SFM n AFM Formulae #pdf

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C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
Score 60+ thro’ SYSTEMATIC & SMART Study Page 1 of 35
S F M n A F M Formulae
Revised Edition Dt. 31.03.2016
P V Ram
B.Sc., ACA, ACMA Hyderabad
98481 85073
ram_pv@rocketmail.com
C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
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P R E F A C E
A Formula is a simple way of expressing information. These are usually used
in Science and Mathematics apart from commerce areas.
In Commerce, formulae are used in several areas like Interest and Annuity
calculations, Capital Budgeting, Portfolio Management, Standard Costing ,
Marginal Costing, PERT Analysis, Learning Curve effects etc. In commerce
areas, unlike Science and Mathematics, the derivations and proving of
formulae is of not much importance nor ever asked in examinations. What
is required is the awareness of the formula with all its components,
nomenclature and meanings of the terms used in it. More important thing i s,
the areas where formulae can be applied and the assumptions under which
they hold good is also required to be known.
When formulas are expressed in the form of equations they help in finding
the value of the unknown variable, given the rest of the variables an d the
result. This helps us in doing iterations and performing sensitivity an alysis
and “what if? ” analysis. Formulae can be used in spread sheet computations
also to express relationships and their inter linkages.
Formulae help in solving the problems in a faster and simple way. Fu rther,
we can devise shortcuts as well through which we can save lot of time and
laborious workings.
Very often, I come across with students saying that they have mugged up all
the formulae but yet not able to solve the problems in examination s. This is
something like that a person who knows all the alphabets from A to Z wants
to claim that he is an expert in English literature. It is not just sufficient to
know a formula. As said earlier, it is also required to know all its
components, their nomenclatures, the areas where they can be applied and
the more important thing is the underlying assumptions and limitat ions
under which it can be used. Students are required to be familiar with these
aspects to fully enjoy the luxury of formulas through which they can save
time and laborious workings. This can be achieved by following two things.
Firstly, you need to understand the theory of respective areas of the
formulae and secondly, solving several varieties of problems using the
formulae and practicing them. This principle holds good for mnemonics also.
In this case you must be able to write atleast few small sentences though
not a big paragraph by recollecting a single letter or word.
C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
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Students are suggested to study the theory of the subject well an
d
understand it fully. When formulas are come across they need to jot down
the formulae along with their nomenclature at a single place for quick
reference. They need to solve as many problems as possible. After doin g
this they can memorise the formulae. Further, if you start memorising
formulae after studying theory well and solving problems, it will be very easy
to understand, remember and apply them. In fact, in this method, some of
the formulae would have already got registered in your brain and do not
require the effort of memorising also.
Suggestions and Comments are welcome!
Thanks!
P V Ram
C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
Score 60+ thro’ SYSTEMATIC & SMART Study Page 4 of 35
S F M
n A F M Formulae
1. Capital Budgeting
TYPES OF CAPITAL BUDGETING PROPOSALS
If more than one proposal is under consideration, then these proposals can
be categorised as follows:
1.Mutually Exclusive Proposals : Two or more proposals are said to be
Mutually Exclusive Proposals when the acceptance of one proposal
implies the automatic rejection of other proposals, mutually exclusive to i t.
2.Complementary Proposals: Two or more proposals are said to be
Complementary Proposals when the acceptance of one proposal implies
the acceptance of other proposal complementary to it, rejection of one
implies rejection of all complementary proposals.
3.Independent Proposals: Two or more proposals are said to be
Independent Proposals when the acceptance/rejection of one proposal
does not affect the acceptance / rejection of other proposals.
Present Value (P V) = Annuity (A) / Cost of Capital (K)
O R
Annuity (A) = Present Value (P V) X Cost of Capital (K)
P V of Annuity recd. In Perpetuity = A / R
Where A is Annuity and R is rate of interest.
Discount rate inclusive of inflation is called Money Discount Rate and
discount rate exclusive of inflation is called Real Discount Rate.
Risk Adj. Disc. Rate (RADR): Risk free rate (R f)+ Risk Premium
O R
Risk Adj. Disc. Rate (RADR): Risk free rate (R
f)+
β X Risk Premium
Coefficient of Variation = �6340;
�= � �
�
C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
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The lower coefficient of Variation, the better it is.
Profitability Index (P I) = ��
�
� ��
�
O R
Profitability Index (P I) = ��
�
� ��
�� �
� �
Accept when P I > 1. The higher the better.
Pay Back Period = Ilgrg_j�Iltcqrkclr
Ells_j�G_qf�djmuq
Accept the Project with least Payback Period.
Discounted Payback period is calculated by the same formula as payback
period with the exception that discounted cashflows are considered instead
of actual cashflows
�� = � ∑m
‾
:
+ ~ ;
=
Where A‾t is the expected cashflow in period t and Rf is risk free rate of
interest.
Accept when NPV is +ve. The higher the better.
Project NPV is the one which is calculated for the whole Project. Equit y NPV
is the one which is calculated to know the return of equity holde rs. In this
case funds relating to equity holders alone are considered for computation.
I R R is the rate at which the present value cash inflows equal the present
value of cash outflows i.e. NPV is zero. For Project IRR all cashflows of the
project are considered and in case of Equity IRR only cashflows relating to
equity holders are considered. In case IRR is greater than interest rate on
loan, then, the excess rate will accrue to the benefit of equity holders.
Variance For one year period:
Variance = ∑Probability X (Given Value - Expected Value) 2
C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
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Standard Deviation = Variance
1/2
When Cashflows are independent, Standard Deviation is calculated by the
formula:
� =√
∑ �
:
+ ~ ;
=
Where, σ
r Standard deviation of possible net cashflows in period t.
When Cash flows are perfectly correlated over time:
�� = �∑ �
:
+ ~ ;
=
In case cashflows are moderately correlated over time: �� = √
∑
:�� − �� ‾;
=
�
In case if two or more projects have same mean cashflows, then, the project
with lesser standard deviation is preferred.
Certainty Equivalent approach: In this case certain cashflows are
discounted instead of all project cashflows.
Joint probability: Joint Probability is the product of two or more than two
dependent probabilities. Sum of Joint Probabilities will always be equ al to 1.
Conditional Event: If A & B are two events, then, if event B occurs after
occurrence of event A, it is called conditional event and is denoted as (B /A)
Conditional Probability: If A & B are 2 events of a sample, then the
probability of B after the occurrence of event A is called conditio nal
Probability of B given A and is denoted as P(B/A).
P(B/A) = P:E�∩�F;
P:E;
⇨ � �(�� ∩ �� )= � (� )����:�/�;�
Notation of Events: Event A or Event B Occurs A U B
Event A & Event B Occur �� ∩ ��
C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
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Neither A Nor B Occur (A U B)
c
= A c
∩ B c
= A‾ ∩ B‾
A Occurs but B does not Occur �� ∩ ��c
= A / B
2. Leasing
Evaluation of lease for Lessee: In this case comparison is to be made
between the NPV of outflows: a. in case an asset is leased and used, or
b. the asset is bought and used.
BELR in case of lessee is the amount at which he will be indifferen t between
buying an asset and leasing an asset.
Evaluation of lease for Lessor: In this case comparison of P V of
cashflows is to be made between: a. buying an asset and leasing it getting lease income or
b. return expected by investing the funds elsewhere.
BELR for lessor is the amount at which he will be indifferent betwee n buying
the asset and giving it for lease and / or investing the funds elsewh ere and
earning desired cost of capital. Equated yearly Installment = Loan amount / Cumulative Annuity
Factor of desired period
While ascertaining Present Values, people are using different rates for
discounting like interest rate, net of tax interest rate, cost of capital etc.
based on respective views. Ideal one will be the one using net of tax
interest rate in case of borrowing or using the cost of capital in case o f using
own funds. 3. Dividends
Rate of Dividend = Hgtgbclb�
Pcp�Sf_pc�
J_ac�V_jsc� Pcp�Sf_pc
��srr
Dividend Yield = Hgtgbclb�
Pcp�Sf_pc�
M_picr�Ppgac� Pcp�Sf_pc
��srr
Dividend Payout = Hgtgbclb�
Pcp�Sf_pc�
I_plgleq� Pcp�Sf_pc
��srr
Equity dividends are to be paid after paying preference dividends.
C A & C M A Coaching Centre, Nallakunta, Hyderabad. P V Ram, B. Sc., ACA, ACMA – 98481 85073
Score 60+ thro’ SYSTEMATIC & SMART Study Page 8 of 35
Traditional Theory:
= �:

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