ࡱ> Y[Xx[ bjbj .ΐΐD||l?,R hhhoQqQqQqQqQqQqQ$SV|QQhhhhhQQhoQhoQOLDOp6&M&[QQ0,RMBWWLOWO`hhhhhhhQQhhh,RhhhhWhhhhhhhhh| : BUISNESS FINANCE FORMULAS 1-22 By IQRA JAHANGIR The Balance Sheet Identity is: Assets a" Liabilities + Stockholder s Equity Net Working Capital a" Current Assets  Current Liabilities NWC > 0 when Current Assets > Current Liabilities NWC < 0 when Current Assets < Current Liabilities NWC = 0 when Current Assets = Current Liabilities The Income Statement Revenue  Expenses a" Income Average vs. Marginal Tax Rates Suppose a Corporation has a taxable income of $200,000. So the Tax calculation will be: $ 50,000 x 15% = $ 7,500 ($ 75,000 50,000) x 25% = 6,250 ($ 100,000 75,000) x 34% = 8,500 ($ 200,000 100,000) x 39% = 39,000 $ 61,250 Our total tax is $61,250 Average tax rate is $61,250 / 200,000 = 30.625% Marginal rate is 39% Cost of a Tax Deductible Expense Corporation A Corporation B Earnings before interest and taxes $400,000 $400,000 - Interest Expense 100,000 0 Earning before taxes (taxable income) 300,000 400,000 - Taxes @35% 105,000 140,000 Earning after taxes $195,000 $260,000 Difference in earning after taxes $65,000 It can also be computed as: Interest Expense (1 Tax rate) $100,000 (1 35%) = $65,000 Depreciation as a Tax Shield Corporation A Corporation B Earnings before interest and taxes $400,000 $400,000 - Interest Expense 100,000 0 Earning before taxes (taxable income) 300,000 400,000 - Taxes @35% 105,000 140,000 Earning after taxes $195,000 $260,000 + Dep. charged without cash outlay 100,000 0 Cash flow $295,000 $260,000 Difference $35,000 It can also be computed as: Depreciation x Tax rate $100,000 x 35% = $35,000 Cash Flow identity Cash flow from Assets = Cash Flow to creditors + Cash flow to Stockholders Cash flow from Assets Cash flow from assets = Operating Cash Flow- Net Capital Spending- Change in Net Working Capital Where, Operating cash flow = Earnings before Interest and taxes+ Depreciation Taxes Net Capital Spending = Ending Net Fixed Assets- Beginning Net Fixed Assets +Depreciation Change in NWC = Ending NWC Beginning NWC Cash flow to creditors (bondholders) Cash flow to creditors = Interest paid Net new borrowings Cash flow to stockholders (owners) Cash flow to stockholders = Dividends Paid Net new equity raised Current Ratio Current Assets Current Ratio= ------------------------ Current Liabilities Quick (or Acid-Test) Ratio Current Assets Inventory Quick Ratio= ------------------------------------ Current Liabilities Cash Ratio Cash Cash Ratio= ----------------------- Current Liabilities Total Debt Ratio Total Assets Total Equity Total Debt Ratio= ------------------------------------ Total Assets Total Debt Ratio A2Z has 28% debt against total assets, thus there is 72% equity against total assets. Total Debt Ratio DebtEquity ratio = Total Debt / Total Equity Equity Multiplier = Total Assets / Total Equity Interest Coverage Ratio Also known as Times Interest Earned (TIE) ratio, refers to the ability of the firm to cover is interest obligations. Earning before Interest & Taxes Interest Coverage ratio = ----------------------------------------- Interest Cash Coverage Ratio EBIT + Depreciation Cash Coverage ratio = ----------------------------------------- Interest Inventory Turnover Ratio Cost of goods Sold Inventory Turnover ratio = -------------------------------- Inventory Days Sales in Inventory If we know sales were turned over 3.2 times during the year, we can calculate easily how long it took to turnover on average. 365 days Days Sales in Inventory = -------------------------------- Inventory Turnover Receivables Turnover Sales Receivables Turnover = ------------------------------- Accounts Receivables Days Sales in Receivables 365 days Days Sales in Receivables = ------------------------------- Receivables Turnover A Variation: Payables Turnover Cost of Goods Sold Payables Turnover = ------------------------------- Accounts payables Capital Intensity Ratio Total Assets Capital Intensity Ratio = -------------------- Sales Profit Margin Net income Profit Margin= -------------------- Sales Return on Assets Return on Assets (ROA) is a measure of profit per dollar of assets: Net income Return on Assets = -------------------- Total Assets Return on Equity Return on equity (ROE) is a measure of how the stockholders fared during the year. Net income Return on Equity = -------------------- Total Equity Earnings Per Share Net income EPS = --------------------------- Shares Outstanding Price-Earning Ratio Price-earnings or PE ratio is defined as: Price per share PE ratio = -------------------------- Earnings per share Book Value per share Total equity Book Value = ------------------------------------ No. of shares outstanding Market-to-Book ratio Market value per share Mark-to-Book ratio = ------------------------------------ Book value per share The Du Pont Identity Net Income ROE = -------------------- Total Equity Multiplying it by Assets / Assets (without changing anything) Net Income Net Income Assets ROE = -------------------- = ---------------- x ----------- Total Equity Total Equity Assets Net Income Assets = ---------------- x ---------------- Assets Total Equity The Du Pont Identity Net Income Assets ROE = ---------------- x ---------------- Assets Total Equity So, we have expressed ROE as a product of two other ratios ROA and the equity multiplier ROE = ROA x Equity multiplier = ROA x (1 + Debt-Equity ratio) The Du Pont Identity We can further decompose ROE by multiplying the top and bottom by total sale: Sales Net Income Assets ROE = -------- x ---------------- x ---------------- Sales Assets Total Equity Rearranging a bit, Net Income Sales Assets ROE = --------------- x ----------- x ---------------- Sales Assets Total Equity ROE =Profit Margin x Total Assets Turnover x Equity Multiplier The Du Pont Identity ROE =Profit Margin x Total Assets Turnover x Equity Multiplier This last Expression is called Du Pont identity after the Du Pont Corporation, which popularized its use. Dividend Payout Cash Dividends Dividend Payout ratio = ----------------------- Net Income Retention Ratio Retained Earnings Retention ratio = ----------------------- Net Income The retention ratio is also known as the plowback ratio, as this is the amount which is plowed back into the business Payout and Retention Q: LMN Corporation pays out 40% of net income in form of dividends. What is its retention ratio? A: If payout ratio is 40%, retention ratio is 1 40% = 60% Q: If net income of LMN is $800, how much did stockholders actually receive? A: Dividends are $800 x 40% = $320 Internal Growth Rate ROA x b Internal Growth rate = ------------------ (1 ROA) x b Where ROA is return on assets and b is the retention ratio Sustainable Growth Rate ROE x b Sustainable Growth rate = ------------------ (1 ROE) x b Simple interest. I = P x r x t Where P => principal amount r => interest rate t => time periods (years) I => simple interest Compound interest. I = P x rt Future Value FV = P(1 + rt) In the one-period case, the formula for FV can be written as: FV = C0 (1 + r) Where C0 is cash flow today (time zero) and r is the appropriate interest rate. Generalizing the future value of an investment over many periods: FV = C0 (1 + r)t Where C0 is cash flow at date 0, r is the appropriate interest rate, and t is the number of periods over which the cash is invested. The expression (1 + r)t is the future value interest factor. Present Value FV PV = ---------------- (1+rt) In the one-period case, the formula for PV can be written as:  EMBED Equation.DSMT4  Where C1 is cash flow at date 1 and r is the appropriate interest rate or discount rate General formula for calculating present value of C cash flow in t periods time is:  EMBED Equation.DSMT4  1 /(1 + r)t is used to discount a future cash flow, so it is called the discount factor Or present value interest factor (PVIF r,t), Calculating the present value of a future cash flow to determine its worth today is commonly called discounted cash flow (DCF) valuation Present Value vs. Future Value What we called the present value factor is just the reciprocal of the future value factor. Future value factor = (1 + r)t Present value factor = 1/(1 + r)t If we let FVt stand for the future value after t periods, then the relationship between the future value and the present value is: PV x (1 + r)t = FVt PV = FVt / (1 + r)t = FVt x [1/ (1 + r)t] This is also known as basic present value equation.  EMBED Equation.DSMT4  Finding the Number of Periods: Rule of 72 For reasonable rates of return, the time it takes to double the money, is given approximately by t = 72 / r% Continuing with the example, we have discount rate of 10%, so: t = 72 / 10 = 7.2 years This rule is fairly applicable to discount rates in 5% to 20% range. Time Value Calculations Symbols: PV = Present value, what future cash flows are worth today FVt = Future value, what cash flows are worth in the future r = Interest rate, rate of return, or discount rate per period t = number of periods C = cash amount Future value of C dollars invested at r percent per period for t periods: FVt = C* (1 + r)t The term (1 + r)t is called the future value factor. Present value of C to be received in t periods at r percent per period: PV = C/(1 + r)t The term 1/(1 + r)t is called the present value factor. IV. The basic present value equation giving the relationship between present and future value is: PV = FVt/ (1 + r)t Present Value for Annuity cash flows For annuity calculation, we use a variation of present value equation. The present value of an annuity of C dollars per period for t periods when interest rate is r is: PV=C *(1 - Present value factor)/r = C *[1 - 1/(1 + r)t ]/r Where C = Periodic payment or annuity r = rate of interest t = number of periods The term in the parenthesis is called present value interest factor of an annuity (PVIFAr,t). PVIFA = (1 Present value factor)/r Future Value for Annuities FVt = C (Future value factor - 1)/r = C [(1 + r)t - 1]/r Perpetuities The present value of perpetuity is: Perpetuity PV = C / r Summary of Annuity and Perpetuity Symbols PV = Present value, what future cash flows bring today FVt = Future value, what cash flows are worth in the future r = Interest rate, rate of return, or discount rate per period t = Number of time periods C = Cash amount II. FV of C per period for t periods at r percent per period: FVt = C [(1 + r)t - 1] / r III. PV of C per period for t periods at r percent per period: PV = C (1 - [1/ (1 + r)t]) / r IV. PV of perpetuity of C per period: PV = C / r Effective Annual Rates If a rate is quoted as 10% compounded semiannually, then what this means is that the investment actually pays 5% every six months.Is 5% every six months the same thing as 10% per year? $1 x 1.10 = $1.10 $1 x 1.052 = $1.1025 10% compounded semiannually is equivalent to 10.25% compounded annually. 10.25% is called effective annual rate (EAR) Effective Annual Rates EAR is computed in three steps Divide the quoted rate by the number of times the interest is compounded Add 1 and raise it to the power of number of times the interest is compounded. Subtract 1 So EAR = (1 + Quoted rate / m)m 1 Where m is the number of times the interest is compounded Annual Percentage Rates A typical credit card agreement quotes an interest rate of 18% APR. Monthly payments are required. What is the actual interest rate you pay on such a credit card? APR of 18% with monthly payments is really 0.18 / 12 = 0.015 or 1.5% per month. So, EAR = (1 + 0.18/12)12 1 = 10.1512 1 = 19.56% Valuing a Bond If a bond has a face value of F paid at maturity a coupon of C paid per period t periods to maturity a yield of r per period Its value is Bond value = C x [1 1/(1+r)t]/r + F/ (1+r)t Valuing Bonds Bond value = C x [1 1/(1+r)t]/r + F/ (1+r)t = Present value of coupons + Present value of face amount Summary of Bond Valuation I. Finding the value of a bond Bond value = C x [1 - 1/(1 + r)t]/r + F/(1 + r)t Where: C = the promised coupon payment F = the promised face value t = number of periods until the bond matures r = the markets required return, YTM II. Finding the yield on a bond Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates until the calculated bond value equals the given bond value. Remember that increasing the rate decreases the bond value. The Fisher Effect The relationship between real and nominal returns is described by the Fisher Effect. 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So, the current price of stock can be written as the present value of the dividends beginning in one period and extending out forever Alternatively, we can say that the price of stock today is equal to the present value of all of future dividends.  EMBED Equation.DSMT4  Zero Growth Stocks A share of common stock in a company with a constant dividend is termed as zero growth type of stocks. This implies: D1 = D2 = D3 = D = constant So the value of the stock is:  EMBED Equation.DSMT4  Since dividend is always the same, the stock can be viewed as an ordinary perpetuity with a cash flow equal to D every period. 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