 # CA Final n CMA Final

SFM n AFM Formulae #pdf on 01 April 2016

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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 Score 60+ thro’ SYSTEMATIC & SMART Study Page 2 of 35 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 Score 60+ thro’ SYSTEMATIC & SMART Study Page 3 of 35 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 Score 60+ thro’ SYSTEMATIC & SMART Study Page 5 of 35 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 = I l g r g _ j�I l t c q r k c l r E l l s _ j� G _ q f� d j m u q 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 Score 60+ thro’ SYSTEMATIC & SMART Study Page 6 of 35 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 Score 60+ thro’ SYSTEMATIC & SMART Study Page 7 of 35 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 = H g t g b c l b� P c p�S f _ p c� J _ a c�V _ j s c� P c p�S f _ p c ��srr Dividend Yield = H g t g b c l b� P c p�S f _ p c� M _ p i c r�P p g a c� P c p�S f _ p c ��srr Dividend Payout = H g t g b c l b� P c p�S f _ p c� I _ p l g l e q� P c p�S f _ p c ��srr 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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