PV IF = 1 - (1+i)^-n = (1-(1+i)^-n)/i (to use in Excel worksheet)
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FV IF = (1+i)^n - 1 = (1+i)^(n) -1 )/i
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FV = PV*(1+i)^n PV = FV/(1+i)^n i = (Future Payment/Present Value)^1/n - 1 1. Fundamental Accounting Equation and Double Entry Principle. • Assets +Expense = Liabilities + Shareholders’ Equity + Revenue Liabilities = Equity = Net Worth Revenue – Expense = Income
Total Equity = Common Par Stock Issued + Paid In Capital + Retained Earnings
= Current Assets / Current Liabilities
= (Current Assets – Inventory) / Current Liabilities
= Average Accounts Receivable /(Annual Sales/360)
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] 6. ASSET MANAGEMENT RATIOS Inventory Turnover: = Sales / inventories Total Assets Turnover: = Sales / Total Assets
Debt-Assets: = Total Debt / Total Assets Debt-Equity: = Total Debt / Total Equity Times-Interest-Earned: = EBIT / Interest Charges
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
MVA (Rupees) = Market Value of Equity – Book Value of Equity Capital
EVA (Rupees) = EBIT (or Operating Profit) – Cost of Total Capital
• 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 The explanation of these determinants of interest rates is given as under:
F V = PV + (PV x i x n)
Annual (yearly) compounding: F V = PV x (1 + i) n Monthly compounding: F V = PV x (1 + (i / m) m x n
= [Current assets for the current year/Current sales] x Estimated sales for the next year
= estimated sales x profit margin x plowback ratio
= estimated total assets – estimated total liabilities –estimated total equity
= return on equity x (1- pay out ratio)
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
• 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
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) + ...+ ∞
FV = CCF (1 + i) n – 1 Annual Compounding (at end of every year) PV =FV / (1 + i ) n . n = life of Annuity in number of years
Future Value of annuity =CCF (constant cash flow)*(1+ (i/m) m*n-1/i/n Multiple Compounding: PV =FV / [1 + (i/m)] mxn
=constant cash flow/interest rate
FV =CCF [(1+i) n - 1]/ i
ROI= (ΣCF/n)/ IO
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
PI = [Σ CFt / (1+ i) t ]/ IO
NPV= -IO +CF1/ (1+IRR) + CF2/ (1+IRR) ^2......
The formula is similar to NPV NPV = 0 = -Io + CFt / (1+IRR)t = -Io + CF1/(1+IRR) + CF2/(1+IRR) ^2 + ..
(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
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
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 = it is very important term which you should understand it care fully. It is Bondholder’s (or Investor’s) Required Rate of Return for investing in Bond (Debt).As conservative you can choose minimum interest rate. It is derived from Macroeconomic or Market Interest Rate. Different from the Coupon Rate! Recall Macroeconomic or Market Interest Theory: i = iRF + g + DR + MR + LP + SR CF = cash flow = Coupon Receipt Value (in Rupees) = Coupon Interest Rate x Par Value. Represents cash receipts (or in-flow) for Bondholder (Investor). Often times an ANNUITY pattern Coupon Rate derived from Macroeconomic or Market Interest Rate. The Future Cash Flows from a bond are simply the regular Coupon Receipt cash in-flows over the life of the Bond. But, at Maturity Date there are 2 Cash In-flows: (1) the Coupon Receipt and (2) the Recovered Par or Face Value (or Principal) n = Maturity or Life of Bond (in years) In the next lectures, you would study that how the required rate of return is related to market rate of return
FV = CCF (1 + rD/m )nxm - 1/rD/m Use Monthly Basis for this example. n = 1 year m = 12 months CCF = Constant Cash Flow = Rs 1,000 = Monthly Coupon rD = Annual Nominal Required Rate of Return for investment in Bond (Debt) = 10% pa. Periodic Monthly Required Rate of Return is rD/m = 10/12 = 0.833 % = 0.00833 p.m. m = 12 months
= Interest Yield + Capital Gains Yield
= Coupon / Market Price
= YTM - Interest Yield
N=1 year ,m= no. of intervals in a year =12 CCF=constant cash flow n = Maturity or Life of Bond (in years)
=par value +I, year copoun receipts Another thing to keep in mind is that YTM has two components first is
=interest yield on bond +capital gain yield on bond 1. INTEREST YIELD =annual copoun interest /market price 2. CAPITAL YIELD =YTM –INTEREST YIELD
– PV = DIV 1 / r PE
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
Dividend Value is derived from Dividend Cash Stream and Capital Gain / Loss from Difference between Buying & Selling Price.
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
If Market Price > Fair Value then Stock is Over Valued Share Price Valuation -Perpetual Investment in Common Stock:
DIV1 = DIV 2 = DIV3
PV = Po*= DIV1 / (1+ rCE) + DIV1 / (1+ rCE) 2 + DIV1 / (1+ rCE) 3 + ... +... = DIV 1 / rCE
DIVt+1 = DIVt x (1 + g) t. t = time in years.
PV = Po* = DIV1 / rCE
PV = Po* = DIV1 / (rCE -g)
Zero Growth: Po*=DIV1 / rCE (Po* is being estimated)
Similarly,
rCE*= ( DIV 1 / Po) + g use this formula to calculate the required rate of return.
rCE*= (DIV 1 / Po) + g In this the first part (DIV 1 / Po) is the dividend yield g is the Capital gain yield.
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
Where NI = Net Income from P/L Statement and DIV = Dividend, RE1= REo+ NI1+ DIV1 ROE = Net income /# Shares of Common Stock Outstanding.
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
Overall Return on Stock = Dividend Yield + Capital Gains Yield (Gordon’s Formula)
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.
Risk = Std Dev = ( r i - <> )2 p i . = Summed over each possible outcome “ i ” with return “r i ” and probability of occurrence “p i .” <> is the Expected (or weighted average) Return
Measuring Stand Alone Risk for Single Stock Investment Std Dev = δ = √ Σ (r i - <>) 2 p i.
= Standard Deviation / Expected Return. CV = σ/ <>. <> = Exp or Weighted Avg ROR = pi ri
Risk = Std Dev = σ = √ ( r i - <> )2 p i . = “Sigma”
Types of Stock-related Risks which cause Uncertainty in future possible Returns & Cash Flows: Total Stock Risk = Diversifiable Risk + Market Risk
Portfolio Expected ROR Formula: rP * = r1 x1 + r2 x2 + r3 x3 + … + rn xn .
p = √ XA2 σ A 2 +XB2 σ B 2 + 2 (XA XB σ A σ B AB)
rP * = xA rA + xB rB + xC rC |
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