The Review Sheets of Corporate FinanceKey Concepts and Questions1. What Is Corporate Finance?Corporate finance addresses several important questions:1) What long-term investments should the firm take on? (Capital budgeting)2) Where will we get the long-term financing to pay for the investment? (Capital structure)3）How will we manage the everyday financial activities of the firm? (Working capital)2.The financial manager is concerned with three primary categories of financial decisions.1) Capital budgeting –process of planning and managing a firm’s investments in fixed assets. The key concerns are the size, timing and riskiness of future cash flows.2) Capital structure –mix of debt (borrowing) and equity (ownership interest) used by a firm. What are the least expensive sources of funds? Is there an optimal mix of debt and equity? When and where should the firm raise funds?3) Working capital management – managing short-term assets and liabilities. How much inventory should the firm carry? What credit policy is best? Where will we get our short-term loans?3.The Balance Sheetassets = liabilities + owners’ equity4. Net Working CapitalThe difference between a firm’s current assets and its current liabilities.Assets are listed on a balance sheet in order of how long it takes to convert them to cash. Liability order reflects time to maturity.5.Noncash ItemsThe largest noncash deduction for most firms is depreciation. It reduces a firm’s taxes and its net income. Noncash deductions are part of the reason that net income is not equivalent to cash flow.6.Cash FlowFree Cash Flow (FCF)FCF= Operating cash flow – net capital spending – changes in net working capitalOperating cash flow (OCF) = EBIT + depreciation – taxesNet capital spending (NCS) = ending fixed assets – beginning fixed assets + depreciation Changes in NWC = ending NWC – beginning NWCWorking capital = current assets-current liabilities7. Sources and Uses of CashActivities that bring cash in are sources. Firms raise cash by selling assets, borrowing money, or selling securities.Activities that involve cash outflows are uses. Firms use cash to buy assets, pay off debt, repurchase stock, or pay dividends.Mechanical Rules for determining Sources and Uses:Sources:Decrease in asset accountIncrease in liabilities or equity accountUses:Increase in asset accountDecrease in liabilities or equity account8. The Statement of Cash FlowsThe idea is to group cash flows into one of three categories: operating activities, investment activities, and financing activities.A general Statement of Cash FlowsOperating Activities+ Net Income+ Depreciation+ Decrease in current asset accounts (except cash)+ Increase in current liability accounts (except notes payable)- Increase in current asset accounts (except cash)- Decrease in current liability accounts (except notes payable)Investment Activities+ Ending net fixed assets- Beginning net fixed assets+ DepreciationFinancing Activities± Change in notes payable± Change in long-term debt± Change in common stock- DividendsPutting it all together:± Net cash flow from operating activities± Fixed asset acquisition± Net cash flow from financing activities= Net increase (decrease) in cash over the period9. Categories of Financial Ratios:A. Short-term Solvency, or Liquidity, MeasuresCurrent Ratio = current assets / current liabilitiesQuick Ratio = (current assets – inventory) / current liabilitiesCash Ratio = cash / current liabilitiesNWC to TA = (current assets – current liabilities) / total assetsInterval Measure = current assets / average daily operating costsB. Long-Term Solvency MeasuresTotal debt ratio = (total assets – total equity) / total assetsvariations:debt/equity ratio = (total assets – total equity) / total equityequity multiplier = 1 + debt/equity ratioC.Asset Management, or Turnover, MeasuresInventory turnover = cost of goods sold / inventoryDays’ sales in inventory = 365 days / inventory turnoverReceivables turnover = sales / accounts receivableDays’ sales in receivables = 365 days / receivables turnoverThis ratio may also be called “average collection period” or “days’ sales outstanding.”D. Profitability MeasuresThese measures are based on book values, so they are not comparable with returns that you see on publicly traded assets.Profit margin = net income / salesReturn on assets = net income / total assetsReturn on equity = net income / total equityE. Market Value MeasuresEarnings per share = net income / shares outstandingPrice-earnings ratio = price per share / earnings per sharePrice-sales ratio = price per share / sales per shareMarket-to-book ratio = market value per share / book value per shareTobin’s Q = market value of firm’s assets / replacement cost of firm’s assetsEnterprise Value = total market value of the stock + book value of all liabilities – cashEBITDA ratio = Enterprise Value / EDITDATotal asset turnover = sales / total assetsLong-term debt ratio = long-term debt / (long-term debt + total equity)10. Future Value and CompoundingInvesting for a single periodIf you invest $X today at an interest rate of r, you will have $X + $X(r) = $X(1 + r) in one period.Example: $100 at 10% interest gives $100(1.1) = $110Investing for more than one periodReinvesting the interest, we earn interest on interest, i.e., compoundingFV = $X(1 + r)(1 + r) = $X(1 + r)2In general, for t periods, FV = $X(1 + r)t, where (1 + r)t is the future value interest factor, FVIF(r,t)11.Present Value and DiscountingThe Single-Period CaseGiven r, what amount today (Present Value or PV) will produce a given future amount? Remember that FV = $X(1 + r). Rearrange and solve for $X, which is the present value. Therefore,PV = FV / (1 + r).Example: $110 in 1 period with an interest rate of 10% has a PV = 110 / (1.1) = $100 Discounting – the process of finding the present value.Present Values for Multiple PeriodsPV of future amount in t periods at r is:PV = FV [1 / (1 + r)t], where [1 / (1 + r)t] is the discount factor, or the present value interest factor, PVIF(r,t)Example: If you have $259.37 in 10 periods and the interest rate was 10%, how much did you deposit initially?PV = 259.37 [1/(1.1)10] = 259.37(.3855) = $100Discounted Cash Flow (DCF) – the process of valuation by finding the present value12.Present Value for Annuity Cash FlowsOrdinary Annuity – multiple, identical cash flows occurring at the end of each period for a fixed number of periods.The present value of an annuity of $C per period for t periods at r percent interest:PV = C[1 – 1/(1 + r)t] / rExample: If you are willing to make 36 monthly payments of $100 at 1.5% per month, what size loan can you obtain?PV = 100[1 – 1/(1.015)36] / .015 = 100(27.6607) = 2766.0713.Future Value for AnnuitiesFV = C[(1 + r)t– 1] / rExample: If you make 20 payments of $1000 at the end of each period at 10% per period, how much will be in your account after the last payment?FV = 1,000[(1.1)20– 1] / .1 = 1,000(57.275) = $57,27514.PerpetuitiesPerpetuity – series of level cash flows foreverPV = C / rPreferred stock is a good example of a perpetuity. Present Valuea.The Basic IdeaNet present value –the difference between the market value of an investment and its cost. Estimating cost is usually straightforward; however, finding the market value of assets can be tricky.b. Estimating Net Present ValueDiscounted cash flow (DCF) valuation – finding the market value of assets or their benefits by taking the present value of future cash flows, i.e., by estimating what the future cash flows would trade for in today’s dollars.16.The Internal Rate of ReturnInternal rate of return (IRR) – the rate that makes the present value of the future cash flows equal to the initial cost or investment. In other words, the discount rate that gives a project a $0 NPV.IRR decision rule – the investment is acceptable if its IRR exceeds the required return.Problems with the IRR – If cash flows change sign more than once, then you will have multiple internal rates of return. This is problematic for the IRR rule; however, the NPV rule still works fine.17.Relevant Cash FlowsRelevant cash flows –cash flows that occur (or don’t occur) because a project is undertaken. Cash flows that will occur whether or not we accept a project aren’t relevant.Incremental cash flows –any a nd all changes in the firm’s future cash flows that are a direct consequence of taking the project18.Incremental Cash Flowsa.Sunk cost –a cash flow already paid or accrued. These costs should not be included in the incremental cash flows of a project. From a financial standpoint, it does not matter what investment has already been made. We need to make our decision based on future cash flows, even if it means abandoning a project that has already had a substantial investment. Examples: the compensation for the president’s son, no matter whether he is hired for the new projectb. Opportunity CostsOpportunity costs –any cash flows lost or forgone by taking one course of action rather than another. Applies to any asset or resource that has value if sold, or leased, rather than used.c.Side EffectsWith multi-line firms, projects often affect one another – sometimes helping, sometimes hurting. The point is to be aware of such effects in calculating incremental cash flows.Erosion (or Cannibalization) –new project revenues gained at the expense of existing products/services.Examples: Coca-cola new products: coca-cola zero vs. Coca-cola diet Working Capitalworking capital=current assets- current liabilitiesNew projects often require incremental investments in cash, inventories, and receivables that need to be included in cash flows if they are not offset by changes in payables. Later, as projects end, this investment is often recovered.20. Tax considerationUse after-tax cash flows, not pretax (the tax bill is a cash outlay, even though it is based on accounting numbers).21.Project Cash FlowsFrom the pro forma statements compute:Operating cash flow = EBIT + depreciation – taxes = NI + depreciation (in the absence of interest expense)Cash flow from assets = operating cash flow – net capital spending – changes in NWCBased on the form of the equation, you subtract increases in NWC and add decreases in NWC. Or, Free Cash Flow =EBIT*(1-t) + Non-Cash Expenses- Capital Expenditures - Incremental Working Capital“Free” refers to those cash flows that are available to stakeholders (e.g., equity and debt holders) after consideration for taxes, capital expenditures and working capital needs.22.Returnsa.Dollar ReturnsIncome component – direct cash payments such as dividends or interestPrice change – loosely, capital gain or lossTotal dollar return = income component + price changeThe return is unaffected by the decision to sell or hold securities.b.Percentage ReturnsPercentage return = dollar return / initial investment= dividend yield + capital gains yieldDividend yield = D t+1 / P tCapital gains yield = (P t+1– P t) / P t23.Total riskTotal risk = nondiversifiable risk + diversifiable risk = systematic risk + unsystematic risk24. Systematic risk and unsystematic riskSystematic risk is a surprise that affects a large number of assets, although at varying degrees. It is sometimes called market risk.Unsystematic risk is a surprise that affects a small number of assets (or one). It is sometimes called unique or asset-specific risk.Example: Changes in GDP, interest rates, and inflation are examples of systematic risk. Strikes,accidents, and takeovers are examples of unsystematic risk.25.Diversification and Unsystematic RiskWhen securities are combined into portfolios, their unique or unsystematic risks tend to cancel out, leaving only the variability that affects all securities to some degree. Thus, diversifiable risk is synonymous with unsystematic risk. Large portfolios have little or no unsystematic risk.26.Diversification and Systematic RiskSystematic risk cannot be eliminated by diversification since it represents the variability due to influences that affect all securities to some degree. Therefore, systematic risk and nondiversifiable risk are the same.27.Beta coefficientBeta coefficient – measures how much systematic risk an asset has relative to an asset of average risk.28.The Security Market LineThe line that gives the expected return/systematic risk combinations of assets in a well functioning, active financial market is called the security market line.29.Market PortfoliosConsider a portfolio of all the assets in the market and call it the market portfolio. This portfolio, by definition, has “average” systematic risk with a beta of 1. Since all assets must lie on the SML when appropriately priced, the market portfolio must also lie on the SML. Let the expected return on the market portfolio = E(R M). Then, the slope of the SML = reward-to-risk ratio = [E(R M) – R f] / βM = [E(R M) – R f] / 1 = E(R M) – R f30.CAPM: Capital Asset Pricing ModelE(R j) = R f + slope(βj)E(R j) = R f + (E(R M) – R f)(βj)The CAPM states that the expected return for an asset depends on:-The time value of money, as measured by R f-The reward per unit risk, as measured by E(R M) - R f-The asset’s systematic risk, as measured by β31. Cost of CapitalCost of capital –the minimum expected return an investment must offer to be attractive. Sometimes referred to as the required return.32.The Cost of EquityA. The Dividend Growth Model ApproachAccording to the dividend growth model,P0 = D1 / (R E– g)Rearranging and solving for the cost of equity gives:R E = (D1 / P0) + gwhich is equal to the dividend yield plus the growth rate (capital gains yield).B. The SML ApproachCAPM, R E = R f + E(E(R M) – R f)33.The Cost of DebtCost of debt (R D) –the interest rate on new debt can easily be estimated using the yield to maturity on outstanding debt or by knowing the bond rating and looking up rates on new issues with the same rating.The Cost of Preferred Stock34.Preferred stock is generally considered to be a perpetuity, so you rearrange the perpetuity equation to get the cost of preferred, R PR P = D / P035.Taxes and the Weighted Average Cost of Capital(WACC)After-tax cash flows require an after-tax discount rate. Let T C denote the firm’s marginal tax rate. Then, the weighted average cost of capital is:WACC = (E/V)R E + (D/V)R D(1-T C)36.The SML and the WACCThe W ACC is the appropriate discount rate only if the proposed investment is of similar risk as the firm’s existing assets.37.Capital Structure and the Cost of CapitalThe “optimal” or “target” capital structure is that debt/equity mix that simultaneously (a) maximizes the value of the firm, (b) minimizes the weighted average cost of capital, and (c) maximizes the market value of the common stock.Maximizing the value of the firm is the goal of managing capital structure.38.Capital Structure and the Cost of Equity CapitalM&M Proposition I: The Pie ModelM&M Proposition I –without corporate taxes and bankruptcy costs, the firm cannot affect its value by altering its capital structure.The Cost of Equity and Financial Leverage: M&M Proposition IIM&M Proposition II –a firm’s cost of equity capital is a positive linear function of its capital structure (still assuming no taxes):WACC = R A = (E/V)R E + (D/V)R D;R E = R A + (R A– R D)(D/E)As more debt is used, the return on equity increases, but the change in the proportion of debt versus equity just offsets that increase and the W ACC does not change.According to Proposition II,R E = R A + (R A– R D)(D/E). An alternative explanation is as follows: In the absence of debt, the required return on equity equals the return on the firm’s assets, R A. As we add debt, we increase the variability of cash flows available to stockholders, thereby increasing stockholder risk.39.Business and Financial RiskYou may wish to skip over the distinction between the asset beta and the equity beta. The key point is that Proposition II shows that return on equity depends on both business risk and financial risk.Business risk –the risk inherent in a firm’s operations; it depends on the systematic risk of the firm’s assets and it determines the first component of the required return on equity, R A. Financial risk – the extra risk to stockholders that results from debt financing; it determines the second component of the required return on equity, (R A– R D)(D/E).40.Optimal Capital Structurea.The Static Theory of Capital Structure-Firms borrow because tax shields are valuable-Borrowing is constrained by the costs of financial distress-The optimal capital structure balances the incremental benefits and costs of borrowingb.Optimal Capital Structure and the Cost of CapitalThe optimal capital structure is the debt-equity mix that minimizes the WACC.c.Optimal Capital Structure: A RecapCase I – No taxes or bankruptcy costs; firm value is unaffected by the choice of capital structure Case II – Corporate taxes, no bankruptcy costs; firm value is maximized when the firm uses as much debt as possible due to the interest tax shieldCase III – Corporate taxes and bankruptcy costs; firm value is maximized where the additional benefit from the interest tax shield is just offset by the increase in expected bankruptcy costs –there is an optimal capital structure41.The Cash BudgetCash budget – a schedule of projected cash receipts and disbursementsa. cash budget requires sales forecasts for a series of periods. The other cash flows in the cash budget are generally based on the sales estimates. We also need to know the average collection period on receivables to determine when the cash inflow from sales actually occurs.b.Cash OutflowsCommon cash outflows:-Accounts payable – what is the accounts payables period?-Wages, taxes and other expenses – usually expressed as a percent of sales (implies that they are variable costs)-Fixed expenses, when applicable-Capital expenditures – determined by the capital budget-Long-term financing expenses – interest expense, dividends, sinking fund payments, etc.-Short-term borrowing – determined based on the other informationThe Cash BalanceNet cash inflow is the difference between cash collections and cash disbursements42.Line of credit – formal or informal prearranged short-term loans43.Pro Forma Operating StatementThis statement is built around an estimate of the expected sales for the forecast period.44.Pro Forma Balance SheetThe balance sheet is partially based on the information represented in the operating statement, as well as the schedule and budgets, if any, supporting the latter.45.Financial Leverage and riskExpected return=risk free rate+risk premiumExpected return=risk-free rate+ business risk premium + financial risk premiumUnder the assumption of CAPM there is a simple relationship between levered and unlevered betas.β(L)=β(U)[1+D/E], or β(U)=β(L)/(1+D/E)A stock’s levered beta is equal to its levered beta multiplied by one plus the firm’s ratio of debt to equity, D/E therefore, a stock’s beta ( and its expected return) increases as its debt ratio increases. Expected return = RF + β(U)[Rm-Rf]+β(L)(D/E)(Rm-Rf)46. The Du Pont IdentityA Closer Look at ROEThe Du Pont Identity provides analysts with a way to break down (i.e., decompose) ROE and investigate what areas of the firm need improvement.ROE = (NI / total equity)multiply by one (assets / assets) and rearrangeROE = (NI / assets) (assets / total equity) = ROA*EMmultiply by one (sales / sales) and rearrangeROE = (NI / sales) (sales / assets) (assets / total equity)ROE = PM*TAT*EMThese three ratios indicate that a firm’s return on equity depends on its operating efficiency (profit margin), asset use efficiency (total asset turnover) and financial leverage (equity multiplier).47.EFN and GrowthFinancial Policy and GrowthThe internal growth rate (IGR) is the growth rate the firm can maintain with internal financing only.IGR = (ROA*b) / [1 – ROA*b]The sustainable growth rate (SGR) is the maximum growth rate a firm can achieve without external equity financing, while maintaining a constant debt-to-equity ratio.SGR = (ROE*b) / [1 – ROE*b]48.Calculating and Comparing Effective Annual Rates (EAR)EAR = [1 + (quoted rate)/m]m– 1, where m is the number of periods per yearExample: 18% compounded monthly is [1 + (.18/12)]12– 1 = 19.56%49. Bonds and Bond ValuationA. Bond Features and PricesBonds – long-term IOUs, usually interest-only loans (interest is paid by the borrower every period with the principal repaid at the end of the loan).Coupons – the regular interest payments (if fixed amount – level coupon).Face or par value – principal, amount repaid at the end of the loanCoupon rate – coupon quoted as a percent of face valueMaturity – time until face value is paid, usually given in yearsB. Bond V alues and YieldsThe cash flows from a bond are the coupons and the face value. The value of a bond (market price) is the present value of the expected cash flows discounted at the market rate of interest.Yield to maturity (YTM) – the required market rate or return, or rate that makes the discounted cash flows from a bond equal to the bond’s market price.Bond value = present value of coupons + present value of parBond value = C[1 – 1/(1+r)t] / r + FV / (1+r)tSemiannual coupons – coupons are paid twice a year. Everything is quoted on an annual basis so you divide the annual coupon and the yield by two and multiply the number of years by 2.Example: A $1,000 bond with an 8% coupon rate, with coupons paid semiannually, is maturing in 10 years. If the quoted YTM is 10%, what is the bond price?Bond value = 40[1 – 1/(1.05)20] / .05 + 1,000 / (1.05)20Bond value = 498.49 + 376.89 = $875.38Inflation and Interest RatesA. Real versus Nominal RatesNominal rates – rates that have not been adjusted for inflationReal rates – rates that have been adjusted for inflationB. The Fisher EffectThe Fisher Effect is a theoretical relationship between nominal returns, real returns, and the expected inflation rate. Let R be the nominal rate, r the real rate, and h the expected inflation rate; then,(1 + R) = (1 + r)(1 + h)A reasonable approximation, when expected inflation is relatively low, is R = r + h.A definition whereby the real rate can be found by deflating the nominal rate by the inflation rate: r = [(1 + R) / (1 + h)] – 1.50. Common Stock ValuationA. Cash FlowsStock valuation is more difficult than bond valuation because the cash flows are uncertain, the life is infinite, and the required rate of return is unobservable.The cash flows to stockholders consist of dividends plus a future sale price. You can illustrate that the current stock price is ultimately the present value of all expected future dividends:P0 = D1/(1+R) + D2/(1+R)2 + D3/(1+R)3+ …B. Some Special Cases1)Zero-growth – implies that D0 = D1 = D2… = DSince the cash flow is always the same, the PV is that for a perpetuity:P0 = D / RExample: Suppose a stock is expected to pay a $2 dividend each period, forever, and the required return is 10%. What is the stock worth?P0 = 2 / .1 = $202)Constant growth – Dividends are expected to grow at a constant percentage rate each period. D1 = D0(1+g); D2 = D1(1+g); in general D t = D0(1+g)t Note that this is really just a future value.P0 = D1 / (R – g)=D0(1+g)/(1+g)C. Components of the Required ReturnRearrange P0 = D1 / (R – g) to find R:R = (D1 / P0 ) + gDividend yield = D1 / P0Capital gains yield = g, andR = dividend yield + capital gains yieldD. Stock Valuation Using MultiplesFor stocks that do not currently pay dividends, a common valuation approach is to make use of the PE ratio. For instance, using a benchmark PE ratio for a firm and their current earnings per share, we can calculate a projected price for the firm:Price at time t = P t =Benchmark PE ratio x EPS t51. Alternative Definitions of Operating Cash FlowSuppose that sales = 1,000; operating costs = 600; depreciation = 200 and the tax rate = 34% With our standard definition of OCF = EBIT – taxes + depreciation, we compute the following: EBIT = 1,000 – 600 – 200 = 200Taxes = 200(.34) = 68OCF = 200 – 68 + 200 = 332A. The Bottom-Up ApproachOCF = NI + depreciationNI = 200 – 68 = 132OCF = 132 + 200 = 332It is extremely important to remember that this definition will only work when there is no interest expense. For that reason, it is often ideal for capital budgeting problems, but not for finding historical OCF.B. The Top-Down ApproachOCF = Sales – Costs – TaxesOCF = 1,000 – 600 – 68 = 332C. The Tax Shield ApproachOCF = (Sales – Costs)*(1 – T) + Depreciation * TOCF = (1,000 – 600)(1 - .34) + 200(.34)OCF = 264 + 68 = 332Under this approach we consider the cash flow without any noncash deductions and then add back the depreciation tax shield. If we had other noncash deductions, we would need to compute the tax shield associated with each one and add those back as well.D. ConclusionThe best choice of operating cash flow calculation method is determined by the convenience for the problem at hand.52.Break-Even AnalysisBreak-even analysis is a widely used technique for analyzing sales volume and profitability. More to the point, it determines the sales volume necessary to cover costs and implicitly asks, “Are things likely to go that well?”A. Fixed and Variable CostsVariable costs (VC) are the costs that change as the volume of sales changes (direct labor and materials, for example)variable costs = quantity*cost per unitVC = Q*vB. Accounting Break-EvenThe sales volume at which the project net income = $0.P = price per unitv = variable cost per unitQ = # of units or quantityFC = fixed costsD = depreciationT = tax rateNet income = sales – costs – taxesNI = [Q*P – FC – Q*v – D](1 – T) = 0Q*P – Q*v = FC + DQ(P – v) = FC + DQ = (FC + D) / (P – v)*:Again, ignore taxes for simplification, OCF = net income + depreciation53.Operating LeverageA. The Basic IdeaOperating leverage is the degree to which a project or firm uses fixed costs in production. Plant and equipment and non-cancelable rentals are typical fixed cost items.B. Implications of Operating LeverageSince fixed costs do not change with sales, they make good situations better and bad situations worse, i.e., they “lever” results.C. Measuring Operating LeverageDegree of Operating Leverage (DOL) is the percentage change in OCF relative to a percentage change in quantity.Percentage change in OCF = DOL*(percentage change in Q)DOL = 1 + FC / OCFDOL depends on your starting point – what quantity you use to determine the OCF.54.Risk PremiumsUsing the T-bill rate as the risk-free return and aggregate common stocks as an average risk, define excess return as the difference between an average-risk return and the return on T-bills.Risk premium –reward for bearing risk, the difference between a risky investment return and the risk-free rate.55. The Variability of Returns: The Second LessonA. Frequency Distributions and VariabilityVariance and standard deviation are the most commonly used measures of volatility.B. The Historical Variance and Standard DeviationVariance – the average squared deviation between actual returns and their meanStandard Deviation – square root of variance56. The Forms of Market EfficiencyA. Strong form efficiency – All information, both public and private, is already incorporated in the price. Empirical evidence indicates that this form of efficiency does NOT hold.。