This document has everything that you need to know to pass your CISI Corporate Finance Technical Foundations Exam, which a lot of bankers have to take at the start of their finance careers.
It includes all the key regulatory rules, ratios and formulas as well as additional notes based on the qu...
Quantitative Methods for Corporate Finance
Random sampling: A random sample should ensure that every member of the population
has an equal chance of selection, and therefore the selection process is free from any bias.
This may not lead to a sample that is the most representative of the population, as the
sample may not cover the full range of the population.
Non-random samples may use techniques to create a more representative sample
(compared to a random sample).
Diversification (reducing portfolio risk): A portfolio with many different types of investment
is less risky than portfolio with only one type.
Total portfolio risk is measured by the variance of the portfolio which is due to both
systematic risk and specific risk where systematic risk is correlated to the market while
specific risk is variance which is independent of market, such as poor company performance.
Diversification diversifies away the specific risk. The systematic risk is not diversifiable and is
also known as β risk
Time value of money: The value of a pound today is worth more than the value of a pound
tomorrow. This is because money today you could invest and earn interest.
TVN
PV =
( 1+ r )N
Risk/Reward trade off: To earn a higher return on an investment, you have to accept a higher
level of risk. Required return on investments = risk free rate + risk premium. This infers that
investors are risk averse in nature.
Risk and Return on Investments:
A gilt is a UK government bond which represents the
risk free rate as you assume there is zero default risk.
Corporate bonds include investment grade bonds (AAA
-> BBB) and high yield bonds (BB -> D)
Investment grade bonds are often known as the senior
bonds while the high yield bonds are known as the
junior bonds.
Preference shares are paid ahead of ordinary shares,
which are the last to be paid.
Something even riskier than ordinary shares could be
warrants.
Holding Period Return Formula:
Val END −Val START +Cash flows
HPR=
Val START
Va l END −Va l START represents capital gain or loss
To make the HRR more comparable we can use a formula that annualise returns:
( 1+ HPR )n
Measuring Average Return:
,Arithmetic mean (central tendency): x=
∑x
n
x typically means that it is the sample mean
Greek letters is used for population data, and roman letters used for sample data.
Historic vs. expected returns
Historic: Known and may not repeat themselves
Historic returns are a better indicator of the expected returns of an asset class than it is of a
specific asset
Expected: Effects the period of investment but estimated and may not occur. Expected mean
you weight the probabilities.
Measuring risk: Risk: the risk that an investment’s future actual return will differ from an
expected return
Measures of dispersion: Variance and standard deviation
The mean of the squared differences
Calculated by using the squared deviations of each value { ( x−μ )2 ¿ from the
arithmetic mean
2 ∑ ( x −μ )
2
Population variance: σ =
n
2 ∑ ~
( x− x )2
Sample variance: s = – smaller samples will be more adjusted by the
n−1
adjustment on the denominator, without which you might have a biased estimator.
This helps to address the biasedness.
Example: Consider the following investment returns for five fund managers:
30 % , 12 % , 25 % , 20 % ,23 %
Calculate the variance and sample variance of returns:
X x (x−x ) ( x−x )2
30 22 8 64
12 22 -10 100
25 22 3 9
20 22 -2 4
23 22 1 1
rd
The sum of the differences (in the 3 column) will always sum to zero.
Fourth column sums to 178
178 178
So variance: =35.6 Sample variance: =44.5
5 4
Standard deviation: Population standard deviation (square root of the population variance):
σ=
√ ∑ ( x −μ )2
n
Sample standard deviation (square root of the sample variance):
s=
√ ∑ ( x−x )2
n−1
, Correlation and Covariance: Correlation: measures how two assets returns may be related
Combining assets which are not perfectly positively correlated allows diversification.
Positive correlation is where two variables move in the same direction while negative
correlation (r=-1) is where two variables move in opposite directions. Perfect correlation is
where two variables move at the same rate (r = +1).
Maximum diversification occurs at r = -1 but the risk return trade off is best at 0.
∑ X∑Y
∑ XY − n
CORR ( X , Y )=
√( (∑ X )
)(∑ (∑ Y )
)
2 2
∑X −
2
n
2
Y −
n
Covariance measures the variance/relationship between the returns
on two different investments
cov ( x , y )=
∑ ( x−μ ) ( y−μ)
n
Negative covariance tells us the two assets move in opposite
directions
Covariance can also be calculated from correlation:
Cov ( x , y )=S D x +S D y × CORR( x , y )
Exam trick: The covariance is always going to be less than the product of the two standard
deviations.
TV
DCF, NPV and IRR: For single cash flows: PV =
( 1+ r )n
NPV = P V inflows−P V outflows
Interpretation: NPV ≥ 0then accept the project
Positive NPV increases shareholder value
For mutually exclusive projects accept the project with highest NPV.
If the market agrees, the market cap of the company should go up by the NPV of a project
upon announcement as it directly enhances equity value
Internal Rate of Return (No calculation on this): Definition: Given a set of cash flows and an
NPV, the IRR is the rate of return that, when used to discount the cash flows, leaves the NPV
equal to zero.
Interpretation of IRR: Discount rate where NPV = 0. If IRR > required rate then accept project
(NPV > 0). If IRR < required rate then reject project (NPV < 0).
But IRR makes no comment on the size of cash flows, so cannot be used for comparison. It
can be used project by project however, not used for ranking.
Example: A three-year investment opportunity has an initial cost of £200,000 and is
expected to generate cash flows of £80,000, £100,000 and £100,000 during this time. What
is the IRR?
Do trial and error to see what which value gets you closest to NPV = 0.
Financial Statements Analysis: Basic Principles:
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