - represents return over and above risk free rate per unit of risk
Expected Standard Deviation
= Root of Sum of P(x-E(x))^2
- Denominator = n = 1 (Sum of all P =1)
Expected Variance
Sum of P(x-E(x))^2
Expected Skewness
Sum of P(x-E(x))^3 / SD^3
Expected Kurtosis
Sum of P(x-E(x))^4 / SD^4
Expected Covariance
Sum of P[(x-E(x))*(y-E(y))]
Expected Correlation
Sum of P(Cov(x,y)) / E(SDx)*E(SDy)
= Sum of P(Cov(x,y)) / Root of Sum of P(x-E(x))^2 * Root of Sum of P(y-E(y))^2
Growth v Value Stock
Growth Stock: Exponential Growth, outperforming economy, doesn’t fluctuate too much w market changes ie is less sensitive to market as future earnings are priced in. P/BV is high
Value Stock: Available for cheap, riskier & sensitive to market, P/BV is low
Liquidity
Ability to convert asset into cash at a fair and reasonable price in a short period of time
Illiquidity = Liquidity Risk
Types of Risk
Liquidity Risk
Maturity Risk (risk due to change in rates/volatility in longer term)
Default Risk
MV v BV v IV
Market Value: Price at which asset is sold/bought in the market, based on demand, future CFs
Book Value: As per books of accounts, based on historical pricing
Intrinsic Value: Based on one’s own opinion on what the price SHOULD be, based on models, forecasts, projections
Principal Agent Conflict
Principal - who agent works for
Example of PAC: broker recommending stock to customer based on his commissions instead of for purpose of clients wealth maximization
Compound Interest v Simple Interest
Simple Interest = prt/100
Compound interest = (1+r/100m)^tm
m= periods of compounding
t = number of years
Sum of Infinite GP Series
a/(1-r)
Quadratic Equation
+/-b + [Root of (b^2 - 4ac)] / 2a
HPR
Pn-Po / Po
HPR to EAY
EAY to HPR
HPR to EAY = (1+HPR)^365/n -1
EAY to HPR = (1+EAY)^n/365 -1
BEY
Compounded semi annually
= (1+r/2)^2n
BEY to EAY = (1+BEY/2)^2
BDY
(Pn-Po / Pn) * 360/n
= Discount Rate x 360/n
MMY
(Pn-Po / Po) * 360/n
= HPR x 360/n
Quoted Price
100 - BDY
Purchase Price
Quoted Price x n/360
Nominal Rate
(1+Nominal) = (1+real)x(1+inflation)
Approx Nominal = Real + Inflation
Other risk premiums
Default, Liquidity, Maturity
Annuity Due v Ordinary Annuity
Annuity Due - Investment at start of period
Ordinary Annuity - Investment at the end
PV(Annuity Due) = PV(Ordinary) x (1+r), same for FV
Perpetuity
PMT/r
Continously Compounded Rate
P*e^r
RCC to EAY/Discrete = e^r -1
EAY to Rcc = ln(1+r)
Outstanding Principal at any time
PV of remaining EMIs
Principal Repaid
Outstanding at yn-1 - Oustanding at yn
Interest Repaid
EMI - Principal repaid
Growth rate
(FV/PV)^1/n -1
Time Weighted Return
= (1+r1)(1+r2)….*(1+rn)
Like an average, quantum and timing does not matter
Money Weighted Return
=IRR
Quantum & Timing matters, tips towards higher return
NPV
- assumes reinvestment at Re
= PV(inflows) - PV(outflows)
IRR
- assumes reinvestment at IRR
= Rate at which PV(outflows) = PV(inflows)
NPV & IRR
- NPV is positive when PV(I) > PV(O), ie IRR > Re
- NPV is negative when PV(I) <(O) ie IRR < Re
- NPV is 0 when PV(I) = PV(O), ie IRR = Re (indifferent to acceptance of project, depends on management decision taking other factors into consideration)
- NPV & IRR will always give same decision but might give different ranks - we generally accept NPV ranks in case of conflict (independent projects)
Types of Capital Investment
- Going Concern: necessary for survival of business or to reduce costs
- Regulatory/Compliance: necessary by law, enforced by Gov or authorities - usually due to safety or environmental concerns
- Expansion: Vertical/Horizontal integration, involves complex and detailed analysis
- New Business: Entering into a completely new market, also involves complex and detailed analysis
Principals of Capital Allocation
- Based on Cashflows not Accounting Income
- Based on After Tax Cashflows
- Opportunity Costs to be taken into account
- Timing of Cashflows to be taken into account
- Financing cost to be taken into account
Sunk Costs
- Costs that will be incurred irrespective of whether a project is accepted or not
- Sunk costs not to be taken into account while calculating (may be taken after if relevant)
Hard Rationing of Capital
- Calculate Profitability Index
- Rank by PI
- Calculate best combination based on capital budget
Profitability Index
Pv(Inflows)/PV(outflows)
Capital Allocation Pitfalls - Cognitive Biases
- Poor forecasting
- Not considering opportunity Costs/Internal Costs
- Incorrectly accounting for inflation
Capital Allocation Pitfalls - Behavioural Biases
- Pet Project of Management
- Inertia of setting Capital Budget (not being updated)
- Basing investment decisions on EPS/ROE (as incentives may be tied to it/short term outlook)
- Failure to generate alternate investment ideas
Real Options
are future actions that a f irm can take, given that they invest in a project today
Timing Options
allows a co to take delayed a delayed decision as it expects to have more/better information in the future
Abandonment Option
If NPV today exceeds NPV of in future - abandonment is better
Expansion Options or Growth Options
Will allow company to make further investments based on future performance of project
Flexibility Options
Price-setting Flexibility: change prices in future
Production Flexibility: change operational factors
Return on Invested Capital
= NI + Interest*(1-t) / Avg BV of Capital (E+P+D)
= NOPAT / Avg BV of Capital
= NOPAT/Sales * Sales/Avg BV of Capital
= Operating Margin After Tax * Asset/Capital Turnover
Is the Co creating value for Shareholders? (ROIC)
ROIC > Kc, +ve , Yes
ROIC < Kc, -ve, No
ROIC = Kc, 0, No
Process of Capital Allocation
- Idea generation
- Analysing Project Proposals (Expected Profitability)
- Creating firm wide capital budget (prioritise profitability and consider timing of cashflows, available resources and overall strategy)
- Monitor decisions and conduct post-audit (identify systematic errors, improve performance)
Hurdle Rate
Minimum IRR at which a project will be accepted
NPV Advantage
Direct measure of profitability
IRR Advantage
measures profitability as a %, allows calculation of safety margin
IRR Disadvantages
- Assumes reinvestment at IRR instead of Re, more realistic to assume Re
- For multiple sign changes, may have multiple IRRs or no IRR - difficult to interpret
Range
Highest Value - Lowest Value
Variance
Sum of (x-xbar)^2 / n-1
n-1 for sample
N for population
Standard Deviation
Root of [Sum of (x-xbar)^2 / n-1]
Geometric Mean
[(1+r1)(1+r2)…*(1+rn)]^1/n] -1
Harmonised Mean
= N / Sum of 1/xi
- used for calculating average price per share
AM v GM v HM
HM < GM < AM
Skewness
Sum of (x-xbar)^3 / n* SD^3
- Postively skewed ie right tailed ie outliers lie above the mean
- Negatively skewed ie left skewed ie outliers lie below the mean
- Sample skewness = 0
Kurtosis
Sum of (x-xbar)^4 / n*SD^4
- Sample kurtosis = 3 (mesokurtic)
- Fat Tailed ie peaked ie K >3 ie Leptokurtic
- Thin tailed ie flat, K<3 ie Platykurtic
- Excess Kurtosis = K - 3
Covariance
= Sum of (x-xbar)*(y-ybar) / N
- only indicates whether a relationship exists and the direction
- does not indicate the degree/strength
- has units so not universally comparable
- +ve = move in same direction
- -ve = move in opposite direction
- 0 = no clear directional relationship
Correlation
= Cov(x,y) / SDx *SDy
- -1 <= Correlation <= 1
- suggests the same as covariance
- suggests strength of relationship as follows:
- -1 = perfect -ve correlation, close to -1 - high -ve correlation
- 1 = perfect +ve correlation, close to 1 - high +ve correlation
- close to 0 - low +ve/-ve correlation
- = 0 ie no linear relationship (may have non-linear one)
- CORRELATION DOES NOT IMPLY CAUSATION
Trimmed Mean
x% Trimmed mean = deleted top-most and bottom-most x/2% of the observations and then calculate mean
Winsorized Mean
x% winsorized mean = replace (1-x)2% top-most and bottom-most observations with the (1-x)/2th top & bottom observations resp.
- keeps numer of obs same.
Percentile formula
n+1 * y/100 th term
where y is number of divisons
Financial Statement Analysis Framework
- State Objective & Context (questions, resources, time)
- Gather Data (primary, secondary)
- Process Data (ratios, analysis, graphs)
- Analyze data (Answer Step 1 Qs)
- Report the Conclusions & recommendations
- Update analysis: periodically repeat the above steps
Role of FSA
To help make informed business/economic decisons
Standard Setting Bodies
Professional Orgs of accountants and auditors that establish the financial reporting standards
India - ICAI - Institute of Chartered Accountants of India
US - FASB - Financial Accounting Standards Board
Outside US - IASB - International Accounting Standards Board
Regulatory Bodies
Authorities that enforce the application of the standards
India - SEBI
USA - SEC
UK - FCA
IOSCO
- International Organization of Securities Commissions
- Regulates 95% of the global financial market through its members
- members comprise of various regulatory bodies of the world
Objectives of IOSCO
- Protecting Investors
- Ensuring markers are fair, efficient and transparent
- Reducing systematic risk
Sarbanes-Oxley Act 2002
- Enforced by SEC
- Prohibits company’s external auditors from providing other services to the firm
- to avoid a conflict of interest and promote auditor independence
- Company’s exec management need to certify that accounts are presented fairly, include statement of effectiveness of Co’s internal controls of financial reporting
- External auditor must also confirm Co’s effectiveness of internal controls
Footnotes
To include detailed info of Financial Statements and disclosures as follows:
- Basis of presentation (GAAP/IFRS)
- Accounting Methods, assumptions, estimations
- Acquisitions, disposals, legal action, contingencies, commitments, related party transactions etc
- audited along with Primary accounts
Form S-1
Prior to sale of new securities
Includes audited F/s, risk assessment, underwriter identification, estimated amount and use of proceeds
Form 10-K
-Required annual filing, similar to annual report but not a substitute
- Audited F/s. disclosures, info re biz & management
Form 10-Q
- Quarterly Filing
- unaudited F/s (updated) & disclosures
- Non-US Cos - Form 6K (semi annually)
Form DEF 14-K
For proxy statements prior to AM/shareholder vote
Form 8-K
To disclose material events
Form 144
To issue securities to certain qualified buyers without SEC registration
Form 3,4,5
Beneficial ownership by Corporate Insiders
Segment Data Reporting
Business Segment: if accounts for more than 10% of Co’s revenue/Assets/Income & atleast 75% of external sale
Geographic segment: same as above for different geographic locations
Must report the following:
- Revenue, measure of P&L, measure of Assets & Liabilities, Interest (Revenue & Expense), Depreciation/Amortisation, Non cash exp, Income Tax Exp
Management Commentary/Management Report/Management Discussion & Analysis (MDA)
- Address nature of business, mgmt objectives, co’s past performance, perf measures used, key relationships, resources and risks
- impact of inflation, changing prices, purchase commitments
- accounting policies, forward looking expenses, divestures
Audit
Independent review of Company’s F/s to enable auditor to provide an opinion on fairness and reliability of F/s
Standard Auditors Opinon
- F/s prepared by Management are its responsibility and auditor has performed independent review
- Generally accepted accounting measures are followed - proved reasonable assurance of no material errors
- Compliance is present, estimates are reasonable
Types of Opinions
Unqualified Opinion: Free from material omissions and errors
Qualified Opinion: If any exception to accounting principles is present and explanation of these exceptions
Adverse Opinion: Non-conforming, unfairly presented
If unable to express opinion, a disclaimer of opinion is issued.
Any opinion other than unqualified may be referred as modified opinion
Internal Controls
Process by which company ensures accuracy of financial statements
Key audit matters
section of audit report containing accounting choices of great significance to users of F/s
Sources of Info other than F/s
- Issuer Sources
- Public Third Party Sources
- Proprietary Third Party Resources
- Proprietary Primary Research
IASB Framework - Qualitative Characteristics
Relevance & Faithful Representation
Characteristics to enhance the above:
- Comparability
- Verifiability
- Timeliness
- Understanding
Required Reporting Elements
- Assets
- Liabilities
- Income
- Expenses
- Equity
Assumptions & Constraints of F/s
Assumptions: Going Concern, Accrual accounting
Constraints:
- Cost-benefit trade off; Benefit should be > cost
- Non-quantifiable info can’t be captured
General Requirements - IFRS - Financial Statements
- Balance Sheets
- Profit & Loss and OCI, Statement of comprehensive income
- Cash Flow Statement
- Statement of change in owners equity
- Explanatory Notes, including a summary of A/c policies
General Requirements - IFRS - General Features
- Fair representation
- Consistency
- Materiality
- Aggregation
- No offsetting
- Reporting Frequency (atleast annually)
- Comparative Information
- Going Concern
- Accrual basis
General Requirements - IFRS - Structure & Content of F/s
- Classified Balance Sheet
- Minimum Information
- Comparative Information
Market Capitalization
(Market Value or Price per share) x number of shares
P/E Ratio
Price to Earnings Ratio
= Market price / Earnings per share
= MPS/EPS
= Market Cap / Total Earnings
ROE
Return on Equity
= Net Profit / Equity
Return on Investment
= HPY
Growth Rate
g = b x r
b = retention ratio
r = ROE
Retention Ratio
= 1 - Dividend Payout Ratio
= 1 - Dividend Per Share/Earnings per Share
EPS
Earnings Per Share
= EAFSH or Net Profit / No. of Shares
Book Value per Share
= Book Value of Equity / No. of shares
Tangible Assets
Definite Life: P&M, Depreciation Applies
Indefinite Life: Land, may need to check for impairments
Intangible Assets
Definite Life: Licence, Amortisation applies
Indefinite Life: Trademark
Identifiable: Patent/Brand
Unidentifiable: Goodwill
Financial Assets
Identifiable
Intangible
Definite: Bonds
Indefinite: Equity
Types of Depreciation
Straight Line Method - same amount of depreciation charged every line (% of depn every year keeps increasing)
By Capacity: (Origanl - SV) * Units produced/Total Capacity - when a machine has a certain capacity it can produce over its lifetime
Accelerated Depreciation: 2 methods:
Written Down Value: Constant Percentage of Depreciation (Amount of Depn goes down every year)
Double Declining Balance Method: Written down at double the rate = 2 x Book Value / Useful Life
Component Depreciation: parts of an asset may depreciate at a different rate and need treating accordingly
When do we change accounting policy?
- Due to new law
- Due to new accounting standard
- To represent true and fair accounts
Reflection of change in Depreciation method
Needs to be shown retrospectively
Reflection of change in estimate
Needs to be shown prospectively
Matching Principle
Costs & sales need to match for the year
Revenue Recognition
Accounts receivable: ASSET
Unearned Revenue: LIABILITY
Prepaid Expenses: ASSET
Delayed Expenses: LIABILITY
Contract
Agreement between two or more parties specifying their rights and obligations
Steps for recognising revenue
- Identify the contract with the customer
- Identify distinct performance obligations in the contract
- Determine the Transaction price
- Allocate the Transaction price to the performance obligation
- Recognise revenue when PO is satisfied
Performance Obligation
- Promise to deliver goods/services
PO is satisfied when: - Customer receives goods/services & its benefits
- Supplier enhances an existing asset or creates a new asset that the customer controls over the period in which the asset is created/enhanced
- Asset has no alternative use for supplier, and the supplier has the right to enforce payment for work completed to date
How is revenue recognised in a long term contract?
- Revenue is recognised based on % completed
Revenue Recognition Disclosures
- Contracts with customer by Category
- Assets & Liabilities related to contracts including balances and changes
- Outstanding POs & TPs allocated to them
- Management Judgements used to determine amount & timing of revenue recognition including any changes to those judgements
Goods & Services
- The customer can bene fit from the good or service on its own or combined with other resources that are readily available.
- The promise to transfer the good or service can be identi fied separately from any other promises.
Transaction Price
- The amount a f irm expects to receive from a customer in exchange for transferring a good or service to the customer.
- A transaction price is usually a f ixed amount, but it can also be variable (e.g., if it includes a bonus for early delivery).
Capitalization
- Application of the matching principle whereby costs are initially capitalized as assets on the balance sheet and then expensed, using depreciation or amortization, to the income statement over the asset’s life as its bene its are consumed.
- If potential future economic benefit - capitalise, otherwise, expense
Period Costs
Not all expenses can be directly tied to revenue generation. Period Costs such as administrative costs, are expensed in the period incurred.
Amortn v Deprn v Depln
Amortisation: Intangible Assets
Depreciation: Tangible Assets
Depletion: Natural Resources
Capitalised Interest
Interest paid on asset under construction
Capitalised until asset is built completely
Capitalisation of Research Costs & Development Costs
- Research costs, which are costs aimed at the discovery of new scientif ic or technical knowledge and understanding, are expensed as incurred.
Development costs may be capitalized. Development costs are incurred to translate research findings into a plan or design of a new product or process. To capitalise development costs, a firm must show that it can complete the asset and intends to use or sell the completed asset, among other criteria.
US GAAP Treatment of Research & Development Costs
Both research and development costs are generally expensed as incurred. However, the costs of creating software for sale to others are treated in a manner similar to the treatment of research and development costs under IFRS. Costs incurred to develop software for sale to others are expensed as incurred until the product’s technological feasibility has been established, after which the costs of developing a salable product are capitalized.
How to make F/s comparable for development costs capitalised in one firm and expensed in the other?
- Convert capitalised one to expensed one by:
- Expensing the Development Costs
- Removing amortisation of Capitalised Dev costs charged previously
- Remove Dev costs from Balance Sheet
- Adjust Cash Flow Statements: Remove from CFI, Decrease from CFO
Non Recurring Items
- Unusual infrequent items
- should consider if should be excluded from forecasting
Discontinued Operation
- Decided to dispose of but not done yet or disposed of in the current year after the operation had generated income or losses
- Measurement Date: Date when co develops a formal plan for disposing operation
Phase out Period: Actual disposal date - Should be excluded from forecasts
Discontinued operations - where is it reported on Income Statement
Reported below income from continuing operations, net of tax (reported separately)
Unusual or infrequent items - where is it reported on Income Statement
Reported before taxes, above net income from
continuing operations (included in)
change in accounting principle - where is it reported on Income Statement
requires retrospective application
Simple v Complex Capital Structure
Simple capital structure: is one that contains no potentially dilutive securities. A simple capital structure contains only common stock, nonconvertible debt, and nonconvertible preferred stock.
Complex capital structure: contains potentially dilutive securities such as employee stock options, warrants, or convertible securities.
Basic EPS
= (Net Income - Preferred Dividend) / Weighted Avg number of common shares outstanding
Stock dividend
Bonus Shares - distribution of additional shares to each shareholder in an amount proportional to their current number of shares
- ownership % remains unchanged
- applies to the beginning of the period of calculating weighted average shares
Stock Split
- refers to the division of each “old” share into a specif ic number of “new” (post-split) shares
- ownership % remains unchanged
Dilutive v Anti-dilutive securities
Dilutive: stock options, warrants, convertible debt, or convertible preferred stock that would decrease EPS if exercised or converted to common stock.
Anti-dilutive stock: stock options, warrants, convertible debt, or convertible preferred stock that would increase EPS if exercised or converted to common stock.
Diluted EPS
= Adjusted Income available for common shares / Weighted average common and potential common shares outstanding
where, Adjusted Income = Net Income - Preferred Dividend + Dividends on convertible preferred stock + After Tax Interest on convertible preferred debt (Interest x 1-t)
Comprehensive Income
Profit + Other Comprehensive Income
Other Comprehensive Income
= PUFE
= Pension Adjustment, unrealised gains/lossed from available for sale securities, foreign currency translation gains/losses, Effective portion of Cash Flow Hedges
Reasons for Change in Equity
Owner Related:
- New shares issued
- Dividend
- Buyback
Others:
- P&L
- OCI
How to check if convertible stock/debt is dilutive
Convertible debt (1-t) / Convertible debt shares > Basic EPS, then antidilutive
Dilutive EPS > Basic EPS, then antidilutive
Preferred Dividend / Convertible Preferred stock
Common Size Statements
Balance Sheets: Represented as % of Total Assets (Equity + Liability)
Cash Flow: represented as % of total inflows/outflows
Gross Profit Margin
= Gross Profit / Revenue
Net Profit Margin
= Net Profit / Revenue
Operating Profit Margin
= Operating Profit / Revenue
Pre Tax Margin
= Pre Tax Accounting Profit / Revenue
Revise Financial Assets Table
HTM, HTT, AFS - US GAAP, IFRS
