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Thread: MGT201 Fm formulas for attempting the final term exam fall 2010

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    MGT201 Fm formulas for attempting the final term exam fall 2010

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    These are the formulas which will help students when they are going to attempt the final term exams. Just try to memories them. So i am sharing this file please check it.
    Fundamental Accounting Equation and Double Entry Principle.

    Assets +Expense = Liabilities + Shareholders’ Equity + Revenue

    Liabilities = Equity = Net Worth

    Revenue – Expense = Income
    Statement of Retained Earnings or Shareholders’ Equity Statement

    Total Equity = Common Par Stock Issued + Paid In Capital + Retained Earnings
    Current Ratio:

    = Current Assets / Current Liabilities

    Quick/Acid Test ratio:

    = (Current Assets – Inventory) / Current Liabilities

    Average Collection Period:

    = Average Accounts Receivable / (Annual Sales/360)

    PROFITABILITY RATIOS:

    Profit Margin (on sales):
    = [Net Income / Sales] X 100
    Return on Assets:
    = [Net Income / Total Assets] X 100
    Return on equity:
    = [Net Income/Common Equity]
    ASSET MANAGEMENT RATIOS

    Inventory Turnover:
    = Sales / inventories
    Total Assets Turnover:
    = Sales / Total Assets

    DEBT (OR CAPITAL STRUCTURE) RATIOS:

    Debt-Assets:
    = Total Debt / Total Assets

    Debt-Equity:
    = Total Debt / Total Equity
    Times-Interest-Earned:
    = EBIT / Interest Charges

    Market Value Ratios:
    Price Earning Ratio:
    = Market Price per share / *Earnings per share

    Market /Book Ratio:
    = Market Price per share / Book Value per share
    *Earning Per Share (EPS):
    = Net Income / Average Number of Common Shares Outstanding

    M.V.A (Market Value Added):

    MVA (Rupees) = Market Value of Equity – Book Value of Equity Capital
    E.V.A (Economic Value Added):

    EVA (Rupees) = EBIT (or Operating Profit) – Cost of Total Capital

    Interest Theory: Economic Theory:

    i = iRF + g + DR + MR + LP + SR
    – i is the nominal interest rate generally quoted in papers. The “real” interest rate = i – g
    Here i = market interest rate, g = rate of inflation, DR = Default risk premium
    MR = Maturity risk premium, LP = Liquidity preference, SR = Sovereign Risk

    Market Segmentation:
    Simple Interest (or Straight Line):

    F V = PV + (PV x i x n)
    Discrete Compound Interest:
    Annual (yearly) compounding:
    F V = PV x (1 + i) n

    Monthly compounding:
    F V = PV x (1 + (i / m) m x n

    Continuous (or Exponential) Compound Interest:
    F V (Continuous compounding) = PV x e i x n


    Estimated current assets for the next year
    = [Current assets for the current year/Current sales] x Estimated sales for the next year

    Expected Estimated retained earnings
    = estimated sales x profit margin x plowback ratio

    Estimated discretionary financing
    = estimated total assets – estimated total liabilities –estimated total equity

    G (Desired Growth Rate)
    = return on equity x (1- pay out ratio)

    Cash Flow Statement

    Net Income
    Add Depreciation Expense

    Subtract Increase in Current Assets:
    Increase in Cash
    Increase in Inventory

    Add Increase in Current Liabilities:
    Increase in A/c Payable

    Cash Flow from Operations
    Cash Flow from Investments
    Cash Flow from Financing
    Net Cash Flow from All Activities
    Interest Rates for Discounting Calculations
    Nominal (or APR) Interest Rate = i nom
    Periodic Interest Rate = i per
    It is defined as
    iper = ( i nominal Interest rate) / m
    Where
    m = no. of times compounding takes place in 1 year i.e.
    If semi-annual compounding then m = 2

    Effective Interest Rate = i eff
    i eff = [1 + ( i nom / m )]m – 1

    Calculating the NPV of the Café Business for 1st Year:
    NPV = Net Present Value (taking Investment outflows into account)
    NPV = −Initial Investment + Sum of Net Cash Flows from Each Future Year.
    NPV = − Io +PV (CF1) + PV (CF2) + PV (CF3) + PV (CF4) + ...+ ∞

    Annual Compounding (at end of every year):

    FV = CCF [(1 + i) n– 1] / i

    Annual Compounding (at end of every year)

    PV =FV / (1 + i ) n n = life of Annuity in number of years

    Multiple Compounding:
    Future Value of annuity =CCF (constant cash flow)*[(1+ (i/m) m*n-1] / ( i/m )

    Multiple Compounding:
    PV =FV / [1 + (i/m)] mxn
    Future value of perpetuity:
    =constant cash flow/interest rate
    Future value by using annuity formula
    FV =CCF [(1+i) n- 1]/ i

    Return on Investments:
    ROI= (ΣCF/n)/ IO

    Net Present Value (NPV):
    NPV= -IO+ΣCFt/ (1+i) t
    Detail
    NPV = -Io + CFt / (1+i)t = -Io + CF1/(1+i) + CF2/(1+i) 2 + CF` /(1+i) 3 +..

    -IO= Initial cash outflow
    i=discount /interest rate
    t=year in which the cash flow takes place

    Probability Index:
    PI = [Σ CFt / (1+ i) t]/ IO

    Internal Rate Of Return(IRR) Equation:
    NPV= -IO +CF1/ (1+IRR) + CF2/ (1+IRR) 2

    Internal Rate of Return or IRR:
    The formula is similar to NPV
    NPV = 0 = -Io + CFt / (1+IRR)t = -Io + CF1/(1+IRR) + CF2/(1+IRR) 2+ ..

    Modified IRR (MIRR):
    (1+MIRR) n= Future Value of All Cash Inflows….
    Present Value of All Cash Outflows
    (1+MIRR) n= CF in * (1+k) n-t
    CF out / (1+k) t

    Equivalent Annual Annuity Approach:

    EAA FACTOR = (1+ i) n/ [(1+i) n-1]
    Where n = life of project & i=discount rate

    BONDS’ VALUATION

    The relationship between present value and net present value
    NPV = -Io + PV
    Present Value formula for the bond:
    n
    PV= Σ CFt / (1+rD)t=CF1/(1+ rD)+CFn/(1+ rD)2+..+CFn/ (1+ rD) n+PAR/ (1+ rD) n
    t =1
    In this formula
    PV = Intrinsic Value of Bond or Fair Price (in rupees) paid to invest in the bond. It is the Expected or Theoretical Price and NOT the actual Market Price.
    rD= Bondholder’s (or Investor’s) Required Rate of Return for investing in Bond (Debt). Different from the Coupon Rate!

    YTM =Total or Overall Yield:
    = Interest Yield + Capital Gains Yield
    Interest Yield or Current Yield:
    = Coupon / Market Price

    Capital Gains Yield:
    = YTM - Interest Yield

    FV=CCF[(1+rD/m)n*m-1]/ rD /m
    N=1 year ,m= no. of intervals in a year =12
    CCF=constant cash flow
    n = Maturity or Life of Bond (in years)

    Call:
    =par value +I, year coupon receipts

    Another thing to keep in mind is that YTM has two components first is
    YTM:
    =interest yield on bond +capital gain yield on bond


    INTEREST YIELD =annual coupon interest /market price
    CAPITAL YIELD =YTM –INTEREST YIELD

    Perpetual Investment in Preferred Stock
    PV = DIV 1 / r PE

    Perpetual Investment in Common Stock:
    PV = DIV1/(1+rCE) +DIV2/(1+rCE)2 +…..+ DIVn/(1+rCE)n + Pn/(1+rCE)n
    PV = Po* = Expected or Fair Price = Present Value of Share, DIV1= Forecasted Future Dividend at end of Year 1, DIV 2 = Expected Future Dividend at end of Year 2, …, Pn = Expected Future Selling Price, rCE = Minimum Required Rate of Return for Investment in the Common Stock for you (the investor). Note that Dividends are uncertain and n = infinity
    PV (Share Price) = Dividend Value + Capital Gain.
    Dividend Value is derived from Dividend Cash Stream and Capital Gain / Loss from Difference
    Between Buying & Selling Price.

    Simplified Formula (Pn term removed from the equation for large investment durations i.e. n =
    Infinity):
    PV = DIV1/ (1+rE) + DIV2/ (1+rE) 2+ … DIVn/(1+rE)n
    = DIVt / (1+ rE) t. t = year. Sum from t =1 to n

    Fair Value. Dynamic Equilibrium.
    If Market Price > Fair Value then Stock is Over Valued
    Share Price Valuation -Perpetual Investment in Common Stock:

    Zero Growth Dividends Model:
    DIV1 = DIV 2 = DIV3

    The Formula for common stock
    PV = Po*= DIV1 / (1+ rCE) + DIV1 / (1+ rCE) 2 + DIV1 / (1+ rCE) 3 + ... +...
    = DIV 1 / rCE

    Dividends Cash Flow Stream grows according to the Discrete Compound Growth Formula
    DIVt+1 = DIVt x (1 + g) t.
    t = time in years.

    Zero Growth Model Pricing
    PV = Po* = DIV1 / rCE

    Constant Growth Model Pricing
    PV = Po* = DIV1 / (rCE -g)

    Dividends Pricing Models:
    Zero Growth: Po*=DIV1 / rCE (Po* is being estimated)

    rCE*= DIV1 / Po (rCE* is being estimated)
    Similarly,

    Constant Growth: Po*= DI V1/ (rCE -g)
    rCE*= ( DIV 1 / Po) + g


    use this formula to calculate the required rate of return.

    Gordon’s Formula:
    rCE*= (DIV 1 / Po) + g

    In this the first part
    (DIV 1 / Po) is the dividend yield
    g is the Capital gain yield.

    Earning per Share (EPS) Approach:
    PV = Po* = EPS 1 / rCE + PVGO
    Po = Estimated Present Fair Price,
    EPS 1 = Forecasted Earnings per Share in the next year (i.e. Year 1),
    rCE = Required Rate of Return on Investment in Common Stock Equity.
    PVGO = Present Value of Growth Opportunities. It means the Present Value of Potential


    Growth in Business from Reinvestments in New Positive NPV Projects and Investments PVGO is perpetuity formula.
    The formula is
    PVGO = NPV 1 / (rCE - g) = [-Io + (C/rCE)] / (rCE -g)
    In this PVGO Model: Constant Growth “g”. It is the growth in NPV of new Reinvestment Projects (or Investment).g= plowback x ROE
    Perpetual Net Cash Flows (C) from each Project (or reinvestment).
    Io = Value of Reinvestment (Not paid to share holders)
    = Pb x EPS
    Where Pb= Plough back = 1 – Payout ratio
    Payout ration = (DIV/EPS) and

    EPS Earnings per Share= (NI - DIV) / # Shares of Common Stock Outstanding
    Where NI = Net Income from P/L Statement and DIV = Dividend, RE1= REo+ NI1+ DIV1
    ROE = Net income /# Shares of Common Stock Outstanding.

    NPV 1 = [-Io + (C/rCE)] / (rCE -g)
    If we compare it with the traditional NPV formula
    -Io = Value of initial investment
    (C/rCE) = present value formula for perpetuities where you assume that you are generating the net cash
    inflow of C every year.
    C = Forecasted Net Cash Inflow from Reinvestment = Io x ROE
    Where ROE = Return on Equity = NI / Book Equity of Common Stock Outstanding

    Range of Possible Outcomes, Expected Return:
    Overall Return on Stock = Dividend Yield + Capital Gains Yield (Gordon’s Formula)

    Expected ROR = < r > = pi ri
    Where pi represents the Probability of Outcome “i” taking place and ri represents the Rate of Return (ROR) if Outcome “i” takes place. The Probability gives weight age to the return. The Expected or Most Likely ROR is the SUM of the weighted returns for ALL possible Outcomes.

    Stand Alone Risk of Single Stock Investment:
    Risk = Std Dev = ( r i - < r i > )2 p i . = Summed over each possible outcome “ i ” with return “r i ” and probability of occurrence “p i .” < r I > is the Expected (or weighted average) Return

    Possible Outcomes Example Continued:
    Measuring Stand Alone Risk for Single Stock Investment
    Std Dev = δ= √ Σ(r i - < r i >) 2 p i.

    Coefficient of Variation (CV):
    = Standard Deviation / Expected Return.
    CV = σ/ < r >.
    < r > = Exp or Weighted Avg ROR = pi ri

    Risk Basics
    Risk = Std Dev = σ = √ ( r i - < r i > )2 p i . = “Sigma”
    Types of Risks for a Stock:
    Types of Stock-related Risks which cause Uncertainty in future possible Returns & Cash Flows:
    Total Stock Risk = Diversifiable Risk + Market Risk

    Portfolio Rate of Return
    Portfolio Expected ROR Formula:
    rP * = r1 x1 + r2 x2 + r3 x3 + … + rn xn .

    Stock (Investment) Portfolio Risk Formula:
    p = √ XA2 σ A 2 +XB2 σ B 2 + 2 (XA XB σA σ B AB)

    Efficient Portfolios:
    rP * = xA rA + xB rB + xC rC


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