cima - notes

7/28/2019 Cima - Notes

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C01 - Fundamentals of Management Accounting

C02 - Fundamentals of Financial Accounting



C03 - Fundamentals of Business Mathematics

Percent Change Formula 'Change'/Original Value * 100

i.e. (X₂-X₁/X₁) x100%

The Equation of a Straight Line y = a + bX

Where:

A = the intercept on the y axis

b = the slope (gradient) of the line

i.e. b = change in y (y2-y1)/change in x (x2-x1)

Histogram with unequalintervals (adjustment factor)

Adjustment factor = Standard class width/current class width

Coefficient of Variation = Standard Deviation/Mean

The bigger the coefficient of variation, the wider the spread of data.

Fixed base index formula = (value in given year/value in base year) *100

Chain base index formula = (this year's value/last year's value) *100

Deflated/inflated cash flow = actual cash flow in given year * (index number for base

year/index number for given year

Probability of achieving thedesired result

= number of ways of achieving desired result/total number of

possible outcomes

e.g.) probability of rolling a 3 on a normal die = 1/6

Expected Value formula (EV) = ΣnpWhere:

n=outcome

p=probability of outcome occurring

i.e. - a weighted average of probabilities

Simple interest formula S=X+nrX

Where:

X=the original sum invested

r=the interest rate (as a proportion - e.g. 0.05=5%)

n=the number of periods

S=the sum invested after n periods (capital + interest)

e.g.) invest $1000 @ 10% simple interest for 5 years =

1000+(50.101000) = $1500

Compound interest formulawith changing rates

S = X(1+r ₁)^y(1+r²)^n-y

Where:

r ₁ = the initial rate of interest

y = the number of years in which the interest rate r ₁ applies

r² = the next rate of interestn-y = the numbers of (remaining) years in which r² applies



Effective annual rate of interestformula

(1+R)=(1+r)^n

Where:

R=the effective annual rate

r=the period rate

n=the number of periodsThe sum of a GeometricProgression

aka - the terminal value of an investment to which equal annual

amounts will be added

S = [A(R^n -1)]/R-1

Where:

S = the terminal value

A = the first term

R = the common ratio

n = the number of terms

Discounting Formula X = S*[1/(1+r)^n]Where:

S = the sum to be received after n time periods

X = the present value of that sum

r = the rate of return (as a proportion)

n = the number of time periods

r - rate - is sometimes called cost of capital

Internal Rate of Return

IRR=₁ + [(NPV₁/NPV₁-NPV₂)(₂-₁)]%Where:

₁=one interest rate ₂=the otherNPV₁=the NPV at rate ₁

NPV₂=the NPV at rate ₂

(NPV = Net Present Value)

Given a result, how do you find the number from which a percentage has been added toachieve it?



eg) of what number is 16 a 25% increase?

divide the result by 1+the increase proportion

eg) X=16/(1+0.25) = 12.8 ∴16 is a 25% increase over 12.8

Given a result, how do you find the number from which a percentage has been deductedto achieve it? eg) of what number is 16 a 25% decrease?

divide the result by 1-the decrease proportion eg) X=16/(1-0.25)=21.33 ∴16 is a 25% decrease of 21.33

How do you decrease a number by a given percentage?

eg) decrease 16 by 25%

multiply the number by 1-the decrease proportion eg) 16(1-0.25) = 160.75 = 12 ∴12 is a 25% decrease of 16

How do you increase a number by a given percentage? eg) increase 16 by 25%

multiply the number by 1+the increase proportion eg) 16(1+0.25) = 161.25 = 20 ∴20 is a 25% increase over 16



Powers:(1½)^x can also be expressed how?

(3/2)^x

or3^x/2^x(i.e - raising a fraction to a power raises both the numerator and denominator of that

fraction to that power)

Powers:2^-x can also be expressed how?

1/2^x(i.e. raising a number to a negative power is the same as taking 1/the number to the

positive expression of that power)

Powers:1^x can also be expressed how?

Simply 11 raised to any power is 1(i.e. 111*... still equals 1)

Powers:X¹ can also be expressed how?

Simply Xany number raised to the power of 1 is that number

Powers:X⁰ can also be expressed how?

Simply 1any number raised to the power of 0 is 1



Powers:(2^x)^y can also be expressed how?

2^(x*y) or 2^xywhen you raise a number with an exponent to any power, you multiply the exponents.eg) (2³)² = 2⁶

Powers:2⁵/2² = ?

2⁵⁻² = 2³ = 8when you divide two numbers with exponents, you subtract the exponents one from the

other.

Powers:2⁵*2² =?

2⁵⁺² = 2⁷

when you multiply two numbers with exponents, you add the exponents one to theother.

How do you find what one number is as a percentage of another? eg) what is 18 as a percentage of 45

divide the number in question by the total - or number from which you're taking thepercentage. eg) 18/45 = 0.4 = 40% ∴18 is 40% of 45

Quadratic Equation

an equation in the format:



0.15*360 = 54 degrees

Excel:What are the arguments in the FREQUENCY function?

=FREQUENCY(DATARANGE,BIN)Where:DATARANGE is the set of data - eg) B3:D7

BIN is the range used for the X axis - the group limits lain out vertically - eg) E3:E10would be 0, 10, 20, etc.

When using this function, the result is a vertical array, so the cells below it should beempty - you must hold down CTRL and SHIFT as you press enter for it to populate thearray.

Advantages of using the Mean as a measure of tendency

Easy to calculate

Widely understoodRepresentative of the whole data setSuited to further statistical analysis

Disadvantages of using the Mean as a measure of tendency

Value may not correspond to an actual value - eg) 2.3 children per household.Results are distorted by extreme values

Advantages of using the Mode as a measure of tendency

Easy to findNot influenced by extremesCan be used for non-numerical dataCan be the value of an actual item in data set



Disadvantages of using the Mode as a measure of tendency

May not be representative

Does not take all values into accountThere can be more than one in a datasetInstability as a measure

Advantages of using the Median as a measure of tendency

Easy to understandUnaffected by extremes

Can be the value of an actual item in data set

Disadvantages of using the Median as a measure of tendency

Does not reflect the full range of valuesUnsuitable for further statistical analysisCan be tedious to find

Finding Midpoints of Grouped Data

Discrete variables - it's a whole number in the middle of the set - eg) the midpoint for5<10 is 7. Continuous variables - it can be a ".5" - eg) the midpoint for 5<10 is 7.5.

Quartile Deviation

AKA Semi-interquartile range=(Q₃-Q₁)/2Where:Q₁ = the value BELOW which 25% of the population fallQ₃ = the value ABOVE which 25% of the population fall



MEAN - MEDIAN - MODE Mode value is higher than the median

Mean value is lower than median

Excel:Functions of variance

=MIN(DATA) - minimum of the dataset=MAX(DATA) - maximum of the dataset=STDEV(DATA) - finds the standard deviation of the dataset

=VAR(DATA) - calculates the variance of the dataset

Standard Deviation (σ)

=the square root of the variance=the most common/important measure of spread

Formula given on the assessment - for grouped data, use the Σf version, for ungroupeddata use the standard 'n' version.

Index Relatives

= name given to the index number which measures the change in a single distinctcommodity.

Formulae are given on the assessment - just remember that P ₀ or Q₀ are the index baseyear value and P₁ or Q₁ are the values for the year in question.

Index Relatives:Fixed Base vs. Chain Base Methods

Fix base method = for commodities in which the basic nature is unchanged over time:

=(value in given year/value in base year)*100



Chain base method = for commodities where the basic nature changes over time:=(this year's value/last year's value)*100

Splicing an Index (definition)

aka - rebasing - redefining the base year of an index creates a situation where the P₁ value would be <100 eg) if P₁ were for 1993 and P₀ were 2000 and there was inflation in the commodity priceyou might see the index relative for 1993 (P₁) at 97, etc.

Rebase to a Previous Index

=(Value in current index/100)*value of rebase year in previous indexeg)

- in 2006, a commodity had an index score of 111 based on the rebased value in 2001- the value in 2001 of the commodity was 132 in the old index (now 100, since it is the

new base year)

-to express 2006 in terms of the previous index base:=(111/100) *132 = 146.52

General "Or" Probability

General Addition: not mutually exclusive

P(A or B) = P(A)+P(B)-P(A and B)i.e. - you add the probability of each, but subtract those that would be double-counted. e.g. probability of pulling either an Ace or a Spade from a normal deck = P(Ace)[4/52] +P(Spade)[13/52] - P(Ace of Spades)[1/52] = 16/52

Simple "Or" Probability

Simple Addition: mutually exclusive outcomes:



P(A) + P(B) e.g. if delivery will take up to 5 weeks, we can calculate the probability of it taking 3 or 4weeks by adding the probability that it'll take 3 weesk with the probability of it taking 4

weeks (it can't take both, so we don't have to account for double counting)

Simple "And" Probability

Simple Multiplication: not mutually exclusive outcomes P(A and B)=P(A)P(B)

e.g - rolling a die and flipping a coin - they are unrelated, so we multiply the P of rollinga given number on the die (1/6) by the P of getting a desired result on the coin (1/2)∴1/6*1/2=1/12

Probability of Complementary Outcomes (formula)

P(Abar)=1-P(A)

Where Abar is not A Certainty = 1. Probability of something other than the desired outcome is 1-probabilityof desired outcome.

General "And" Probability

General Multiplication: conditional outcomesP(A and B)=P(B)*P(A/B) eg- if sales don't improve, there's a 70% chance we'll go under - P(A). There's a 20%chance that sales will improve - P(B). What's the probability of us going under? (PBdoes not depend on PA, but PA depends on PB) ∴ P(B)P(A/B)=0.80.7=0.56 - there's a56% chance of us going under.

Sinking Fund (definition)



An investment into which equal annual installments are paid in order to earn interest,so that by the end of a given number of years, the investment is large enough to pay off a known commitment at that time.

-calculated using Geometric Progression Formula

Loan Repayment (amount calculation/procedure)

1) Calculate the loan value using the compound interest formula: eg) 50,000 @8% for 5years = 50,000(1.08)⁵ =$73466.402) Use that value in a Geometric Progression to calculate the annual repayment: eg)

73,466.40= A(1.08⁵-1)/.08 = A(5.866600%) ∴ A=73,466.40/5.8660096 = $12,522.82

annual repayment

Effective Annual Rate of Interest (formula)

aka - APR or Compound Annual Rate (CAR):(1+R) = (1+r)^nWhere: R=effective annual rate/APR/CAR

r=the periodic rate (monthly, semi-annually, etc.)n=the number of periods

eg) 1.5% compounded monthly: (1+R)=(1.015)¹² = 1.1956 ∴ R=1.1956-1=.1956... 19.56%APR

Nominal Rate vs. Effective Rate

Nominal Rate = interest rate expressed (not calculated) as a p.a. figure. eg) a bank mayoffer 10%p.a. payable half-yearly. 10% is the nominal rate. Effective rate would be 5% every six months∴ (1+R)=(1+.05)²= 10.25% APR

Limitations of Expected Values

Not appropriate for one-off decisions



Probabilities are estimates/forecasts Does not take into account attitude toward risk

Present Value

= the amount of money that must be invested now for n years at r rate to earn a futuresum-calculated using the discounting formula X=S*[1/(1+r)^n]or-using PV tables provided on the assessment to determine the discount factor

Net Present Value (NPV)

= a calculation of the PVs of cash flows related to an investment at a given cost of capital (interest rate) for a given period of time.- if NPV is positive, it beats the cost of capital- can be used to evaluate a single project or compare different projects

Limitations of using NPV method

a) Future rates can only be estimatesb) Future cashflows are also estimatesc) NPV assumes that all cash flows occur at the end of the year; which is likely to give

rise to inaccurate values.

Internal Rate of Return (IRR) (definition)

= an approximation of the rate of return on an investment. You start by calculating twoNPVs at two interest rates, ideally one one with a positive NPV and the other negative.You can estimate where the NPV might be close to 0 by using 2/3*(profit/cost of project).

Excel:



IRR function arguments

=IRR(Cash movements, guess)Cash movements should include the initial investment and the guess can really be

anything...

Excel:NPV function arguments

=NPV(cost of capital, cash inflows)-initial investment - be careful - if the spreadsheet already expresses the initial investment as a negative #,

you should change the formula to ...+initial investment

Excel:ROI function arguments

=Average(cash inflows)/initial investment

- again be mindful of the sign on initial investment if using a reference to a cell - theformula assumes the initial investment is expressed as a positive #

Pearson's 'r' is also known as

Product Moment Correlation Coefficient -formula is given in assessment

-shows the degree to which two variables are correlated on a scale of -1 to 10=unrelated

Coefficient of Determination

Simply r²



if r=0.9 we can say the two variables are well correlated. r²=0.81 - so we can say that81% of the variation can be explained by one variable's effect on the other (19% notexplained).

-careful - correlation≠cause

Spearman's 'R'

=The correlation between rank-ordered variables -formula given in the assessment, but remember that d² refers to the square of thedifference in the two expressions of rank in absolute terms:

eg) Judge P gives a rank of 1 while Judge Q gives a rank of 3... d=2 (not -2) and d²=4

"Ties" in rank when calculating 'R'

When 2 or more items tie in rank order, assign all the rank of the average of ranks:

eg) 3 people tie for 5th place. Each will be assigned the average of 5,6&7 = 18/3=6 eg) 2 people tie for 1st place. Each will be assigned the average of 1 & 2 = 1.5

Scattergraph Method for estimating best fit

Draw the line that defines the series (equal number of points above and below the line).Where the line crosses the Y (vertical) axis = 'a' in the equation of a straight line(Y=a=bX). i.e.) you can then find 'b' using any two coordinates for X&Y

Least Squares Method for linear regression analysis

Linear Regression formula is given in the assessment. What's important is that you firstfind 'b' and then use 'b' to calculate the value of 'a' and define your equation.



Excel:Least Squares regression formula

=FORECAST(X,Known Y's, known X's)

in a standard sheet you might use this in cell C2:=FORECAST(A2,$B$2:$B:$6,$A$2:$A$6)and drag the formula down

Use F4 to make cell references absolute

4 Components of a time series

1) Trend (long-term)2) Seasonal Variations (short-term fluctuations)3) Cyclical Variations (medium-term)4) Random Variations

Moving Average

A method for removing seasonal variations from a dataset in order to better describethe trend. In an odd # of periods, you'll "assign" the average to the midpoint of the series. In an even # of periods, you'll do a moving average of the moving average to "assign"averages to actual periods.

Additive Model of Seasonal Variation

=finding the differences between the Trend (T) and the actual values (Y):1) use moving averages to define the trend (T)2) use Y=T+S+R ∴ Y-T=S+R to find 'S'3) find the average of the variations (S) for each period4) the sum of these averages should = 0. Take what it actually equals and split among

periods

5) round the variations as appropriate



Multiplicative Model of Seasonal Variation

aka - the Proportional Model- as Y=TSR - assuming R is negligible, S=Y÷T- use the same process as additive model, but use Y/T rather than Y-T- in the summary, the averages should average to 1 (i.e. sum to n or # of periods) - take

any random bits and distribute across your periods

Deseasonalised (Seasonally Adjusted) Data

When given Seasonally Adjusted data, you can reverse the process to obtain the originalamounts: -Additive Model - subtract positive and add negative seasonal variations from the actualamounts -Multiplicative Model - divide actual results by the seasonal variation factors

Residuals

= The differences between the results that would have been predicted using a trend lineand seasonal adjustments and the actual values. eg)Trend line predicts 96.1Seasonal Adjustment 1.0Forecast = 97.1Actual = 98

∴ the residual is 0.9

Limitations of Forecasting Models

-All forecasts are subject to errora) Further into the future = less reliable

b) Less data upon which forecast is modeled = less reliablec) Past results do not always indicate future performance



d) Random variations can upset the patterne) Extrapolation of the trend line requires judgement which can introduce error

Rules for manipulating inequalities:

1) Adding or subtracting the same quantity from both sides leaves the inequalityunchanged

2) Multiplying or dividing both sides by a Positive number leaves the inequalityunchanged

3) Multiplying or dividing both sides by a NEGATIVE number REVERSES theinequality.

Characteristics of good data

It is error free. It is available at the right time. It is available at the right place.

It is available to the appropriate individuals.

Sampling Error

Can not be avoided unless the data collected represents the entire population. Can be reduced with a larger sample size and by ensuring that the sample isrepresentative of the population and unbiased.

Probability Sampling Methods

-Simple Random - use a frame and randomly choose-Stratified Random - stratify population into cohorts and select at random from each-Cluster - randomly select a cluster of folks (e.g. folks living on a given block if the city

were the population)-Systematic - taking every 'n'th member of the pop.



-Quota - NON RANDOM stratified sampling - no frame-Multistage - breaking the population into successively smaller groups before selecting

your sample e.g.) break down the country into regions, then districts, then randomlyselect a sample

How do you get a √ or ∛ etc. in Excel

You'll use "to the power" of the reciprocal.

eg) to get √4, you'd use 4^(1/2), to get the ∛4, you'd use 4^(1/3).

Solve: 6.1/Y=4.9/10-Y

Cross Multiply to get:6.1(10-Y)=4.9Y(6.1*10)-6.1Y=4.9Y61=11YY=5.55

Finding the Midpoint

Discrete Data = odd n - the middle number, even n - (n+1)/2 Continuous Data = (Top + Bottom)/2

Excel:Function to get Pearson's 'r'

=CORREL(Dataset1,Dataset2)

C04 - Fundamentals of Business Economics



C05 - Fundamentals of Ethics, Corporate

Term Definition

IntegrityBeing straightforward, honest and truthful in all professional and

business relationships. You should not be associated with any

information that you believe contains a materially false or misleading

statement, or which is misleading by omission.

Objectivity Not allowing bias, conflict of interest or the influence of other peopleto override your professional judgement.



Professional competenceand due care

An ongoing commitment to your level of professional knowledge and

skill. Base this on current developments in practice, legislation and

techniques. Those working under your authority must also have the

appropriate training and supervision.

ConfidentialityYou should not disclose professional information unless you have

specific permission or a legal or professional duty to do so.

Professional behaviourComply with relevant laws and regulations. You must also avoid any

action that could negatively affect the reputation of the profession.

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