# Unit Return computation with cash purchase vs. margin purchase

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1 FCS 5510 Formula Sheet *Note: The formulas I expect you to know are colored in Red. They are either more conceptually based, or are more commonly used than the others. You need to have a passing familiarity with the rest of the formulas, but I do not expect you to memorize them. If you see these formulas you do need to know in general what they are used for. Note present value (PV) and future value (FV) formulas are not here because I assume you learned them somewhere else in one of the prerequisite classes. You do need to understand the setup of those formulas. Unit Return computation with cash purchase vs. margin purchase P0= the purchase price of the security P1= the selling price of the security M=margin n = number of shares Return with cash purchase = ( P1 *n - P0 *n)/ (P0 * n) Return with margin purchase = (P1 *n - P0 *n ) / (P0 * M *n) If commission/transaction costs C are involved, then Return with cash purchase = ( ( P1 *n - P0 *n) C)/ (P0 * n) Return with margin purchase =( (P1 *n - P0 *n ) C) / (P0 * M *n) Unit 02

2 1. Tax owed or saved Tax owed or saved = Taxable amount * marginal tax rate 2. Expected Return E(r)= the expected return E(D)= the expected dividend or interest income P= the price of the asset E(g)=the expected growth in the value of the asset E( D) E ( r) = + E( g) P 3. Realized Return (Note this formula is pretty much the same as the expected return except the numbers in expected returns are expected instead of real) r= the realized return D= the realized dividend or interest income P= the price of the asset g=the realized growth in the value of the asset D r = + P 4. A Portfolio Standard Deviation (SDP) of Two Assets Notations: SA = Standard Deviation of asset A SB = Standard Deviation of asset B WA = Portfolio weight of asset A WB = Portfolio weight of asset B rab=correlation coefficient of assets A & B. Portfolio SDP of assets A and B is SD = W S + W S + 2W W P 2 A 2 A 2 B 2 B g A B S A S B r AB 5. Beta Coefficient Beta coefficient is an index of volatility of an asset relative to the volatility of the market. Notation:

3 Unit 03 βi = Beta of asset i σi = Standard Deviation of return on asset i σm = Standard Deviation of return on the market rim=correlation coefficient between the return on asset i and the return on the market σ i β = σ i M r im 1. Net Asset Value NAV Total Assets Total Liability = Number of Shares Outs tan ding 2. The Jensen Index (Also called Alpha) 3. The Treynor Index 4. The Sharpe Index Unit 04: 1. Dividend Valuation Model Assuming No Growth in Dividends Over Time

4 V=Valuation D=Dividends k=discount rate=required return V = D k 2. Dividend Valuation Model-Dividend grows at rate g V=Valuation D0=Initial dividend (first year) k=required return g=dividends annual growth rate V = D 0 (1 + g) ( k g) 3. Required Return (k) in some other occasions the notation is rs rf = the risk free rate (i.e.treasure Bill rate) rm = the return on the market β = the stock's beta K=rf + (rm - rf)β 4. Price to Earnings Ratio 5. PEG Ratio 6. Stock Valuation Using P/E Ratio m = the appropriate P/E ratio EPS = earnings per share

5 P = (m)(eps) 7. P/B Ratio 8. Adjusted PEG Ratio 9. Return on Equity 10. Profit Margin 11. Price Weighted Average *Could add any number of stock prices to the equation. 12. Value Weighted Average *Could add any number of stock prices to the equation 13. Equal Weighted Average *Could add any number of stock prices to equation. Also assumes an equal dollar amount is invested in each stock

6 14. Geometric Average *Can add any number of stock prices to the equation. N = the total number of stocks included Geometric average = (Price of Stock A * Price of Stock B)^(1/n) 1P Holding Period Return (HPR) P0 = purchase price P1 = sell price D = dividend P + D P HPR = 16. Dollar Weighted Rate of Return (True Annualized Rate of Return or Internal Rate of Return) D1 P0 = (1 + r) Dn (1 + r) n + P1 (1 + r) n Unit 05: 1. Payout Ratio

7 2. Retention Ratio = 1- Payout Ratio or 3. Growth Rate ROE = return on equity RR = retention ratio Growth Rate g = ROE x RR 4.. Gross Domestic Product GDP C = personal consumption I = gross private domestic investment G = government spending E = net exports GDP = C + I + G + E Unit 06: 1. Current Ratio 2. The Quick Ratio 3. Inventory Turnover 4. Average Collection Period

8 5. Receivable Turnover 6. Fixed Asset Turnover 7. Gross Profit Margin 8. Operating Profit Margin 9. Net Profit Margin 10. Return on Assets 11. Return on Equity 12. Return on Common Equity

9 13. DuPont System Return on Equity Net Profit Margin Total Asset Turnover An equity multiplier that indicates the firm s use of leverage. 14. Debt to Equity Ratio 15. Debt to Total Asset Ratio (Debt Ratio) 16. Times Interest Earned Ratio 17. Expanded Coverage Ratio 18. Payout Ratio

10 Unit 07: Fixed Income Securities: Bond Market and Valuation of Fixed-Income Securities 1. Price of a Perpetual Security: PMT = annual interest payment i = discount rate P = PMT i 2. Price of a Bond PMT = Interest Payments Each Year FV = Final Principal Payment i = annual discount rate n = number of years to maturity P = PMT x 1-1 (1 + i) i n + FV x 1 (1 + i) n 3. Price of a Zero Coupon Bond FV = Final Principal Payment i = annual discount rate n = number of years to maturity

11 P = FV (1 + i) n 4. Current Yield Current Yield = Annual Interest Payment Price of the Bond 5. Duration D = Duration PV = Present Value t = time (from 1 to m where m is maturity time) CFt = cash flow for year t D = m t = 1 PVCF x t t P B 6. Simplified Formula for Duration Computation c = annual coupon (as a percentage) n = number of years to maturity y = the yield to maturity (reinvestment rate) D = 1 + y y - (1 + y) + n(c y) n c[ (1 + y) - 1] + y

12 Unit 08: Government Securities 1. Discount Yield Discount Yield = Par Value - Price Par Value x 360 Days to Maturity 2. Yield to Maturity Discount Yield = Par Value - Price Par Value x 365 Days to Maturity 3. Par Value n = days to maturity/365 Par Value = Price x (1+ r) n 4. Compound Yield Compound Yield r = ( Par Value ) 1/n - 1 Price 5. Determining equivalent yields on tax exempt and non-exempt bonds lc = yield on non-exempt bonds lm = yield on municipal bonds (exempt) tf = federal marginal tax rate ts = state marginal tax rate im = ic(1 tf ts) Unit 09: Options

13 1. Market Price of a call Market price of a call = intrinsic value + time premium 2. Time Value of a Put Time Value of a put = price of the put intrinsic value of the put Unit 11: Portfolio Management 1. Net Worth Net Worth = Total Assets Total Liabilities

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