LOS 32d

An accelerated depreciation method is appropriate if a long term asset generates proportionally more of its economic benefits in the early years of its life. Straight line depreciation is appropriate when an assets economic value decreases at an approximately decreases at approximately constant rate over time.

 

Inventory that can be tracked by individual unit can be valued by specific identification.

FIFO valuation is appropriate for goods with a limited shelf life.

LIFO is widely used in the US because of its tax advantages but is not allowed under IFRS.  The weighted average cost method averages the cost of all units purchased or manufactured and currently available for sale.

Intangible assets with limited lives should be amortized using a method that reflects the flow over time of their economic benefits. Intangible assets with indefinite lives (e.g. goodwill) are not amortized.

 

LOS 32e

Depreciation methods:

• Straight line: Equal amount of depreciation expense in each year of the assets useful life.
• Declining balance: Apply a constant rate of depreciation to the declining book value until book value equals residual value.

Inventory valuation methods:

• FIFO: Inventory reflects cost of most recent purchases. COGS reflects cost of oldest purchases.
• LIFO: COGS reflect cost of recent purchases, inventory reflects cost of oldest purchases.
• Average cost: Unit cost equals cost of goods available for sale divided by total units available and is used for both COGS and inventory
• Average cost: Unit cost equals cost of goods available for sale divided by total units available and is used for both COGS and inventory.
• Specific identification: each item in inventory is identified and its historical cost is used for calculating COGS when the item is sold e.g. Ferarri

Amortization methods for identifiable intangible assets should also approximate the pattern of decrease in their economic values, but intangible assets with indefinite lives are not amortized.

 

LOS 32f

Operating income is generated from the firms normal business operations. For a nonfinancial firm, income that results from investing or financing transactions is classified as non-operating income, while it is operating income for a financial firm since its business operations include investing in and financing securities.

 

LOS 32g  --p78

Results of discontinued operations are reported below income from continuing operations, net of tax, from the date the decision to dispose of the operations is made.

 

Results of discontinued operations are reported below income from continuing operations, net tax, from the date the decision to dispose the operations is made.  These results are segregated because they likely are non-recurring and do not affect future net income.

 

Unusual or infrequent items are reported before tax and above income from continuing operations.  An analyst should determine how ‘unusual’ or ‘infrequent’  these items really are for the company when estimating future earnings and/or firm value.

 

Extraordinary items (both unusual and infrequent) are reported below income from continuing operations, net of tax under US GAPP, but this treatment is not allowed under IFRS, Extraordinary items are not expected to continue in future periods.

 

Changes in accounting standards, changes in accounting methods applied, and corrections of accounting errors require retrospective restatement of all prior period financial statements included in the current statement.a change in accounting estimate, however is applied prospectively (to subsequent periods) with no restatement of prior period results.

 

LOS 32h

 

 

LOS 32i

A dilutive security is one that, if converted to its common equivalent, would decrease EPS.  An  anti dilutive security is one that would not reduce EPS if converted to its common stock equivalent.

 

LOS 32 j

A vertical common size income statement expresses each line item as a % of sales.

Gross profit margin and net profit margin are profitability ratios that can be read directly from a vertical common size income statement.    An analyst should examine changes in items on a vertical common size income statement over time and compare values to those for peer companies or to industry averages.

 

LOS 32k

Transactions with shareholders, such as dividends paid and shares issued or repurchased, are not reported on the income statement.

“Other comprehensive income” includes other transactions that affect equity but do not affect income including:

 

1. Gains and losses from foreign currency translation
2. Pension obligation adjustments
3. Unrealized gains and losses from cash flow hedging derivatives
4. Unrealised gains and losses on available for sale securities

 

LOS 32 l

Comprehensive income is the sum of net income and other comprehensive income

LOS 8a

A random variable is an uncertain value determined by chance

An outcome is the realization of a random variable

An event is a set of one or more outcomes.  Two events that cannot both occur are termed “mutually exclusive”
and a set of events that includes all possible outcomes is an “exhaustive” set of events.

 

LOS 8b

The 2 properties of probabilities are

1. The sum of probabilities of all possible mutually exclusive events is 1
2. The probability of any event cannot be greater than 1 or less than zero

A priori probability measures probabilities based on well defined inputs; empirical probability measures probability from observations or experiments; and subjective probability is an informed guess.

 

LOS 8c

If the probability of an event is A out of B trials (A/B), the ‘odds for’ are A to (B-A) and the ‘odds against’ are (B-A) to A

 

LOS 8d

Unconditional probability (marginal probability)  is the probability of an event occurring; conditional probability, P(A|B), is the probability of an event (A) occurring given that another event (B) has occurred.

 

LOS 8e

The joint probability of 2 events, P(A|B), is the probability that they will both occur.

P(A|B), is the probability of an event (A) occurring given that another event (B) has occurred.

 

The probability that at least one of two events will occur is P(A or B) = P(A) + P(B) – P(AB).
For a mutually exclusive evens, P(A or B) = P(A) + P(B), since P(AB) = 0

 

The joint probability of any number of independent events is the product of their individual probabilities.

 

LOS 8f

The probability of an independent event if unaffected by the occurrence of other events, but the probability of a dependent event is changed by the occurrence of another event.

LOS 8g

Using the total probability rule, the unconditional probability of A is the probability weighted  sum of the conditional probabilities:

 

LOS 8h

Conditional expectations are used in investments to update expectations when a conditioning event has occurred.

 

LOS 8i

A tree diagram shows the probabilities of 2 events and the conditional probabilities of 2 subsequent events

 

LOS 8j

Covariance measures the extent to which 2 random variables tend to be above and below their respective means for each joint realization.  It can be calculated as:

 

 

Correlation is a standardised measure of association between 2 random variables; it ranges in value from –1 to +1 and is equal to

 

Correlation coefficient = Cov A,B / (SD A x SD B)
= -7.2 / (2.450 x 3.098)
= -0.9486

 

LOS 8K

The expected value of a random variable, E(X) equals

 

The variance of a random variable Var(X) equals

 

Standard deviation

The expected returns and variance of a 2 asset portfolio are given by

 

LOS 8l

Given the joint probablities for Xi & Yi ie  P(XiYi) the covariance is calculated as

 

where Bi is a set of mutually exclusive and exhaustive events.

 

LOS 8h

Conditional expectations are used in investments to update expectations when a conditioning event has occurred.

 

LOS 8i

Bayes formula for updating probabilities based on the occurrence of an event O is:

 

LOS 8n

The number of ways to order n objects is n factorial n! = n x (n-1) x (n-2) x…. x1.

 

There are   ways to assign k different labels to N items, where nⁱ 

is the number of items with the label i  

 

The number of ways to choose a subset of size r from a set of size n when order doesnt matter is  

 

when order matters, there are   permutations.

 

Notes

The probability distribution of annual returns from investing in Company A is given below.

Return %  Probability

20              0.1

30              0.6

40              0.3

 

Press 2nd Data. Enter in the following:
X01: 20 Y01: 10
X02: 30 Y02: 60
X03: 40 Y03: 30
You are entering the probabilities as whole numbers in the 'Y'values e.g. a probability of 0.1 = 10% for Y01.
Now press 2nd STAT. Make sure you have 1-V on the screen.
(If it is not keep presssing, 2nd then ENTER until 1-V appears.)
Scroll down until you find the mean as 32% and the population standard deviation of 6%.

LOS 7a

Descriptive statistics summarize the characteristics of a data set; inferential statistics are used to make probabilistic statements about a population based on a sample.

 

A population includes all members of a specified group, while a sample is a subset of the population used to draw inferences about the population.

 

Nominal scale  -- data is put into categories that have no particular order

Ordinal scale – data is put into categories that can be ordered with respect to some characteristic.

Interval scale – differences in data values are meaningful, but ratios, such at twice as much or twice as large are not meaningful

Ratio scale --   ratios of values, such as twice as much or half as large are meaningful, and zero represents the complete absence of the characteristic being measured.

 

LOS 7b

Any measurable characteristic of a population is called a parameter.

A characteristic of a sample is given by a sample statistic.

An interval is a range of values.

A frequency distribution groups observations into classes or intervals.

 

LOS 7c

Relative frequency is the percentage of total observations falling within an interval; cumulative relative frequency for an interval is the sum of the relative frequencies for all values less than or equal to a given maximum value.

Relative frequency is found by dividing the frequency of the interval by the total number of frequencies

 

Histograms and frequency polygons are graphical tools used to illustrate frequency distributions.

 

LOS 7d

median – midpoint of dataset

mode – most frequent value

 

LOS 7e

Quantile is the general term for a value at or below which a stated proportion of the data in a distribution lies.  Examples of quantiles include:

 

1. Quartiles – distribution is divided into quarters
2. Quintile – distribution is divided into fifths
3. Decile – distribution is divided into tenths
4. Percentile – distribution is divided inot hundreths

 

LOS 7f

The range is the difference between the largest and smallest values in the dataset

Mean absolute deviation (MAD) is the average of the absolute values of the deviations from the arithmetic mean:

 

 

 

Standard deviation is the positive square root of the variance and is frequently used as a quantitative measure of risk.

 

LOS 7g

Chebyshev’s inequality states that the proportion of the observations within k standard deviations of the mean is at least 1-1/k² for all k > 1

 

LOS 7h

The coefficient of variation for sample data, is the ratio of the standard deviation of the sample to its mean (expected value of the underlying distribution)

 

The Sharpe ratio measures excess return per unit of risk

 

LOS 7i

Skewness describes the degree to which a distribution is not symmetric about its mean.

• A right skewed distribution has positive sample skewness and has a mean that is greater than its median that is greater than its mode
• A left skewed distribution has a negative skewness and has a mean that is less than its median that is less than its mode.
• Sample skew with an absolute value greater than .5 is considered significantly different from zero

LOS 7j

Kurtosis measures the peakedness of a distribution and the probability of extreme outcomes (thickness of tails)

• Excess kurtosis is measured realtive to a normal distribution, which has a kurtosis of 3.
• Positive values of excess kurtosis indicate a distribution that is leptokurtic (fat tails, more peaked) so that the probability of extreme outcomes is greater than the normal distribution.
• Negative values of excess kurtosis indicate a platykurtic distribution (thin tails, less peaked)
• Excess kurtosis with an absolute value greater that 1 is considered significant

LOS 6a

NPV – The NPV is the present value of a projects future cash flows, discounted at the firms cost of capital, less the projects cost.

NPV = PV of Cash Inflows - PV of Cash Outflows

IRR – Internal rate of return is the discount rate that makes the NPV == 0 (equates the PV of the expected future cash flows to the projects initial cost)

The NPV rule is to accept a project if NPV > 0; the IRR rule is to accept a project if IRR > required rate of return.

For an independent (single) project, these rules produce the exact same decision.

 

For mutually exclusive projects, IRR rankings and NPV rankings may differ due to differences in project size or in the timing of the cash flows.  Choose the project with the higher NPV as long as it is positive.

 

A project may have multiple IRRs or no IRR.

 

The IRR method assumes all cashflows from the project are reinvested at the IRR        

 

LOS 6b

HPR

– Holding Period Return is the  % change in the value of an investment over the period it is held.

The holding period return (or yield) is calculated as:

 

 

HPY

– Holding period yield is the actual return an investor will receive if the money market instrument is held until maturity

LOS 6c

The money weighted rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the PV of cash inflows equal to the PV of cash outflows.

 

Time weighted rate of return – is calculated from the accounts periodic holding period returns and is the preferred performance measure.

LOS 6d

 

BDY -

– Bank Discount Yield is the % discount from face value, annualized by multiplying by 360/days to maturity

 

Bank discount yields are not true yields because they are based on a percentage of face (maturity) value instead of on the original amount invested.  They are annualized without compounding since the actual discount from face value is simply multiplied by the number of periods in a “year”.  The year used in 360 days.

EAY

– Effective annual yield is the annualized HPY on the basis of a 365 day year and incorporates the effects of compounding.  It converts a t-day holding period to a compound annual yield based on a 365 day year.

 

MMY

– Money market yield (or rMM) is the annualized yield that is based on price and a 360 day year and does not account for the effects of compounding – it assumes simple interest

 

 

           NB:// easy in relation to the above!

 

Examples

 

money weighted rate of return

 

Assume an investor purchases a share of stock for $50 at time t=0

and another share at $65 at time = t1

and at the end of year 1 and year 2, the stock paid a $2.00 dividend

Also at the end of year 2, the investor sold both shares for $70 each

 

1. [CF]2nd [CLR WORK]
2. 50 [+/-] [ENTER]
3. 63 [+/-] [ENTER]
4. 144 [+/-] [ENTER]
5. [IRR] [CPT]                      -------------- NB:// Watch your minus signs here or it wont work!

 

time weighted rate of return

HPR1 = (65+2)/50 – 1 = 34%

HPR2 = (140+4)/130 –1 = 10.77%

thus = [(1.34)()1.1077]^{.5 –}1 = 21.83%