**1** FM Notes for Final students on Mon 25 Jan 2010 - 17:34

#### bhomiavarun

CSoC Smart User

FINANCIAL MANAGEMENT

Cash and fund flow statement

Rules for preparing schedule of changes in working capital :-

Increase in a current asset, results in increase in working capital – so Add

Decrease in current asset, results in decrease in working capital – so Decrease

Increase in current liability, results in decrease in working capital – so Decrease

Decrease in current liability results in increase in working capital – so Add

Funds from operations – Format

Particulars Rs. Rs.

Net profit ***

Add : Depreciation

Goodwill written off

Preliminary Exp. Written off

Discount on share written off

Transfer to General Reserve

Provision for Taxation

Provision for Dividend

Loss on sale of asset

Loss on revaluation of asset ***

***

***

***

***

***

***

***

***

***

***

Less : Profit on sale of asset

Profit on Revaluation of asset ***

***

***

Fund flow statement ***

Fund flow statement

Particulars Rs.

Sources of funds : -

Issue of shares

Issue of Debentures

Long term borrowings

Sale of fixed assets

Operating profit ***

***

***

***

***

***

Total Sources ***

Application of funds : -

Redumption of Redeemable preference shares

Redumption of Debentures

Payment of other long term loans

Purchase of Fixed assets

Operating Loss

Payment of dividends, tax etc ***

***

***

***

***

***

***

Total Uses ***

Net Increase / Decrease in working capital

(Total sources – Total uses)

***

Cash flow statement

Cash From Operation : -

= Net profit + Decrease in Current Asset

+ Increase in Current Liability

- Increase in Current Asset

- Decrease in Current Liability

Cash flow statement

Sources Rs. Application Rs.

Opening cash and bank balance

Issue of shares

Raising of long term loans

Sales of fixed assets

Short term Borrowings

Cash Inflow

Closing Bank O/D **

**

**

**

**

**

**

Opening Bank O/D

Redumption of Preference Shares

Redumption of Long term loans

Purchase of fixed assets

Decrease in Deferred payment Liability

Cash Outflow

Tax paid

Dividend paid

Decrease in Unsecured loans, Deposits

Closing cash and bank balance **

**

**

**

**

**

**

**

**

**

** **

Ratio Analysis

A) Cash Position Ratio : -

1) Absolute Cash Ratio = Cash Reservoir

Current Liabilities

2) Cash Position to Total asset Ratio = Cash Reservoir * 100

(Measure liquid layer of assets) Total Assets

3) Interval measure = Cash Reservoir

(ability of cash reservoir to meet cash expenses) Average daily cash expenses

( Answer in days)

Notes : -

• Cash Reservoir = Cash in hand + Bank + Marketable Non trade investment at market value.

• Current liabilities = Creditors + Bills Payable + Outstanding Expenses + Provision for tax (Net of advance tax) + Proposed dividend + Other provisions.

• Total assets = Total in asset side – Miscellaneous expenses – Preliminary expenses + Any increase in value of marketable non trading Investments.

• Average cash expenses =Total expenses in debit side of P & L a/c – Non cash item such as depreciation, goodwill, preliminary expenses written off, loss on sale of investments, fixed assets written off + advance tax (Ignore provision for tax) . The net amount is divided by 365 to arrive average expenses.

Remarks : - In Comparison

• When absolute cash ratio is lower then current liability is higher

• When cash position to Total Asset ratio is lower then the total asset is relatively higher.

• When cash interval is lower the company maintain low cash position. It is not good to maintain too low cash position or too high cash position.

B) Liquidity Ratio : -

1) Current ratio = Current asset

Current Liability

2) Quick ratio or Acid Test ratio = Quick Asset

Quick liability

Notes : -

• Quick Asset = Current Asset – Stock

• Quick Liability = Current liability – Cash credit, Bank borrowings, OD and other Short term Borrowings.

• Secured loan is a current liability and also come under cash credit

• Sundry debtors considered doubtful should not be taken as quick asset.

• Creditors for capital WIP is to be excluded from current liability.

• Current asset can include only marketable securities.

• Loans to employees in asset side are long term in nature and are not part of current assets.

• Provision for gratuity is not a current liability.

• Gratuity fund investment is not a part of marketable securities.

• Trade investments are not part of marketable securities.

Remarks : -

• Higher the current ratios better the liquidity position.

C) Capital structure ratios : -

1) Debt equity ratio = Debt = External Equity

(or) Leverage ratio Equity Internal Equity

= Long term debt = Share holders fund

Long term fund Long term fund

2) Proprietary ratio = Proprietary fund

Total Assets

3) Total Liability to Net worth ratio = Total Liabilities

Net worth

4) Capital gearing ratio = Preference share capital + Debt

Equity – Preference share capital

Notes : -

• Share holders fund (or) Equity (or) Proprietary fund (or) Owners fund (or) Net worth = Equity share + Preference share + Reserves and surplus – P & L a/c – Preliminary Expenses.

• Debt (or) Long term liability (or) Long term loan fund = Secured loan (excluding cash credit) + unsecured loan + Debentures.

• Total asset = Total assets as per Balance sheet – Preliminary expenses.

• Total liability = Long term liability + Current liability (or) short term liability

• Long term fund = Total asset – Current liability = Share holders fund + long term loan fund.

Remarks : -

• In debt equity ratio higher the debt fund used in capital structure, greater is the risk.

• In debt equity ratio, operates favorable when if rate of interest is lower than the return on capital employed.

• In total liability to Net worth Ratio = Lower the ratio, better is solvency position of business, Higher the ratio lower is its solvency position.

• If debt equity ratio is comparatively higher then the financial strength is better.

D) Profitability Ratio : -

1) Gross Profit Ratio = Gross Profit * 100

Sales

2) Net Profit Ratio = Net Profit * 100

Sales

3) Operating Profit ratio = Operating profit * 100

Sales

4) Return to shareholders = Net profit after interest and tax

Share holders fund

5) Return on Net Worth = Return on Net worth * 100

Net worth

6) Return on capital employed (or) Return on investment = Return (EBIT)

Capital Employed

7) Expenses Ratios :-

a) Direct expenses Ratios : -

i) Raw material consumed * 100

Sales

ii) Wages * 100

Sales

iii) Production Expenses * 100

Sales

b) Indirect expenses Ratios : -

i) Administrative Expenses * 100

Sales

ii) Selling Expenses * 100

Sales

iii) Distribution Expenses * 100

Sales

iv) Finance Charge * 100

Sales

Notes : -

• In the above the term “term” is used for business engaged in sale of goods, for other enterprises the word “revenue” can be used.

• Gross profit = Sales – Cost of goods sold

• Operating profit = Sales – Cost of sales

= Profit after operating expenses but before Interest and tax.

• Operating Expenses = Administration Expenses + Selling and distribution expenses, Interest on short term loans etc.

• Return = Earning before Interest and Tax

= Operating profit

= Net profit + Non operating expenses – Non operating Income

• Capital employed = Share holders fund + Long term borrowings

= Fixed assets + Working capital

• If opening and closing balance is given then average capital employed can be substituted in case of capital employed which is

Opening capital employed + Closing capital employed

2

E) Debt service coverage ratios = Profit available for debt servicing

Loan Installments + Interest

Notes : -

• Profit available for debt servicing = Net profit after tax provision + Depreciation + Other non cash charges + Interest on debt.

Remarks : -

• Higher the debt servicing ratio is an indicator of better credit rating of the company.

• It is an indicator of the ability of a business enterprise to pay off current installments and interest out of profits.

F) Turnover Ratios: -

i) Assets turnover = Sales

Total assets

2) Fixed assets turnover = Sales [Number of times fixed assets has

Fixed assets turned into sales]

3) Working capital turnover = Sales

Working capital

4) Inventory turnover = Cost of goods sold

(for finished goods) Average inventory

5) Debtors turnover (or) Average collection period = Credit sales (in ratio)

Average accounts receivable

(or) = Average accounts receivable * 365 (in days)

Credit sales

6) Creditors turnover (or) Average payment period Credit purchases (in ratio)

Average accounts payable

(or) = Average accounts Payable * 365 (in days)

Credit Purchases

7) Inventory Turnover (for WIP) = Cost of production

Average Inventory (for WIP)

Inventory Turnover (for Raw material) = Raw material consumed

Average inventory (for raw material)

10) Inventory Holding Period = 365 .

Inventory turnover ratio

11) Capital Turnover ratio = Cost of sales

Capital employed

Note : -

• Working capital = Current asset – Current liability

= 0.25 * Proprietary ratio

• Accounts Receivable = Debtors + Bills receivable

• Accounts payable = Creditors + Bills Payable

Remarks : -

• If assets turnover ratio is more than 1, then profitability based on capital employed is profitability based on sales.

• Higher inventory turnover is an indicator of efficient inventory movement. It is an indicator of inventory management policies.

• Low inventory holding period lower working capital locking, but too low is not safe.

• Higher the debtors turnover, lower the credit period offered to customers. It is an indicator of credit management policies.

• Higher the creditors turnover, lower the credit period offered by suppliers.

G) Other Ratios: -

1) Operating profit ratio = Net profit ratio + Non operating loss / Sales ratio

2) Gross profit ratio = Operating profit ratio + Indirect expenses ratio

3) Cost of goods sold / Sales ratio = 100% - Gross profit ratio

4) Earnings per share = Net profit after interest and tax

Number of equity shares

5) Price earning ratio = Market price per equity share

Earning per share

6) Pay out ratio = Dividend per equity share * 100

Earning per equity shares

7) Dividend yield ratio = Dividend per share * 100

Market price per share

Fixed charges coverage ratio = Net profit before interest and tax

Interest charges

9) Interest coverage ratio = Earning before interest and tax

Interest charges

10) Fixed dividend coverage ratio = Net profit .

Annual Preference dividend

11) Over all profitability ratio = Operating profit * 100

Capital employed

12) Productivity of assets employed = Net profit .

Total tangible asset

13) Retained earning ratio = Retained earnings * 100

Total earnings

H) General Remarks: -

• Fall in quick ratio when compared with last year or other company is due to huge stock pilling up.

• If current ratio and liquidity ratio increases then the liquidity position of the company has been increased.

• If debt equity ratio increases over a period of time or is greater when comparing two ratios, then the dependence of the company in borrowed funds has increased.

• Direct expenses ratio increases in comparison then the profitability decreases.

• If there is wages / Sales ratio increases, then this is to verified

a) Wage rate

b) Output / Labour rate

• Increment in wage rate may be due to increased rate or fall in labour efficiency.

• Again there are many reasons for fall in labour productivity namely abnormal idle time due to machine failure, power cut etc.

• Reduction in Raw material consumed / sales ratio may be due to reduction in wastage or fall in material price.

• Increase in production expenses ratio may also be due to price raise.

• Stock turnover ratio denotes how many days we are holding stock.

• In stock turnover ratio greater the number of days, the movement of goods will be on the lower side.

• Financial ratios are Current ratio, Quick ratio, Debt equity ratio, Proprietary ratio, Fixed asset ratio.

• Short term solvency ratios are current ratio, Liquidity ratio

• Long term solvency or testing solvency of the company ratios are Debt equity ratio, fixed asset ratio, fixed charges coverage ratio (or) Interest coverage ratio.

• To compute financial position of the business ratios to be calculated are – current ratio, Debt equity ratio, Proprietary ratio, fixed asset ratio.

• Fictitious asset are Preliminary expenses, Discount on issue of shares and debentures, Profit and loss account debit balance.

Assignment

1) Basis of Technique used is minimization Technique

2) It can also be done in maximation Technique

3) Various steps in Assignment Problem are

Step 1: Check whether the problem is balanced or unbalanced by checking

whether row is equal to column, if unbalanced add dummy column or

row to balance the problem

Step 2: Identify Least Number in each row and subtract with all number in that

Row.

Step 3: Identify least number of each column and subtract with all number in that

column.

Step 4: Check whether solution is reached with zero selection in one row and

column, ie. Cover all the zero with minimum number of lines, solution is

reached only when selected zeros is equal to number of rows or columns

or number of lines is equal to order of matrix.

Step 5: If solution is not reached so maximum sticking

Step 6: Select the least element in within the unstriked Element

Step 7: The element selected above is

i) Subtracted with all the unstriked element

ii) Added to all the double striked element (Intersection of two lines)

Step 8: Check the solution

Step 9: If solution is not reached continue with the process from step 5.

Linear Programming

Simplex Method:-

Steps:-

1. Determine the objective function Z. Objective may be maximization or minimization.

2. For maximation problem the constraints would be < sign.

For minimization problem the constraints would be > sign.

3. Introduce slack variable

For < sign – add the slack variable ie. Add S1

For > sign – subtract the slack variable and add artificial variable

ie. Subtract S1, add A1.

4. Change the Objective function

For S1 – Add ‘0S1’

For A1 – Add ‘MA1’

5. Simplex table format:-

Cj

Quantity Variable Const. X Y Z S1 S2 RR

S1

S2

Zj

Cj - Zj

6. Zj is arrived by summation of constant column with X,Y,Z columns

7. Criteria for selecting the key column :-

For Maxima ion Problem – Highest value of Cj – Zj

For Minimization Problem – Lowest Value of Cj – Zj

8. Divide the Quantity Column with Key column to arrive at RR

9. Criteria for Selecting the Key row :-

For Maximation & Minimization Problem – Lowest Positive RR is selected

10. The Meeting Point is key Element

11. Criteria for deciding the optimal solution

For Maximation Problem – All elements in Cj – Zj row is negative or zero.

For Minimization Problem – All elements in Cj – Zj row is positive or zero

Note – For finding whether all the elements in Cj – Zj row is positive or zero

for minimization problem substitute all the ‘M’ with highest value.

12. If solution is not reached next table is formed.

13. Input for next table is

First key row in the next table is filled by dividing all the numbers in the key row of the previous table with the key element.

Remaining all the rows is arrived as follows: -

Corresponding previous _ (Value relating to that * Corresponding

Table row element row in the key column element in key row

in the 2nd table as

filled in previous step)

14. Check the optimal solution, if not reached form the third table.

15. If solution is reached then answer is amount in quantity column corresponding to the variable.

Other Points : -

• We can convert the Minimization Problem into Maximation Problem. This is known as duality.

• We can change the > sign to < sign to match the problem

E.g. X + Y < 100

is converted into -X - Y > -100

Transportation

• The procedure followed is Minimization Procedure

• Problem is generally solved in Vogel’s Approximation Method(VAM)

• Steps for the problem is : -

1. Convert profit matrix into loss matrix.

2. Balance the problem.

3. Arrive at Row penalty and column penalty

Row penalty and column penalty is calculated at (2nd least – 1st least) in the corresponding row or column.

4. Select from the entire Row penalty and column penalty maximum number.

5. From the entire Row or Column minimum is selected.

6. Strike the row or column which gets eliminated.

7. Continue until the entire item in the table is strike.

8. Write separately Initial solution table.

9. Check for Degeneracy. Degeneracy occurs when all the elements in the initial solution is equal to (Row + column – 1)

10. If degeneracy occurs introduce efcilon – ‘e’. ‘e’ is introduced in least independent cell.

11. Form UV Matrix. It is formed by the element in the original solution corresponding to the element in the Initial solution.

12. Find unalloted elements in the UV Matrix

13. Find Ij i.e.(Original Matrix element – Unalloted element found above)

14. Check for optimal solution ie. All items must be zero or positive.

15. If not reached select the maximum negative in Ij matrix.

16. Form a loop and reallocate the solution.

17. Repeat from step 9.

Notes: -

1. If there is zero in Ij matrix while arriving at optimal solution then there is another solution for the problem.

2. Dummy column can be introduced in profit or loss matrix.

3. If there is penalty/redundancy payment for unsatisfying demand etc. is given then fills the dummy row or column with that amount or fill it with zeros.

4. If there is constraint in the problem first satisfy the constraint and then solve.

5. various other methods for solving the problem is

• Least cost method

• North west corner rule

6. Generally VAM method is used

Network Analysis (CPM/PERT)

CPM

• Total float = LS – ES (or) LF – EF

• Free float = Total float – Head event slack

• Independent float = Free float – Tail event slack

• In the diagram Es = Lf in the critical path

• Critical path is the longest duration

• To find the minimum time associated cost (i.e. Additional cost incurred per unit of time saved) following formula is used :-

Crash cost per day (or) Activity cost supply

= Crash cost – Normal cost

Normal time – Crash time

• Interfacing float = It is the part of the total float which causes reduction in the float of the succession activities. In other words it is the portion of activity float which cannot be continued without affecting adversely the float of the subsequent activity or activities.

• Steps in proceeding the problem : -

2. First find and fill the ES and LF column from the diagram.

3. Then find LS and EF as follows :-

Ls = Lf – Duration

Ef = Es + Duration

4. Find total float

5. Find free float. Wherever total float column has zero free float column is also taken has zero and remaining elements is filled as said above

6. Find Independent float. Wherever free float column has zero Independent float column is also taken has zero and remaining elements is filled as said above

Notes: -

1. ES = Earliest Start. Indicates earliest time that the given activity can be scheduled

2. EF = Earliest Finish. Time by which the activity can be completed at the earliest.

3. LF = Latest Finish. Latest allowable occurrence time of the head event of the activity.

4. LS = Latest Start.

5. Total duration of the critical path is the maximum time/amount consumed for the activity. This should be crashed with respect to crashing days and crashing cost. This crashing should not change the critical path.

PERT : -

• Expected (or) Average time is found by assigning weights as follows : -

1 for optimistic

4 for Most likely

1 for pessimistic

Average time = 1 optimistic + 4 most likely + 1 pessimistic

6

• Standard Deviation = (Pessimistic time – Optimistic time)

6

• Variance = (Standard Deviation)2

• Probability of completing the project in N days

= Required time(N) (-) Expected time (critical path duration)

Standard Deviation

[Nothing but Z = (X - Mean) / Standard deviation]

= Y (say)

= Find Z(y)

= Probability %

- If required time > Expected time then = 0.5 + Z(Y)

- If required time < Expected time then = 0.5 – Z(Y)

Learning Curve

Learning is the process of acquiring skill, Knowledge, and ability by an individual. According to learning curve theory the productivity of the worker increases with increase in experience due to learning effect. The learning theory suggests that the best way to master a task is to “learn by doing”. In other words, as people gain experience with a particular job or project they can produce each unit more efficiently than the preceding one.

The speeding up of a job with repeated performance is known as the learning effect or learning curve effect.

The cumulative average time per unit produced is assumed to fall by a constant percentage every time the total output is doubled. So generally learning effect is found in the multiples of 2. If learning curve effect is asked between two even numbers then Learning curve equation is formed ie. Learning curve effect is expressed mathematically as follows:

Learning curve equation =

Y = a(x) -b Where Y = Average time per unit

a = Total time for first unit

x = Cumulative number of units manufactured

b = the learning curve index

Learning curve index (b) = log (1- % decrease)

Log 2

Management Accounting and Financial Analysis

International Financial Management

1. Direct Quote (eg) 1$ = Rs.49

2. Indirect Quote (eg) Rs.1 = .0204$

3. TT Rate = Telegraphic Transfer Rate

4. TOM Rate = Tomorrow Rate

5. Spot Rate = Today’s rate. Normally it will be 3td day rate from TT Rate.

Direct Quote is used in all country except UK where indirect quote is used.

Offer Rate = Selling Rate

Spread Rate = Offer Rate – Bid Rate

Spread Rate (%) = Offer Rate – Bid Rate * 100 (111lr to that of NP Ratio)

Offer Rate

Swap points is ascending stage it is at premium. If it is descending stage it is at discount.

If it is said as INR/$ then the meaning is

• Numerator factor = Local Currency = INR

• Denominator factor = Foreign Currency = $

Forward Quotation (%) (I.e. Premium/Discount expressed at annualized %)

= Forward Rate – Spot Rate * 12 * 100 (in months)

Spot Rate n

= Forward Rate – Spot Rate * 365 * 100 (in days)

Spot Rate n

If the quote is direct or Indirect is to be found and the relation is with £ (pound) both direct and Indirect quote is to be said.

Maturity Value = P (1+r) n

Interest Rate Parity:

i) Domestic Rate < Foreign Rate + Forward Premium / Discount

(In this case invest in foreign currency)

ii) Domestic Rate > Foreign Rate + Forward Premium / Discount

(In this case invest in Domestic Currency)

Forward Rate: It is rate negotiated for the delivery to be made / taken on a future date for present transaction.

Future spot rate: It is actual rate prevailing on the agreed future date.

Other points:-

• Currency country which has less Interest rate will have forward rate at premium and vice versa

• If two rates ie.20.23 / 35 is given then highest rate is offer rate, lowest rate is bid rate.

• If INR / DG is given and we have to DG / INR then it is 1 / (INR / DG)

• 1 / (Bid Rate) = Offer Rate.

• 1 / (Offer Rate) = Bid Rate.

Interest rate swap: - Generally interest rate differs from company to company because of their grade (reputation) and rates can be fixed rates or floting rate. If there is 2 company under different grade and different fixed / floating rate can gin advantage by reducing their interest rate by “Interest rate swap”.

In this if ‘Company A’ wants to borrow at floating rate and ‘Company B’ wants to borrow and fixed rate, then interest rate swap is applied by which company A borrows at floating Rate of company B and company B borrows at fixed rate of company A. By this swap one company gains and other company losses. Net gain is splited between two companies so that the two companies benefits by paying lower interest rate for their barrowing.

To look at the problem quickly the theory followed in “Difference in fixed rate interest of two companies is profit” and “Difference in floating rate interest of two companies is loss”. Then net gain / loss are found.

Capital Budgeting

Process of Capital Budgeting:

• Huge cash outlay.

• Decision taken is irressable.

• Invest in lumsum the receipt is piecemeal

• Wrong decision will affect the very base of the company.

Capital Budgeting Rules:

• Ignore accounting profit and take only cash flows.

• Try only incremental basis ignore Average calculation.

• Consider all incidental effects.

• Ignore sunk cost (ie. Cost remain unaltered for various alternatives available is sunk cost)

• Consider opportunity cost (Opportunity Loss is Opportunity cost)

• Beware of allocated cost – Ignore them

• Depreciation is an important cash flow when taxation is considered. If no taxation, no depreciation.

• Interest should not be considered as part of the cost, in the arrival of cash inflow for investing decision problems. If deducted add back post tax interest.

• Separate investing decision and financing decision.

• Be consistent with inflation rates. All future cash flows is assumed as without inflation. Such cash flows are referred as real cash flows.

• Cash flows under the influence of inflation would be referred to as money cash flows. (Money cash flows (or) Nominal Cash Flows (or) Market cash flows)

• Unless otherwise stated cost of capital is considered after tax basis because cash flows will be considered only on after tax basis. (PV factor is the inverse of compounding factor)

• Equation to find out the PV of an amount if cost of capital and Inflation rate is given

(1 + Money Rate) = (1 + Real Discount rate) * (1 + Inflation Rate)

Method of evaluating Capital Budgeting:

1. Pay back method

2. Annual Rate of Return

3. Discounted cash flow

• Net Present Value (NPV)

• Internal Rate of Return (IRR)

• Profitability Index (PI) (or) Benefit cost Ratio

• Equated Annuity Cost (EAC) (or)

Equated Annuity Benefit (EAB)

• Discounted Pay Back (or) Time adjusted BEP

Expressed

In Bench mark

(Basis of

Selection) Formula When to use

Pay Back

Period Years Shortest Recovery time

of investment When no cost of capital is given

Annual Rate Of Return % Highest 1) AR / II

2) AR / AI When no cost of

capital is given

NPV Rs. Greatest

Value Discounted CI

- Discounted CO When two projects is same in all aspects ie. No disparity

IRR % Highest At this rate

Discounted CI = Discounted CO

and NPV = 1,

PI = 1 Rarely used in

finding Cost of Capital.

Profitability

Index (PI) Points Highest Discounted CI

Discounted CO Size Disparity

EAC (or)

EAB Rs. EAC =

Lowest

EAB =

Highest EAC =

Discounted CO

PV Factor

EAB =

1) Discounted CI

Annuity Factor

2) NPV

PV Factor Life Disparity

Discounted

Pay Back Years Shortest Recovery time of Investment Break even time

Where: - AI = Average Investment CI = Cash Inflow

AF = Annuity Factor CO = Cash Outflow

II = Initial Investment

Internal Rate of Return (IRR):-

IRR otherwise called as yield on investment, Marginal efficiency of capital, Marginal productivity of capital, Rate of Return, Time adjusted rate of return.

Discounting + Difference calculated in present value and required cash outlay

Factor Difference in calculated present values

* Difference in Rate

To approximately locate the factor in which the amount returns

F = I / C Where F = Factor to be located

I = Original Investment

C = Average Cash Inflows per year

In the PV table year column must be seen to trace the nearest fake annuity. Year column is the year of economic life of machine.

Notes: - If actual cash flow is higher than average cash flows in the initial years then increase the fake IRR point a few % upward. If it is lower in the initial years then decrease the percentage few points lower to find fake IRR

If discount rates are not known but cash inflows and outflows are known then IRR is calculated as I = R / (1+r)

Where I = Cash outflow (or) Initial Investment

R = Cash inflow

R = Rate of return yielded by the Investment (or IRR)

Calculating Discounting Factor:-

1 / (1+rate) n Where n = Years

Method of ranking projects:-

Desirability factor (Profitability Index) vs. NPV Method vs. IRR

Selection of projects out of two mutually exclusive projects having same funds at disposal then NPV method is preferred.

In IRR Method the presumption intermediate cash inflows are reinvested at same rate i.e. IRR. But in NPV method it is reinvested at cut off rate.

Reinvestment at cut off rate is more possible than IRR. Hence Net Present Values being obtained from discounting at a fixed cut off rate are more reliable in ranking 2 or more projects than IRR.

Models of Risk Analysis:-

i) Hiller’s Model: He takes into account mean of present value of the cash flows and the SD of such cash flows.

n

M = (1+r)-1 mi (used to determine the present value of mean)

i=0

n

2 = (1+r)-2i * 2i (Used to find the present value of variance)

i=0

Where mi =Mean of cash flow in the ith period – expected cash flow for year i

2i = Variance in the ith period.

r = Discounting Factor

M = Total of Present value of mean

2 = Total of present value of variance

Bench mark = Project with lower SD will be preferred.

1) Real Cash flows restated in terms of nominal cash flows as follows:-

(1 + inflation rate) * Real cash flows

After this discounting cash flow is applied to find NPV.

2) Converting nominal discounting rate into real terms

Real discount rate = 1 + Nominal discount rate - 1

1 + inflation rate

With this real discount rate the Cash Inflows are discounted to find NPV.

3) Pay back reciprocal

= Average annual cash inflows (It is used for reasonable approximation of

Initial Investment IRR)

4) The formula for deflation is

Index Number at the beginning * Cash Inflows

Index Number at the end

(or) Cash Inflows / (1+Inflation Rate) n

Note: If in a problem Real cash flows are given and Inflation Rate and Cost of Capital is given then

i) Convert Real Cash Flows into Normal Cash Flows by using formulae said in (1) above.

ii) Adjust for Depreciation and tax and find Cash Flow after Tax before Depreciation.

iii) Deflate the amount arrived above by using formulae said in (4).

iv) With the amount arrived above find NPV using COC.

Summary:-

i) Risk Adjusted Discount rate approach

= NPV for CFAT at Risk adjusted Discount Rate.

ii) Certainty Equivalent Approach

= NPV for (Certainty Equivalent Coefficient * CFAT) at Risk less Interest rate.

iii) Probality Discount approach

= NPV for (CF) at risk less Interest rate.

Analysis of Risk and Uncertainty

1) Sensitivity Analysis: - It provides different cash flow estimates under 3 assumptions a. worst

b. The expected (Most likely)

c. The best.

NPV is found under these three assumptions and decision is taken.

2) Precise measure of risk:-

a) Standard deviation: - Absolute measure of risk.

n

= √ ∑ Pi ( CF – CF ) 2

i=1

CF = Cash flow i = Year

CF = Mean cash flow (CF of particular projects total divided by number of CF)

= ∑ CF * P

P = Probability

n

b) Variance = ( ) 2 = ∑ Pi ( CF – CF ) 2

i=1

c) Co – Variance (a,b) = Pi ( CFa – CFa ) ( CFb – CFb )

d) Coefficient of correlation of two variable factor = Co – Variance (a,b)

a b

e) Return of portfolio = Wa * Ra + Wb * Rb Where W – Proportion invested

R – Return

f) Risk of portfolio = √ Pa2 * a2 + Pb2 * b2 + 2Pa * Pb * a * b * Cor(a,b)

g) Co – Efficient of variation = A relative measure of risk.

Standard Deviation

V= Expected cash flow (or) mean (or) CF

(Or) Expected NPV (NPV)

NPV = NPV * Probability

h) Risk adjusted discount rate approach: - In this risk adjusted discount rate is taken as PV factor and calculated as NPV method.

=∑ (CFAT) t - CO Where Kr = Risk adjusted discount rate

(1 + Kr) t

i) Certainty Equivalent (CE) approach = Risk less Cash Flow

Risky Cash Flow

j) If Correlation Coefficient [Cor(a,b)] is

Cor(a,b) p .

+1 (Pa * a) + (Pb * b) [ie. If it is perfectly positively correlated]

-1 (Pa * a) – (Pb * b) [ie. If it is perfectly negatively correlated]

0 Above p formula will apply

k) Probability Distribution approach: -

t (SD of CF) = √ ∑ p (CF – CF)2 = ∑ CF - CO = NPV

(1+i) t

Where

CF = Cash Flow CF = Mean i.e. Total of cash flow multiplied by probability for the period (or) expected value for CFAT in period t)

i = Risk less rate of interest.

t = SD for period t (SD for particular period)

l) SD for the probability distribution of NPV is (ie. SD of CF)

(NPV) = √ ∑ ( t2) / (1 + i) 2t (this is used for uncorrelated CF)

(NPV) = ∑ ( t) / (1 + i) t (used for perfectly correlated CF)

Where I = Rate of Return.

m) Optimum proportion at which risk is minimum = Xa = b / ( a + b)

(or) a X - b (1-X) = 0

NPV for the period is calculated by taking CF as CF for respective period and calculated normally

Note:-

i) In certainty Equivalent approach rate of discount is the risk less rate of Interest as the risk is adjusted with CFAT.

ii) In this case CFAT is multiplied with certainty equivalent and PV is calculated by risk less rate of interest.

iii) If projects are ranked with respect of risk and return. Project with respect

to risk requires ∑ NPV (i.e. ∑(NPV * Probability)) and the project with respect to

return find co-efficient of variation = / ∑ NPV

iv) Probability that NPV would be Zero or less

Z = 0 – NPV The Z Value is converted with the ‘Z Table’

values and the probability of the NPV being

zero or less would be = 0.5 – (Z Value).

v) Probability that NPV being greater than Zero would be

1 – (Probability less than Zero)

vi) Probability that NPV within the range X and Y

Z1 = X – NPV Z2 = Y – NPV

vii) If in the Risk adjusted Discount approach both cost of control and Risk adjusted discount rate is given

• For the CF of the years apply Risk adjusted discount rate to find Discounted CF.

• For the Scrap value of the machine after the end of the life the CF on sale is discounted at cost of capital % to find Discounted CF.

viii) If probability (or) Certainty equivalence is given then find the Adjusted

CF (CF * Probability) and then use the Risk less Rate of return to find Discounted CF.

ix) Risk is Standard deviation

Summary:-

i) Risk Adjusted Discount Rate Approach

= NPV for CFAT at Risk Adjusted Discount Rate

ii) Certainty Equivalent Approach

= NPV for (CE coefficient * CFAT) at Risk less interest rate

iii) Probability Discount Approach

= NPV for (CF) at Risk less Interest Rate

Derivatives

Call Option: - Gives buyer “Right but not the obligation” to buy the share.

Put Option: - Gives buyer “Right but not the obligation” to sell the share.

Value of the Call Option:-

i) Black Scholes Model:-

Value of the call option = VO

= [S * N (d1)] – [(x) * (e-t*rf) * (N (d2))]

Where d1 = ln (s/x) + (rf + { 2 / 2}) * t

√t

ln = Natural log

d2 = d1 - √t

s = Present spot rate

x = Future strike (excise) price

rf = Risk free rate

Seven step to solve the problem:-

i) Find log (s/x)

ii) Find d1

iii) Find d2

iv) Find N (d1)

v) Find N (d2)

iv) Find N (d1) Normal Table Value

+ 0.5

v) Find N (d2)

vi) Find ‘e’ value

vii) Apply Black Schools Model.

Sub step to step 1:-

a) Log (s/x) = Log s – Log x

0.4343

b) If x and s are 2 digit figure the value shall be (1 + Log table value).

c) If x and s are 3 digit then the value shall be (2 + Log table value).

Sub step to step 6:-

a) It is to find the power value of ‘e’.

b) e-t*rf = 1 (or) 1 .

1 + r/365 * No. of days (t) 1 + r/365 * No. of Months (t)

Value of Put option: -

= [(x) * (e-t*rf) * (N (-d2))] - [S * N (-d1)]

Excise price:-

It is the price at which the person writes the prices on a share to buy after a period.

Expected Value of the share:-

It is the total of estimate market price of the share multiplied with the respective probability.

Expiration value: - Excise price – Expected Value

Expected (or) Theoretical value of the call option price at expiration (Pay off of Call option) :-

= ∑ (Estimated market price – Excise Price) * Probability (or)

= [Max (s – x), 0] * Probability

Pay off of call option

Expected (or) Theoretical value of the put option price at expiration (Pay of put option):-

= ∑ (Excise Price - Estimated market price) * Probability (or)

= [Max (x – s), 0] * Probability

Pay off of Put option

Where (Estimated market price – Excise Price) is called pay off. If it is negative it is taken as zero.

s = Estimated Market Price.

Put call parity = Put call parity equation is

(Value of call option + Present value of excise price) = (value of put option +

Spot rate)

Note:-

i) Changes to be made in computation of Black Scholes model for dividend stocks:-

Substitute in all the places of “s” with “s – PV of dividend”

ii)In the above all PV is found at Risk free rate.

Beta

Beta means, it measures the volatility of securities to the changes in the market.

β (level of risk) = s * Cor (s,m) where s = SD of return on securities

m m = SD of return on market portfolio

(or) Covariance(s,m) / 2m

β should always be applied on risk premium and not to the entire return.

rs = rf + (rm – rf ) * β Where rf = Risk free rate

rs = Expected return on securities (or) [Capital

Appreciation + Dividend of the company]

rm = Expected return on market portfolio (or)

[Market index {Market rate} appreciation + Market dividend yield %]

Portfolio Theory (PT):-

rp (expected return under CML) = rf + (rm – rf) * ( p / m)

The above formula is based on total risk.

Where p = SD of efficient portfolio.

When expected return under efficient portfolio is asked then

rp (expected return under efficient portfolio) = Capital market line(CML) –

Express equilibrium price relationship between expected return and DS

Capital Asset Pricing Model (CAPM):-

rs (expected return portfolio in CAPM) = rf + (rm – rf) * [( s / m) *

cor(s,m)]

(or) rf + [(rm – rf)] * β

Where rm = rf + Market premium

Beta of the portfolio = ( βa * Pa ) + ( βb * Pb )

Where Pa, Pb = Proportion of investment in Company A and Company B.

Note:-

i) (rm – rf) = Market risk premium (or) Compensation per unit of risk.

ii) Cor(s,m) is +1 under CML

iii) rf + (rm – rf) * [( s / m) * cor(s,m)] = This portion in CAPM formula is

risk premium

iv) (rm – rf) / m = Market risk return trade off (slope).

Notes:-

To find the investment to be made in risk free investments to get a certain β is

β of expected portfolio = (W1 * β1) +(W2 * β2)

(or) = (W1 * β1) + (1-W1) β2

Where W1 is weitage given to existing securities.

W2 is weitage given to risk free securities.

In this case β1 is β of existing securities and

Β2 is β of rf securities (ie.0)

This can also be use to find investment in other then rf securities. In that case that β is substituted in β2.

The weitage (W1,W2) is multiplied with market value of existing portfolio to find the proportion of investment.

Holding Companies

Index of Main Points:-

1. If there is a Debit balance in Minority Interest first it is adjusted against uncalled capital and balance is adjusted against reserve.

2. In case of Cumulative Preference shares of subsidiary dividend declared must be deducted from P & L a/c of subsidiary.

3. If no dividend is declared in above case then don’t deduct.

4. If dividend is declared for Cumulative Preference shares then deduct from P & L a/c of subsidiary and balance is splited. If not declared then it must be shown outside the Balance sheet.

5. But in the case1

6. CFS deduct in the above case whether declared or not.

7. Preference shares of subsidiary held by the holding company is to be cancelled against investment of Holding company while preparing CFS.

8. If Holding company sells goods below cost then unrealized loss is calculated by taking cost or Net Realizable Value whichever is lower for valuation.

9. If there is difference in accounting policy between Holding and subsidiary then both should be brought under uniform policy before consolidation.

10. If uniform policy cannot be brought then it should be disclosed.

11. The effect of change in Accounting Policy before acquit ion must be taken as pre acquit ion reserve and after post acquit ion reserve.

12. If Holding Company holds Debenture in subsidiary then while preparing CFS it should be cancelled as Inter Company loan.

13. In above case if excess is paid for Debenture holders then the excess is adjusted against consolidated reserve.

14. Pre acquit ion reserve and profit is treated as capital profit

15. Post acquition reserve and profit is treated as revenue reserve and revenue profit respectively.

16. Miscellaneous expenses of subsidiary must be deducted against reserve as Capital or Revenue Reserve.

17. In case of Inter Company transactions if it is down stream then unrealized profit of Holding company must be adjusted against Consolidated P & L a/c.

18. In case of Inter Company transaction if it is upstream it is splited into two as belonging to Holding company and Minority Interest and the former is deducted against Consolidated P & L a/c and Minority Interest is deducted from computation of Total Minority Interest.

19. Post acquit ion dividend received is to be retained in P & L a/c.

20. Pre acquit ion dividend received is to be transferred from Holding company P & L a/c to Cost of Investment.

21. Post acquit ion dividend receivable (Proposed) by Holding company out of subsidiary current year profit is to now credited to Holding company Consolidated P & L a/c.

22. In case of analysis of profit Proposed Dividend must be deducted from current year profit only.

23. If in the above case if there is inadequate profit for dividend, the appropriation should be done 1st out of current year profits and thereafter out of b/f profit.

24. In case Inter Company sale or purchase is carried between two subsidiaries then for consolidated stock it is considered as it is 1st transferred from one subsidiary to Holding – upstream rule apply and then from Holding to 2nd subsidiary – Down stream rule apply.

25. In Inter Company transaction if there is sale of Fixed Asset between Holding and Subsidiary unrealized profit should be removed only to the extent of unamortized portion.

26. In the absence of information regarding rate of depreciation, depreciation must be ignored.

27. In case of acquition and sale of shares, profit on such sale must be included in P & L a/c while calculating reserves for CBS.

28. In the event of current year dividend is greater than the trading profits AND if there is another source of income i.e. Subsidiary dividend then the dividend declared must be deducted only in Apportionment of profits.

29. Inter corporate loans in general refer to borrowings from corporate bodies.

30. In case of reverse working

for stock consolidation = Company A + Company B – Stock reserve

for Debtors and creditors = Company A + Company B – Inter company

consolidation transactions

31. In case of Associate accounting Inter Company transaction should not be cancelled only Holding company interest of unrealized profit is only taken.

32. Losses in associate are taken only up to the liability in share capital.

33. Minority Interest calculation is not applicable in case of associate accounting.

34. In the case where subsidiary company is foreign company then convert the accounts into Indian Currency and remaining are same. For conversion rules applicable are:-

Share capital – Rate on the date of acquition of share.

Reserves – Pre – Rate on the date of acquition

Post – Average rate

Current Assets, Current liabilities – Closing rate

Fixed assets, Investments – Rate on the date of acquition

35. Exchange rate difference which occurs on the above conversion is to be setoff against post acquition Profit / Reserves and the balance is only to be apportioned for consolidation procedure.

36. In case of two or more acquition by Holding Co. (or) acquition and sale, In all the cases date for apportionment etc is the date of 1st acquition and share holding pattern is the final share holding pattern.

37. In case of Associate accounting, to find the carrying amount of Investment of the associate in the consolidated balancesheet the calculation is similar to minority interest. Only difference is to add the goodwill found in COC.

,ie, Share Capital ***

(+) Capital Profit ***

(+) Revenue Profit ***

(+) Goodwill *** ***

Amalgamation

Index of Main Points:-

1. Points to be satisfied to treat the amalgamation in the nature of merger

• All assets and liabilities of transforer is to be taken over at their book values by resulting company

• All or at least 90% of the Share Holding of Amalgamating Company must be the Share Holders of Amalgamated Company.

• Equity shares of selling company must be given only equity shares of purchasing company.

• Liabilities of Transferor must not be discharged; it must be taken over by the resulting company. But exemption is the fraction shares can be given in cash.

• Same risk and return and nature of company must be same.

2. Order of Adjustment of consideration is first General Reserve and then P & L a/c. If the problem has statutory reserve it should not be adjusted. It is carried over as such.

3. As per SEBI guidelines, underwriting commission is 2.5% on equity shares and on 1st 5000 Preference Shares it is 1.5% and the balance Preference Shares it is 1%.

4. Capital employed is considered as Net Revaluation amount of Tangible Asset.

5. In case purchasing company holding shares in selling company, Net asset method is applied as usual and outside shareholders portion is calculated separately as balancing figure.

6. If in the above case, settlement of equity share holding of selling company is given then that exchange pertains to outside share holder’s settlement and it should not be splitted.

7. In the books of selling company the shares held by the purchasing company must be cancelled by transferring it to realization a/c

Equity share capital a/c Dr

To Realization

8. If Preference share holders of selling company is discharged by preference share holders of purchasing company at premium then the premium portion must be transferred to realization a/c in the books of selling company.

9. In case of Merger while drafting Journal Entry in the books of purchasing company for Incorporation of Asset & Liability in the workings, the consideration is aggregate consideration including shares already purchased by purchasing company and current purchase payable.

10. In case of merger in the books of purchasing company while calculation excess / shortage to be adjusted against the reserve of selling company. The purchase consideration is aggregate consideration including amount already paid (shares of selling company held by purchasing company) + amount now paid (amount paid to outsiders).

11. Business purchase in case of shares of selling company held by purchasing company is the amount given to outsiders only.

12. If in the asset side of selling company Debtors is given as Gross (–) Reserves / Provision for Doubtful Debts then in the books of selling company while transferring all assets and liabilities to realization account Debtors is transferred at gross amount and provision is transferred along with liability.

But in the above case in the books of purchasing company while

incorporating assets and liabilities of selling company debtors is taken net of

provisions.

13. On entry for takeover of assets and liabilities of selling company in purchasing company books – Assets debited must be excluding goodwill in purchase method and difference in debit or credit is treated as Goodwill / Reserves.

14. Investment allowance Reserve is not a current liability.

15. When purchasing company holding shares in selling company then the shares held by purchasing company must be cancelled in the selling company books.

16. While canceling the shares held by the purchasing company it must be cancelled at fair value.

17. To bring the reserve like Investment allowance reserve in purchasing company books the entry will be Amalgamation adjustment a/c Dr

To Investment allowance reserve

In the amalgamated B/S investment allowance reserve will appear in

the liability side and amalgamation adjustment account will appear in the asset side for same amount.

18. Incase of Inter Company holding if divided is declared by any one company then dividend receivable by other company is to be 1st incorporated as pre amalgamation event. Dividend receivable account Dr

To P & L a/c

Entry in the 1st company which has declared dividend P & L a/c Dr

To proposed dividend

19. In case of Internal reconstruction cancellation of Arrears Dividend forgone by shareholder will not affect the B/S. So no entry. In this case Arrears of dividend is seazed to be contingent liability. Preference shareholders will seize to have the voting right at par with equity shares which was available due to arrears of dividend.

20. In Demerger while making transfer entry of Asset and liability in purchasing company fixed asset net is to be taken but while making the transfer entry in selling company fixed asset gross is taken in credited and provision for depreciation is debited.

21. In case of Inter Company / Single side holding etc. to find the intrinsic value of each company, the investment held by one company in the shares of other company is also to be valued as intrinsic value only and not to be taken at book value. For inter company holding this intrinsic value of shares of each company can be found by framing a linear equation.

22. In case of calculation of purchase consideration (Cross holding)

Total number of shares in selling company ***

(-) Share already held by Purchasing company ***

Number of shares held by outsiders ***

Value of above number of shares Rs. ***

Number of purchasing company to be issued to selling company ***

(-) Number of shares already held by selling company ***

Net number of shares purchasing co. has to issue to selling co. ***

23. In case of settlement of shareholders of selling company the amount will be = Shares now received from purchasing company + Purchasing company shares already held by selling company.

24. In amalgamated B/S if there is Debit in P & L a/c it should be netted of with General Reserve as per schedule VI.

25. In case of assets and liabilities is taken over at revalued amount it is in the nature of purchase and in the journal entry for incorporating account takenover only the revalued amount is to be taken.

26. In case of selling company holding shares in purchasing company then investment is to be valued at intrinsic value if specified.

27. In the above case of holding company gives shares at particular value to the subsidiary company for settlement then investment is to be valued at the value

28. When selling company holding shares in purchasing company then while transferring assets and liabilities to realization account in selling company books, Assets transferred must be excluding the Investment in purchasing company.

Cash and fund flow statement

Rules for preparing schedule of changes in working capital :-

Increase in a current asset, results in increase in working capital – so Add

Decrease in current asset, results in decrease in working capital – so Decrease

Increase in current liability, results in decrease in working capital – so Decrease

Decrease in current liability results in increase in working capital – so Add

Funds from operations – Format

Particulars Rs. Rs.

Net profit ***

Add : Depreciation

Goodwill written off

Preliminary Exp. Written off

Discount on share written off

Transfer to General Reserve

Provision for Taxation

Provision for Dividend

Loss on sale of asset

Loss on revaluation of asset ***

***

***

***

***

***

***

***

***

***

***

Less : Profit on sale of asset

Profit on Revaluation of asset ***

***

***

Fund flow statement ***

Fund flow statement

Particulars Rs.

Sources of funds : -

Issue of shares

Issue of Debentures

Long term borrowings

Sale of fixed assets

Operating profit ***

***

***

***

***

***

Total Sources ***

Application of funds : -

Redumption of Redeemable preference shares

Redumption of Debentures

Payment of other long term loans

Purchase of Fixed assets

Operating Loss

Payment of dividends, tax etc ***

***

***

***

***

***

***

Total Uses ***

Net Increase / Decrease in working capital

(Total sources – Total uses)

***

Cash flow statement

Cash From Operation : -

= Net profit + Decrease in Current Asset

+ Increase in Current Liability

- Increase in Current Asset

- Decrease in Current Liability

Cash flow statement

Sources Rs. Application Rs.

Opening cash and bank balance

Issue of shares

Raising of long term loans

Sales of fixed assets

Short term Borrowings

Cash Inflow

Closing Bank O/D **

**

**

**

**

**

**

Opening Bank O/D

Redumption of Preference Shares

Redumption of Long term loans

Purchase of fixed assets

Decrease in Deferred payment Liability

Cash Outflow

Tax paid

Dividend paid

Decrease in Unsecured loans, Deposits

Closing cash and bank balance **

**

**

**

**

**

**

**

**

**

** **

Ratio Analysis

A) Cash Position Ratio : -

1) Absolute Cash Ratio = Cash Reservoir

Current Liabilities

2) Cash Position to Total asset Ratio = Cash Reservoir * 100

(Measure liquid layer of assets) Total Assets

3) Interval measure = Cash Reservoir

(ability of cash reservoir to meet cash expenses) Average daily cash expenses

( Answer in days)

Notes : -

• Cash Reservoir = Cash in hand + Bank + Marketable Non trade investment at market value.

• Current liabilities = Creditors + Bills Payable + Outstanding Expenses + Provision for tax (Net of advance tax) + Proposed dividend + Other provisions.

• Total assets = Total in asset side – Miscellaneous expenses – Preliminary expenses + Any increase in value of marketable non trading Investments.

• Average cash expenses =Total expenses in debit side of P & L a/c – Non cash item such as depreciation, goodwill, preliminary expenses written off, loss on sale of investments, fixed assets written off + advance tax (Ignore provision for tax) . The net amount is divided by 365 to arrive average expenses.

Remarks : - In Comparison

• When absolute cash ratio is lower then current liability is higher

• When cash position to Total Asset ratio is lower then the total asset is relatively higher.

• When cash interval is lower the company maintain low cash position. It is not good to maintain too low cash position or too high cash position.

B) Liquidity Ratio : -

1) Current ratio = Current asset

Current Liability

2) Quick ratio or Acid Test ratio = Quick Asset

Quick liability

Notes : -

• Quick Asset = Current Asset – Stock

• Quick Liability = Current liability – Cash credit, Bank borrowings, OD and other Short term Borrowings.

• Secured loan is a current liability and also come under cash credit

• Sundry debtors considered doubtful should not be taken as quick asset.

• Creditors for capital WIP is to be excluded from current liability.

• Current asset can include only marketable securities.

• Loans to employees in asset side are long term in nature and are not part of current assets.

• Provision for gratuity is not a current liability.

• Gratuity fund investment is not a part of marketable securities.

• Trade investments are not part of marketable securities.

Remarks : -

• Higher the current ratios better the liquidity position.

C) Capital structure ratios : -

1) Debt equity ratio = Debt = External Equity

(or) Leverage ratio Equity Internal Equity

= Long term debt = Share holders fund

Long term fund Long term fund

2) Proprietary ratio = Proprietary fund

Total Assets

3) Total Liability to Net worth ratio = Total Liabilities

Net worth

4) Capital gearing ratio = Preference share capital + Debt

Equity – Preference share capital

Notes : -

• Share holders fund (or) Equity (or) Proprietary fund (or) Owners fund (or) Net worth = Equity share + Preference share + Reserves and surplus – P & L a/c – Preliminary Expenses.

• Debt (or) Long term liability (or) Long term loan fund = Secured loan (excluding cash credit) + unsecured loan + Debentures.

• Total asset = Total assets as per Balance sheet – Preliminary expenses.

• Total liability = Long term liability + Current liability (or) short term liability

• Long term fund = Total asset – Current liability = Share holders fund + long term loan fund.

Remarks : -

• In debt equity ratio higher the debt fund used in capital structure, greater is the risk.

• In debt equity ratio, operates favorable when if rate of interest is lower than the return on capital employed.

• In total liability to Net worth Ratio = Lower the ratio, better is solvency position of business, Higher the ratio lower is its solvency position.

• If debt equity ratio is comparatively higher then the financial strength is better.

D) Profitability Ratio : -

1) Gross Profit Ratio = Gross Profit * 100

Sales

2) Net Profit Ratio = Net Profit * 100

Sales

3) Operating Profit ratio = Operating profit * 100

Sales

4) Return to shareholders = Net profit after interest and tax

Share holders fund

5) Return on Net Worth = Return on Net worth * 100

Net worth

6) Return on capital employed (or) Return on investment = Return (EBIT)

Capital Employed

7) Expenses Ratios :-

a) Direct expenses Ratios : -

i) Raw material consumed * 100

Sales

ii) Wages * 100

Sales

iii) Production Expenses * 100

Sales

b) Indirect expenses Ratios : -

i) Administrative Expenses * 100

Sales

ii) Selling Expenses * 100

Sales

iii) Distribution Expenses * 100

Sales

iv) Finance Charge * 100

Sales

Notes : -

• In the above the term “term” is used for business engaged in sale of goods, for other enterprises the word “revenue” can be used.

• Gross profit = Sales – Cost of goods sold

• Operating profit = Sales – Cost of sales

= Profit after operating expenses but before Interest and tax.

• Operating Expenses = Administration Expenses + Selling and distribution expenses, Interest on short term loans etc.

• Return = Earning before Interest and Tax

= Operating profit

= Net profit + Non operating expenses – Non operating Income

• Capital employed = Share holders fund + Long term borrowings

= Fixed assets + Working capital

• If opening and closing balance is given then average capital employed can be substituted in case of capital employed which is

Opening capital employed + Closing capital employed

2

E) Debt service coverage ratios = Profit available for debt servicing

Loan Installments + Interest

Notes : -

• Profit available for debt servicing = Net profit after tax provision + Depreciation + Other non cash charges + Interest on debt.

Remarks : -

• Higher the debt servicing ratio is an indicator of better credit rating of the company.

• It is an indicator of the ability of a business enterprise to pay off current installments and interest out of profits.

F) Turnover Ratios: -

i) Assets turnover = Sales

Total assets

2) Fixed assets turnover = Sales [Number of times fixed assets has

Fixed assets turned into sales]

3) Working capital turnover = Sales

Working capital

4) Inventory turnover = Cost of goods sold

(for finished goods) Average inventory

5) Debtors turnover (or) Average collection period = Credit sales (in ratio)

Average accounts receivable

(or) = Average accounts receivable * 365 (in days)

Credit sales

6) Creditors turnover (or) Average payment period Credit purchases (in ratio)

Average accounts payable

(or) = Average accounts Payable * 365 (in days)

Credit Purchases

7) Inventory Turnover (for WIP) = Cost of production

Average Inventory (for WIP)

Inventory Turnover (for Raw material) = Raw material consumed

Average inventory (for raw material)

10) Inventory Holding Period = 365 .

Inventory turnover ratio

11) Capital Turnover ratio = Cost of sales

Capital employed

Note : -

• Working capital = Current asset – Current liability

= 0.25 * Proprietary ratio

• Accounts Receivable = Debtors + Bills receivable

• Accounts payable = Creditors + Bills Payable

Remarks : -

• If assets turnover ratio is more than 1, then profitability based on capital employed is profitability based on sales.

• Higher inventory turnover is an indicator of efficient inventory movement. It is an indicator of inventory management policies.

• Low inventory holding period lower working capital locking, but too low is not safe.

• Higher the debtors turnover, lower the credit period offered to customers. It is an indicator of credit management policies.

• Higher the creditors turnover, lower the credit period offered by suppliers.

G) Other Ratios: -

1) Operating profit ratio = Net profit ratio + Non operating loss / Sales ratio

2) Gross profit ratio = Operating profit ratio + Indirect expenses ratio

3) Cost of goods sold / Sales ratio = 100% - Gross profit ratio

4) Earnings per share = Net profit after interest and tax

Number of equity shares

5) Price earning ratio = Market price per equity share

Earning per share

6) Pay out ratio = Dividend per equity share * 100

Earning per equity shares

7) Dividend yield ratio = Dividend per share * 100

Market price per share

Fixed charges coverage ratio = Net profit before interest and tax

Interest charges

9) Interest coverage ratio = Earning before interest and tax

Interest charges

10) Fixed dividend coverage ratio = Net profit .

Annual Preference dividend

11) Over all profitability ratio = Operating profit * 100

Capital employed

12) Productivity of assets employed = Net profit .

Total tangible asset

13) Retained earning ratio = Retained earnings * 100

Total earnings

H) General Remarks: -

• Fall in quick ratio when compared with last year or other company is due to huge stock pilling up.

• If current ratio and liquidity ratio increases then the liquidity position of the company has been increased.

• If debt equity ratio increases over a period of time or is greater when comparing two ratios, then the dependence of the company in borrowed funds has increased.

• Direct expenses ratio increases in comparison then the profitability decreases.

• If there is wages / Sales ratio increases, then this is to verified

a) Wage rate

b) Output / Labour rate

• Increment in wage rate may be due to increased rate or fall in labour efficiency.

• Again there are many reasons for fall in labour productivity namely abnormal idle time due to machine failure, power cut etc.

• Reduction in Raw material consumed / sales ratio may be due to reduction in wastage or fall in material price.

• Increase in production expenses ratio may also be due to price raise.

• Stock turnover ratio denotes how many days we are holding stock.

• In stock turnover ratio greater the number of days, the movement of goods will be on the lower side.

• Financial ratios are Current ratio, Quick ratio, Debt equity ratio, Proprietary ratio, Fixed asset ratio.

• Short term solvency ratios are current ratio, Liquidity ratio

• Long term solvency or testing solvency of the company ratios are Debt equity ratio, fixed asset ratio, fixed charges coverage ratio (or) Interest coverage ratio.

• To compute financial position of the business ratios to be calculated are – current ratio, Debt equity ratio, Proprietary ratio, fixed asset ratio.

• Fictitious asset are Preliminary expenses, Discount on issue of shares and debentures, Profit and loss account debit balance.

Assignment

1) Basis of Technique used is minimization Technique

2) It can also be done in maximation Technique

3) Various steps in Assignment Problem are

Step 1: Check whether the problem is balanced or unbalanced by checking

whether row is equal to column, if unbalanced add dummy column or

row to balance the problem

Step 2: Identify Least Number in each row and subtract with all number in that

Row.

Step 3: Identify least number of each column and subtract with all number in that

column.

Step 4: Check whether solution is reached with zero selection in one row and

column, ie. Cover all the zero with minimum number of lines, solution is

reached only when selected zeros is equal to number of rows or columns

or number of lines is equal to order of matrix.

Step 5: If solution is not reached so maximum sticking

Step 6: Select the least element in within the unstriked Element

Step 7: The element selected above is

i) Subtracted with all the unstriked element

ii) Added to all the double striked element (Intersection of two lines)

Step 8: Check the solution

Step 9: If solution is not reached continue with the process from step 5.

Linear Programming

Simplex Method:-

Steps:-

1. Determine the objective function Z. Objective may be maximization or minimization.

2. For maximation problem the constraints would be < sign.

For minimization problem the constraints would be > sign.

3. Introduce slack variable

For < sign – add the slack variable ie. Add S1

For > sign – subtract the slack variable and add artificial variable

ie. Subtract S1, add A1.

4. Change the Objective function

For S1 – Add ‘0S1’

For A1 – Add ‘MA1’

5. Simplex table format:-

Cj

Quantity Variable Const. X Y Z S1 S2 RR

S1

S2

Zj

Cj - Zj

6. Zj is arrived by summation of constant column with X,Y,Z columns

7. Criteria for selecting the key column :-

For Maxima ion Problem – Highest value of Cj – Zj

For Minimization Problem – Lowest Value of Cj – Zj

8. Divide the Quantity Column with Key column to arrive at RR

9. Criteria for Selecting the Key row :-

For Maximation & Minimization Problem – Lowest Positive RR is selected

10. The Meeting Point is key Element

11. Criteria for deciding the optimal solution

For Maximation Problem – All elements in Cj – Zj row is negative or zero.

For Minimization Problem – All elements in Cj – Zj row is positive or zero

Note – For finding whether all the elements in Cj – Zj row is positive or zero

for minimization problem substitute all the ‘M’ with highest value.

12. If solution is not reached next table is formed.

13. Input for next table is

First key row in the next table is filled by dividing all the numbers in the key row of the previous table with the key element.

Remaining all the rows is arrived as follows: -

Corresponding previous _ (Value relating to that * Corresponding

Table row element row in the key column element in key row

in the 2nd table as

filled in previous step)

14. Check the optimal solution, if not reached form the third table.

15. If solution is reached then answer is amount in quantity column corresponding to the variable.

Other Points : -

• We can convert the Minimization Problem into Maximation Problem. This is known as duality.

• We can change the > sign to < sign to match the problem

E.g. X + Y < 100

is converted into -X - Y > -100

Transportation

• The procedure followed is Minimization Procedure

• Problem is generally solved in Vogel’s Approximation Method(VAM)

• Steps for the problem is : -

1. Convert profit matrix into loss matrix.

2. Balance the problem.

3. Arrive at Row penalty and column penalty

Row penalty and column penalty is calculated at (2nd least – 1st least) in the corresponding row or column.

4. Select from the entire Row penalty and column penalty maximum number.

5. From the entire Row or Column minimum is selected.

6. Strike the row or column which gets eliminated.

7. Continue until the entire item in the table is strike.

8. Write separately Initial solution table.

9. Check for Degeneracy. Degeneracy occurs when all the elements in the initial solution is equal to (Row + column – 1)

10. If degeneracy occurs introduce efcilon – ‘e’. ‘e’ is introduced in least independent cell.

11. Form UV Matrix. It is formed by the element in the original solution corresponding to the element in the Initial solution.

12. Find unalloted elements in the UV Matrix

13. Find Ij i.e.(Original Matrix element – Unalloted element found above)

14. Check for optimal solution ie. All items must be zero or positive.

15. If not reached select the maximum negative in Ij matrix.

16. Form a loop and reallocate the solution.

17. Repeat from step 9.

Notes: -

1. If there is zero in Ij matrix while arriving at optimal solution then there is another solution for the problem.

2. Dummy column can be introduced in profit or loss matrix.

3. If there is penalty/redundancy payment for unsatisfying demand etc. is given then fills the dummy row or column with that amount or fill it with zeros.

4. If there is constraint in the problem first satisfy the constraint and then solve.

5. various other methods for solving the problem is

• Least cost method

• North west corner rule

6. Generally VAM method is used

Network Analysis (CPM/PERT)

CPM

• Total float = LS – ES (or) LF – EF

• Free float = Total float – Head event slack

• Independent float = Free float – Tail event slack

• In the diagram Es = Lf in the critical path

• Critical path is the longest duration

• To find the minimum time associated cost (i.e. Additional cost incurred per unit of time saved) following formula is used :-

Crash cost per day (or) Activity cost supply

= Crash cost – Normal cost

Normal time – Crash time

• Interfacing float = It is the part of the total float which causes reduction in the float of the succession activities. In other words it is the portion of activity float which cannot be continued without affecting adversely the float of the subsequent activity or activities.

• Steps in proceeding the problem : -

2. First find and fill the ES and LF column from the diagram.

3. Then find LS and EF as follows :-

Ls = Lf – Duration

Ef = Es + Duration

4. Find total float

5. Find free float. Wherever total float column has zero free float column is also taken has zero and remaining elements is filled as said above

6. Find Independent float. Wherever free float column has zero Independent float column is also taken has zero and remaining elements is filled as said above

Notes: -

1. ES = Earliest Start. Indicates earliest time that the given activity can be scheduled

2. EF = Earliest Finish. Time by which the activity can be completed at the earliest.

3. LF = Latest Finish. Latest allowable occurrence time of the head event of the activity.

4. LS = Latest Start.

5. Total duration of the critical path is the maximum time/amount consumed for the activity. This should be crashed with respect to crashing days and crashing cost. This crashing should not change the critical path.

PERT : -

• Expected (or) Average time is found by assigning weights as follows : -

1 for optimistic

4 for Most likely

1 for pessimistic

Average time = 1 optimistic + 4 most likely + 1 pessimistic

6

• Standard Deviation = (Pessimistic time – Optimistic time)

6

• Variance = (Standard Deviation)2

• Probability of completing the project in N days

= Required time(N) (-) Expected time (critical path duration)

Standard Deviation

[Nothing but Z = (X - Mean) / Standard deviation]

= Y (say)

= Find Z(y)

= Probability %

- If required time > Expected time then = 0.5 + Z(Y)

- If required time < Expected time then = 0.5 – Z(Y)

Learning Curve

Learning is the process of acquiring skill, Knowledge, and ability by an individual. According to learning curve theory the productivity of the worker increases with increase in experience due to learning effect. The learning theory suggests that the best way to master a task is to “learn by doing”. In other words, as people gain experience with a particular job or project they can produce each unit more efficiently than the preceding one.

The speeding up of a job with repeated performance is known as the learning effect or learning curve effect.

The cumulative average time per unit produced is assumed to fall by a constant percentage every time the total output is doubled. So generally learning effect is found in the multiples of 2. If learning curve effect is asked between two even numbers then Learning curve equation is formed ie. Learning curve effect is expressed mathematically as follows:

Learning curve equation =

Y = a(x) -b Where Y = Average time per unit

a = Total time for first unit

x = Cumulative number of units manufactured

b = the learning curve index

Learning curve index (b) = log (1- % decrease)

Log 2

Management Accounting and Financial Analysis

International Financial Management

1. Direct Quote (eg) 1$ = Rs.49

2. Indirect Quote (eg) Rs.1 = .0204$

3. TT Rate = Telegraphic Transfer Rate

4. TOM Rate = Tomorrow Rate

5. Spot Rate = Today’s rate. Normally it will be 3td day rate from TT Rate.

Direct Quote is used in all country except UK where indirect quote is used.

Offer Rate = Selling Rate

Spread Rate = Offer Rate – Bid Rate

Spread Rate (%) = Offer Rate – Bid Rate * 100 (111lr to that of NP Ratio)

Offer Rate

Swap points is ascending stage it is at premium. If it is descending stage it is at discount.

If it is said as INR/$ then the meaning is

• Numerator factor = Local Currency = INR

• Denominator factor = Foreign Currency = $

Forward Quotation (%) (I.e. Premium/Discount expressed at annualized %)

= Forward Rate – Spot Rate * 12 * 100 (in months)

Spot Rate n

= Forward Rate – Spot Rate * 365 * 100 (in days)

Spot Rate n

If the quote is direct or Indirect is to be found and the relation is with £ (pound) both direct and Indirect quote is to be said.

Maturity Value = P (1+r) n

Interest Rate Parity:

i) Domestic Rate < Foreign Rate + Forward Premium / Discount

(In this case invest in foreign currency)

ii) Domestic Rate > Foreign Rate + Forward Premium / Discount

(In this case invest in Domestic Currency)

Forward Rate: It is rate negotiated for the delivery to be made / taken on a future date for present transaction.

Future spot rate: It is actual rate prevailing on the agreed future date.

Other points:-

• Currency country which has less Interest rate will have forward rate at premium and vice versa

• If two rates ie.20.23 / 35 is given then highest rate is offer rate, lowest rate is bid rate.

• If INR / DG is given and we have to DG / INR then it is 1 / (INR / DG)

• 1 / (Bid Rate) = Offer Rate.

• 1 / (Offer Rate) = Bid Rate.

Interest rate swap: - Generally interest rate differs from company to company because of their grade (reputation) and rates can be fixed rates or floting rate. If there is 2 company under different grade and different fixed / floating rate can gin advantage by reducing their interest rate by “Interest rate swap”.

In this if ‘Company A’ wants to borrow at floating rate and ‘Company B’ wants to borrow and fixed rate, then interest rate swap is applied by which company A borrows at floating Rate of company B and company B borrows at fixed rate of company A. By this swap one company gains and other company losses. Net gain is splited between two companies so that the two companies benefits by paying lower interest rate for their barrowing.

To look at the problem quickly the theory followed in “Difference in fixed rate interest of two companies is profit” and “Difference in floating rate interest of two companies is loss”. Then net gain / loss are found.

Capital Budgeting

Process of Capital Budgeting:

• Huge cash outlay.

• Decision taken is irressable.

• Invest in lumsum the receipt is piecemeal

• Wrong decision will affect the very base of the company.

Capital Budgeting Rules:

• Ignore accounting profit and take only cash flows.

• Try only incremental basis ignore Average calculation.

• Consider all incidental effects.

• Ignore sunk cost (ie. Cost remain unaltered for various alternatives available is sunk cost)

• Consider opportunity cost (Opportunity Loss is Opportunity cost)

• Beware of allocated cost – Ignore them

• Depreciation is an important cash flow when taxation is considered. If no taxation, no depreciation.

• Interest should not be considered as part of the cost, in the arrival of cash inflow for investing decision problems. If deducted add back post tax interest.

• Separate investing decision and financing decision.

• Be consistent with inflation rates. All future cash flows is assumed as without inflation. Such cash flows are referred as real cash flows.

• Cash flows under the influence of inflation would be referred to as money cash flows. (Money cash flows (or) Nominal Cash Flows (or) Market cash flows)

• Unless otherwise stated cost of capital is considered after tax basis because cash flows will be considered only on after tax basis. (PV factor is the inverse of compounding factor)

• Equation to find out the PV of an amount if cost of capital and Inflation rate is given

(1 + Money Rate) = (1 + Real Discount rate) * (1 + Inflation Rate)

Method of evaluating Capital Budgeting:

1. Pay back method

2. Annual Rate of Return

3. Discounted cash flow

• Net Present Value (NPV)

• Internal Rate of Return (IRR)

• Profitability Index (PI) (or) Benefit cost Ratio

• Equated Annuity Cost (EAC) (or)

Equated Annuity Benefit (EAB)

• Discounted Pay Back (or) Time adjusted BEP

Expressed

In Bench mark

(Basis of

Selection) Formula When to use

Pay Back

Period Years Shortest Recovery time

of investment When no cost of capital is given

Annual Rate Of Return % Highest 1) AR / II

2) AR / AI When no cost of

capital is given

NPV Rs. Greatest

Value Discounted CI

- Discounted CO When two projects is same in all aspects ie. No disparity

IRR % Highest At this rate

Discounted CI = Discounted CO

and NPV = 1,

PI = 1 Rarely used in

finding Cost of Capital.

Profitability

Index (PI) Points Highest Discounted CI

Discounted CO Size Disparity

EAC (or)

EAB Rs. EAC =

Lowest

EAB =

Highest EAC =

Discounted CO

PV Factor

EAB =

1) Discounted CI

Annuity Factor

2) NPV

PV Factor Life Disparity

Discounted

Pay Back Years Shortest Recovery time of Investment Break even time

Where: - AI = Average Investment CI = Cash Inflow

AF = Annuity Factor CO = Cash Outflow

II = Initial Investment

Internal Rate of Return (IRR):-

IRR otherwise called as yield on investment, Marginal efficiency of capital, Marginal productivity of capital, Rate of Return, Time adjusted rate of return.

Discounting + Difference calculated in present value and required cash outlay

Factor Difference in calculated present values

* Difference in Rate

To approximately locate the factor in which the amount returns

F = I / C Where F = Factor to be located

I = Original Investment

C = Average Cash Inflows per year

In the PV table year column must be seen to trace the nearest fake annuity. Year column is the year of economic life of machine.

Notes: - If actual cash flow is higher than average cash flows in the initial years then increase the fake IRR point a few % upward. If it is lower in the initial years then decrease the percentage few points lower to find fake IRR

If discount rates are not known but cash inflows and outflows are known then IRR is calculated as I = R / (1+r)

Where I = Cash outflow (or) Initial Investment

R = Cash inflow

R = Rate of return yielded by the Investment (or IRR)

Calculating Discounting Factor:-

1 / (1+rate) n Where n = Years

Method of ranking projects:-

Desirability factor (Profitability Index) vs. NPV Method vs. IRR

Selection of projects out of two mutually exclusive projects having same funds at disposal then NPV method is preferred.

In IRR Method the presumption intermediate cash inflows are reinvested at same rate i.e. IRR. But in NPV method it is reinvested at cut off rate.

Reinvestment at cut off rate is more possible than IRR. Hence Net Present Values being obtained from discounting at a fixed cut off rate are more reliable in ranking 2 or more projects than IRR.

Models of Risk Analysis:-

i) Hiller’s Model: He takes into account mean of present value of the cash flows and the SD of such cash flows.

n

M = (1+r)-1 mi (used to determine the present value of mean)

i=0

n

2 = (1+r)-2i * 2i (Used to find the present value of variance)

i=0

Where mi =Mean of cash flow in the ith period – expected cash flow for year i

2i = Variance in the ith period.

r = Discounting Factor

M = Total of Present value of mean

2 = Total of present value of variance

Bench mark = Project with lower SD will be preferred.

1) Real Cash flows restated in terms of nominal cash flows as follows:-

(1 + inflation rate) * Real cash flows

After this discounting cash flow is applied to find NPV.

2) Converting nominal discounting rate into real terms

Real discount rate = 1 + Nominal discount rate - 1

1 + inflation rate

With this real discount rate the Cash Inflows are discounted to find NPV.

3) Pay back reciprocal

= Average annual cash inflows (It is used for reasonable approximation of

Initial Investment IRR)

4) The formula for deflation is

Index Number at the beginning * Cash Inflows

Index Number at the end

(or) Cash Inflows / (1+Inflation Rate) n

Note: If in a problem Real cash flows are given and Inflation Rate and Cost of Capital is given then

i) Convert Real Cash Flows into Normal Cash Flows by using formulae said in (1) above.

ii) Adjust for Depreciation and tax and find Cash Flow after Tax before Depreciation.

iii) Deflate the amount arrived above by using formulae said in (4).

iv) With the amount arrived above find NPV using COC.

Summary:-

i) Risk Adjusted Discount rate approach

= NPV for CFAT at Risk adjusted Discount Rate.

ii) Certainty Equivalent Approach

= NPV for (Certainty Equivalent Coefficient * CFAT) at Risk less Interest rate.

iii) Probality Discount approach

= NPV for (CF) at risk less Interest rate.

Analysis of Risk and Uncertainty

1) Sensitivity Analysis: - It provides different cash flow estimates under 3 assumptions a. worst

b. The expected (Most likely)

c. The best.

NPV is found under these three assumptions and decision is taken.

2) Precise measure of risk:-

a) Standard deviation: - Absolute measure of risk.

n

= √ ∑ Pi ( CF – CF ) 2

i=1

CF = Cash flow i = Year

CF = Mean cash flow (CF of particular projects total divided by number of CF)

= ∑ CF * P

P = Probability

n

b) Variance = ( ) 2 = ∑ Pi ( CF – CF ) 2

i=1

c) Co – Variance (a,b) = Pi ( CFa – CFa ) ( CFb – CFb )

d) Coefficient of correlation of two variable factor = Co – Variance (a,b)

a b

e) Return of portfolio = Wa * Ra + Wb * Rb Where W – Proportion invested

R – Return

f) Risk of portfolio = √ Pa2 * a2 + Pb2 * b2 + 2Pa * Pb * a * b * Cor(a,b)

g) Co – Efficient of variation = A relative measure of risk.

Standard Deviation

V= Expected cash flow (or) mean (or) CF

(Or) Expected NPV (NPV)

NPV = NPV * Probability

h) Risk adjusted discount rate approach: - In this risk adjusted discount rate is taken as PV factor and calculated as NPV method.

=∑ (CFAT) t - CO Where Kr = Risk adjusted discount rate

(1 + Kr) t

i) Certainty Equivalent (CE) approach = Risk less Cash Flow

Risky Cash Flow

j) If Correlation Coefficient [Cor(a,b)] is

Cor(a,b) p .

+1 (Pa * a) + (Pb * b) [ie. If it is perfectly positively correlated]

-1 (Pa * a) – (Pb * b) [ie. If it is perfectly negatively correlated]

0 Above p formula will apply

k) Probability Distribution approach: -

t (SD of CF) = √ ∑ p (CF – CF)2 = ∑ CF - CO = NPV

(1+i) t

Where

CF = Cash Flow CF = Mean i.e. Total of cash flow multiplied by probability for the period (or) expected value for CFAT in period t)

i = Risk less rate of interest.

t = SD for period t (SD for particular period)

l) SD for the probability distribution of NPV is (ie. SD of CF)

(NPV) = √ ∑ ( t2) / (1 + i) 2t (this is used for uncorrelated CF)

(NPV) = ∑ ( t) / (1 + i) t (used for perfectly correlated CF)

Where I = Rate of Return.

m) Optimum proportion at which risk is minimum = Xa = b / ( a + b)

(or) a X - b (1-X) = 0

NPV for the period is calculated by taking CF as CF for respective period and calculated normally

Note:-

i) In certainty Equivalent approach rate of discount is the risk less rate of Interest as the risk is adjusted with CFAT.

ii) In this case CFAT is multiplied with certainty equivalent and PV is calculated by risk less rate of interest.

iii) If projects are ranked with respect of risk and return. Project with respect

to risk requires ∑ NPV (i.e. ∑(NPV * Probability)) and the project with respect to

return find co-efficient of variation = / ∑ NPV

iv) Probability that NPV would be Zero or less

Z = 0 – NPV The Z Value is converted with the ‘Z Table’

values and the probability of the NPV being

zero or less would be = 0.5 – (Z Value).

v) Probability that NPV being greater than Zero would be

1 – (Probability less than Zero)

vi) Probability that NPV within the range X and Y

Z1 = X – NPV Z2 = Y – NPV

vii) If in the Risk adjusted Discount approach both cost of control and Risk adjusted discount rate is given

• For the CF of the years apply Risk adjusted discount rate to find Discounted CF.

• For the Scrap value of the machine after the end of the life the CF on sale is discounted at cost of capital % to find Discounted CF.

viii) If probability (or) Certainty equivalence is given then find the Adjusted

CF (CF * Probability) and then use the Risk less Rate of return to find Discounted CF.

ix) Risk is Standard deviation

Summary:-

i) Risk Adjusted Discount Rate Approach

= NPV for CFAT at Risk Adjusted Discount Rate

ii) Certainty Equivalent Approach

= NPV for (CE coefficient * CFAT) at Risk less interest rate

iii) Probability Discount Approach

= NPV for (CF) at Risk less Interest Rate

Derivatives

Call Option: - Gives buyer “Right but not the obligation” to buy the share.

Put Option: - Gives buyer “Right but not the obligation” to sell the share.

Value of the Call Option:-

i) Black Scholes Model:-

Value of the call option = VO

= [S * N (d1)] – [(x) * (e-t*rf) * (N (d2))]

Where d1 = ln (s/x) + (rf + { 2 / 2}) * t

√t

ln = Natural log

d2 = d1 - √t

s = Present spot rate

x = Future strike (excise) price

rf = Risk free rate

Seven step to solve the problem:-

i) Find log (s/x)

ii) Find d1

iii) Find d2

iv) Find N (d1)

v) Find N (d2)

iv) Find N (d1) Normal Table Value

+ 0.5

v) Find N (d2)

vi) Find ‘e’ value

vii) Apply Black Schools Model.

Sub step to step 1:-

a) Log (s/x) = Log s – Log x

0.4343

b) If x and s are 2 digit figure the value shall be (1 + Log table value).

c) If x and s are 3 digit then the value shall be (2 + Log table value).

Sub step to step 6:-

a) It is to find the power value of ‘e’.

b) e-t*rf = 1 (or) 1 .

1 + r/365 * No. of days (t) 1 + r/365 * No. of Months (t)

Value of Put option: -

= [(x) * (e-t*rf) * (N (-d2))] - [S * N (-d1)]

Excise price:-

It is the price at which the person writes the prices on a share to buy after a period.

Expected Value of the share:-

It is the total of estimate market price of the share multiplied with the respective probability.

Expiration value: - Excise price – Expected Value

Expected (or) Theoretical value of the call option price at expiration (Pay off of Call option) :-

= ∑ (Estimated market price – Excise Price) * Probability (or)

= [Max (s – x), 0] * Probability

Pay off of call option

Expected (or) Theoretical value of the put option price at expiration (Pay of put option):-

= ∑ (Excise Price - Estimated market price) * Probability (or)

= [Max (x – s), 0] * Probability

Pay off of Put option

Where (Estimated market price – Excise Price) is called pay off. If it is negative it is taken as zero.

s = Estimated Market Price.

Put call parity = Put call parity equation is

(Value of call option + Present value of excise price) = (value of put option +

Spot rate)

Note:-

i) Changes to be made in computation of Black Scholes model for dividend stocks:-

Substitute in all the places of “s” with “s – PV of dividend”

ii)In the above all PV is found at Risk free rate.

Beta

Beta means, it measures the volatility of securities to the changes in the market.

β (level of risk) = s * Cor (s,m) where s = SD of return on securities

m m = SD of return on market portfolio

(or) Covariance(s,m) / 2m

β should always be applied on risk premium and not to the entire return.

rs = rf + (rm – rf ) * β Where rf = Risk free rate

rs = Expected return on securities (or) [Capital

Appreciation + Dividend of the company]

rm = Expected return on market portfolio (or)

[Market index {Market rate} appreciation + Market dividend yield %]

Portfolio Theory (PT):-

rp (expected return under CML) = rf + (rm – rf) * ( p / m)

The above formula is based on total risk.

Where p = SD of efficient portfolio.

When expected return under efficient portfolio is asked then

rp (expected return under efficient portfolio) = Capital market line(CML) –

Express equilibrium price relationship between expected return and DS

Capital Asset Pricing Model (CAPM):-

rs (expected return portfolio in CAPM) = rf + (rm – rf) * [( s / m) *

cor(s,m)]

(or) rf + [(rm – rf)] * β

Where rm = rf + Market premium

Beta of the portfolio = ( βa * Pa ) + ( βb * Pb )

Where Pa, Pb = Proportion of investment in Company A and Company B.

Note:-

i) (rm – rf) = Market risk premium (or) Compensation per unit of risk.

ii) Cor(s,m) is +1 under CML

iii) rf + (rm – rf) * [( s / m) * cor(s,m)] = This portion in CAPM formula is

risk premium

iv) (rm – rf) / m = Market risk return trade off (slope).

Notes:-

To find the investment to be made in risk free investments to get a certain β is

β of expected portfolio = (W1 * β1) +(W2 * β2)

(or) = (W1 * β1) + (1-W1) β2

Where W1 is weitage given to existing securities.

W2 is weitage given to risk free securities.

In this case β1 is β of existing securities and

Β2 is β of rf securities (ie.0)

This can also be use to find investment in other then rf securities. In that case that β is substituted in β2.

The weitage (W1,W2) is multiplied with market value of existing portfolio to find the proportion of investment.

Holding Companies

Index of Main Points:-

1. If there is a Debit balance in Minority Interest first it is adjusted against uncalled capital and balance is adjusted against reserve.

2. In case of Cumulative Preference shares of subsidiary dividend declared must be deducted from P & L a/c of subsidiary.

3. If no dividend is declared in above case then don’t deduct.

4. If dividend is declared for Cumulative Preference shares then deduct from P & L a/c of subsidiary and balance is splited. If not declared then it must be shown outside the Balance sheet.

5. But in the case1

6. CFS deduct in the above case whether declared or not.

7. Preference shares of subsidiary held by the holding company is to be cancelled against investment of Holding company while preparing CFS.

8. If Holding company sells goods below cost then unrealized loss is calculated by taking cost or Net Realizable Value whichever is lower for valuation.

9. If there is difference in accounting policy between Holding and subsidiary then both should be brought under uniform policy before consolidation.

10. If uniform policy cannot be brought then it should be disclosed.

11. The effect of change in Accounting Policy before acquit ion must be taken as pre acquit ion reserve and after post acquit ion reserve.

12. If Holding Company holds Debenture in subsidiary then while preparing CFS it should be cancelled as Inter Company loan.

13. In above case if excess is paid for Debenture holders then the excess is adjusted against consolidated reserve.

14. Pre acquit ion reserve and profit is treated as capital profit

15. Post acquition reserve and profit is treated as revenue reserve and revenue profit respectively.

16. Miscellaneous expenses of subsidiary must be deducted against reserve as Capital or Revenue Reserve.

17. In case of Inter Company transactions if it is down stream then unrealized profit of Holding company must be adjusted against Consolidated P & L a/c.

18. In case of Inter Company transaction if it is upstream it is splited into two as belonging to Holding company and Minority Interest and the former is deducted against Consolidated P & L a/c and Minority Interest is deducted from computation of Total Minority Interest.

19. Post acquit ion dividend received is to be retained in P & L a/c.

20. Pre acquit ion dividend received is to be transferred from Holding company P & L a/c to Cost of Investment.

21. Post acquit ion dividend receivable (Proposed) by Holding company out of subsidiary current year profit is to now credited to Holding company Consolidated P & L a/c.

22. In case of analysis of profit Proposed Dividend must be deducted from current year profit only.

23. If in the above case if there is inadequate profit for dividend, the appropriation should be done 1st out of current year profits and thereafter out of b/f profit.

24. In case Inter Company sale or purchase is carried between two subsidiaries then for consolidated stock it is considered as it is 1st transferred from one subsidiary to Holding – upstream rule apply and then from Holding to 2nd subsidiary – Down stream rule apply.

25. In Inter Company transaction if there is sale of Fixed Asset between Holding and Subsidiary unrealized profit should be removed only to the extent of unamortized portion.

26. In the absence of information regarding rate of depreciation, depreciation must be ignored.

27. In case of acquition and sale of shares, profit on such sale must be included in P & L a/c while calculating reserves for CBS.

28. In the event of current year dividend is greater than the trading profits AND if there is another source of income i.e. Subsidiary dividend then the dividend declared must be deducted only in Apportionment of profits.

29. Inter corporate loans in general refer to borrowings from corporate bodies.

30. In case of reverse working

for stock consolidation = Company A + Company B – Stock reserve

for Debtors and creditors = Company A + Company B – Inter company

consolidation transactions

31. In case of Associate accounting Inter Company transaction should not be cancelled only Holding company interest of unrealized profit is only taken.

32. Losses in associate are taken only up to the liability in share capital.

33. Minority Interest calculation is not applicable in case of associate accounting.

34. In the case where subsidiary company is foreign company then convert the accounts into Indian Currency and remaining are same. For conversion rules applicable are:-

Share capital – Rate on the date of acquition of share.

Reserves – Pre – Rate on the date of acquition

Post – Average rate

Current Assets, Current liabilities – Closing rate

Fixed assets, Investments – Rate on the date of acquition

35. Exchange rate difference which occurs on the above conversion is to be setoff against post acquition Profit / Reserves and the balance is only to be apportioned for consolidation procedure.

36. In case of two or more acquition by Holding Co. (or) acquition and sale, In all the cases date for apportionment etc is the date of 1st acquition and share holding pattern is the final share holding pattern.

37. In case of Associate accounting, to find the carrying amount of Investment of the associate in the consolidated balancesheet the calculation is similar to minority interest. Only difference is to add the goodwill found in COC.

,ie, Share Capital ***

(+) Capital Profit ***

(+) Revenue Profit ***

(+) Goodwill *** ***

Amalgamation

Index of Main Points:-

1. Points to be satisfied to treat the amalgamation in the nature of merger

• All assets and liabilities of transforer is to be taken over at their book values by resulting company

• All or at least 90% of the Share Holding of Amalgamating Company must be the Share Holders of Amalgamated Company.

• Equity shares of selling company must be given only equity shares of purchasing company.

• Liabilities of Transferor must not be discharged; it must be taken over by the resulting company. But exemption is the fraction shares can be given in cash.

• Same risk and return and nature of company must be same.

2. Order of Adjustment of consideration is first General Reserve and then P & L a/c. If the problem has statutory reserve it should not be adjusted. It is carried over as such.

3. As per SEBI guidelines, underwriting commission is 2.5% on equity shares and on 1st 5000 Preference Shares it is 1.5% and the balance Preference Shares it is 1%.

4. Capital employed is considered as Net Revaluation amount of Tangible Asset.

5. In case purchasing company holding shares in selling company, Net asset method is applied as usual and outside shareholders portion is calculated separately as balancing figure.

6. If in the above case, settlement of equity share holding of selling company is given then that exchange pertains to outside share holder’s settlement and it should not be splitted.

7. In the books of selling company the shares held by the purchasing company must be cancelled by transferring it to realization a/c

Equity share capital a/c Dr

To Realization

8. If Preference share holders of selling company is discharged by preference share holders of purchasing company at premium then the premium portion must be transferred to realization a/c in the books of selling company.

9. In case of Merger while drafting Journal Entry in the books of purchasing company for Incorporation of Asset & Liability in the workings, the consideration is aggregate consideration including shares already purchased by purchasing company and current purchase payable.

10. In case of merger in the books of purchasing company while calculation excess / shortage to be adjusted against the reserve of selling company. The purchase consideration is aggregate consideration including amount already paid (shares of selling company held by purchasing company) + amount now paid (amount paid to outsiders).

11. Business purchase in case of shares of selling company held by purchasing company is the amount given to outsiders only.

12. If in the asset side of selling company Debtors is given as Gross (–) Reserves / Provision for Doubtful Debts then in the books of selling company while transferring all assets and liabilities to realization account Debtors is transferred at gross amount and provision is transferred along with liability.

But in the above case in the books of purchasing company while

incorporating assets and liabilities of selling company debtors is taken net of

provisions.

13. On entry for takeover of assets and liabilities of selling company in purchasing company books – Assets debited must be excluding goodwill in purchase method and difference in debit or credit is treated as Goodwill / Reserves.

14. Investment allowance Reserve is not a current liability.

15. When purchasing company holding shares in selling company then the shares held by purchasing company must be cancelled in the selling company books.

16. While canceling the shares held by the purchasing company it must be cancelled at fair value.

17. To bring the reserve like Investment allowance reserve in purchasing company books the entry will be Amalgamation adjustment a/c Dr

To Investment allowance reserve

In the amalgamated B/S investment allowance reserve will appear in

the liability side and amalgamation adjustment account will appear in the asset side for same amount.

18. Incase of Inter Company holding if divided is declared by any one company then dividend receivable by other company is to be 1st incorporated as pre amalgamation event. Dividend receivable account Dr

To P & L a/c

Entry in the 1st company which has declared dividend P & L a/c Dr

To proposed dividend

19. In case of Internal reconstruction cancellation of Arrears Dividend forgone by shareholder will not affect the B/S. So no entry. In this case Arrears of dividend is seazed to be contingent liability. Preference shareholders will seize to have the voting right at par with equity shares which was available due to arrears of dividend.

20. In Demerger while making transfer entry of Asset and liability in purchasing company fixed asset net is to be taken but while making the transfer entry in selling company fixed asset gross is taken in credited and provision for depreciation is debited.

21. In case of Inter Company / Single side holding etc. to find the intrinsic value of each company, the investment held by one company in the shares of other company is also to be valued as intrinsic value only and not to be taken at book value. For inter company holding this intrinsic value of shares of each company can be found by framing a linear equation.

22. In case of calculation of purchase consideration (Cross holding)

Total number of shares in selling company ***

(-) Share already held by Purchasing company ***

Number of shares held by outsiders ***

Value of above number of shares Rs. ***

Number of purchasing company to be issued to selling company ***

(-) Number of shares already held by selling company ***

Net number of shares purchasing co. has to issue to selling co. ***

23. In case of settlement of shareholders of selling company the amount will be = Shares now received from purchasing company + Purchasing company shares already held by selling company.

24. In amalgamated B/S if there is Debit in P & L a/c it should be netted of with General Reserve as per schedule VI.

25. In case of assets and liabilities is taken over at revalued amount it is in the nature of purchase and in the journal entry for incorporating account takenover only the revalued amount is to be taken.

26. In case of selling company holding shares in purchasing company then investment is to be valued at intrinsic value if specified.

27. In the above case of holding company gives shares at particular value to the subsidiary company for settlement then investment is to be valued at the value

28. When selling company holding shares in purchasing company then while transferring assets and liabilities to realization account in selling company books, Assets transferred must be excluding the Investment in purchasing company.

**2** Great job!!!!!!!!!! on Wed 27 Jan 2010 - 18:00

#### Ankita

Great job done!!!!!

i must have studied these notes before the Dec 2009 exams. anyway i will read again now.

Thanks!

i must have studied these notes before the Dec 2009 exams. anyway i will read again now.

Thanks!

**3** Re: FM Notes for Final students on Wed 3 Feb 2010 - 13:22

#### bhomiavarun

CSoC Smart User

koi baat nahi madam , Forward it ot your juniors let them to take benefit of the same.

n however it is also useful in M. Com n B.Com as well.

n however it is also useful in M. Com n B.Com as well.

**4** Re: FM Notes for Final students on Fri 14 Sep 2012 - 15:39

**5** Re: FM Notes for Final students on Mon 17 Sep 2012 - 11:46

#### mione

CSoC Master

thanx a lot

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