Finance Summary.docx

Finance summary Module 1 – Tools of Finance Financial Markets Shift future resources to present to increase consumption and satisfaction. Shift resources to the future by lending and common shares to increase future value. CF1 NPV = -------- – CF0 (1+ i) CF0 IRR = NPV = 0 = – CF1 + ----------- (1+ IRR) IRR > market rate = acceptable investment and + NPV. IRR < market rate = unacceptable and –NPV. Compound Interest = CF0 = [1 + (i/m)]m t YTM = Bond Market Value = Coupon + Coupon + Coupon + (Bond Face Value + Coupon) 1+r (1+r)2 (1+r)3 (1+r)4 Forward Interest Rates: 1f4 = Cube Root (1 + Spot Rate4)4 / (1 + Spot Rate1)1 1f3 = Square Root (1 + Spot Rate3)3 / (1 + Spot Rate1)1 1f2 = (1 + Spot Rate2)2 / (1 + Spot Rate1)1 Module 2 – Investment Decisions Shareholder Wealth Residual claim Equity has no contract that requires money to be paid to shareholders at any time. Shareholders have entitlement to vote for the directors of the company. Directors and management are agents of the shareholders. Shareholders have ownership claim on remaining corporate resources Limited liability Possible losses are limited to the value of the shares that the shareholder owns. Maximize shareholder wealth. Maximize the market value of shares. Investment Decisions Total value of company increases by NPV of investment - costs to undertake. Shareholders wealth increase = NPV of investments Share Values and Price/Earnings Ratios Earnings per share = Earnings / # shares P/E ratio = Share price / earnings per share Price per share = (Earnings per share x payout ratio) / (re-g) Share Price = (Div + Growth Rate) / (re – Growth Rate) Payout ratio = Dividends / Total Earnings Module 3 – Earnings, Profit, and Cash Flow Corporate Cash Flows – activity across time Financial cash flows - cash amounts that are expected to occur at the times for which the expectations are recorded. Typical Cash Flows (Company with zero debt, 100% equity financed) (‘000s) Now Year 1 Year 2 Year 3 Customers 0 +17 500 +23 500 +4 000 Operations 0 -7 000 -3 830 -5 200 Assets -10 000 -4 000 -2 000 0 Government 0 -4 000 -8 085 +5 600 Capital (FCF) -10 000 +2 500 +9 585 +4 400 2 500 000 9 585 000 4 400 000 NPV = -10 000 000 + -------------- + ------------- + ------------- = +3 500 000 (1.10) (1.10)2 (1.10)3 Module 4 – Investment Decisions using the WACC WACC is the discount rate which: Operating risks of the project; Proportional debt and equity financing Interest deductibility for debt financed portion. Debt Cost = Debt Required Rate x (1-Corporate Income Tax Rate) To calculate WACC Required rate for equity Debt’s after tax cost rate “All equity” free cash flows Proportions intended for debt and equity financing. NPV = FCF(t) * (1 + rv*)t WACC = rv* = D (rd*) + E (re) V V FCF(t) * = Unleveraged (ungeared) free cash flow: the amount of free cash flow that the company is expected to generate at time t due to the project not including ITS. rd* = Cost of debt as a rate to the investment; equal to rd x (1 – Corp Tax Rate) rd = Return on debt of investment re = Return on equity of investment D = Debt amount E = Equity amount V = Total investment = D + E It Interest cash flow at time t. Tc Corporate income tax rate. ITSt Interest tax shield cash flow, equal to It x TC. FCF*t Unleveraged (ungeared) free cash flow: amount of free cash flow a company is expected to generate at t due to a project, not including ITS. Equal to FCFt – ITSt. Income tax shield = expected interest payment each period X the corporate income tax rate. Adjusted Present Value APV = when amounts of debt that projects will use are known but not proportions. Calculate PV assuming all equity financing Calculate PV of tax shield All Equity Value + Interest Tax Shield Value - Present Outlay = APV n FCF*t WACC/NPV0 = ? --------- t=0 (1+rv*)t n FCF*t ITSt APV0 = ? -------- + -------- t=0 (1+rv)t (1+rd)t Module 5 – Estimating Cash Flows for Investment Projects #1 - Depreciation Expenses for Tax Purposes Straight-line depreciation involves equal amounts for each year. #2 - Change in Taxes Should Company Accept the Project with P&L Sales Revenue Other Revenue Total Revenue Direct Expense Labor Other Management Marketing Total Direct Expenses Depreciation Subtotal Total Expense Profit Before Tax Less Taxes Net Income SR + OR – DE – D = EBIT – T = NI #3 - Working Capital = AR – AP + C + I = WC Accounts Receivable Accounts Payable Cash and Inventories #4 - Project Cash Flows = S – DE + WC + A – T = FCF Sales Revenue Total Direct Expense Change in Net Working Capital Assets Taxes FCF-Free Cash Flow Module 6 – Investment Analysis Payback Period Problems with the payback period; Ignores CF beyond the maximum acceptable payback period. Does not DCF within the maximum acceptable period and gives equal weight to all. Inconsistent with shareholder opportunity costs. 1 1 Payback: ------- - ---------------- rv* rv*(1+rv*)n where n is the number of periods in the projects total lifetime. Average (Accounting) Return on Investment (AROI) AROI = accounting profits / NBV investments. Result compared to a minimal acceptable return based on an industry or company average. AROI does not DCF. IRR vs. NPV Cash flow sign changes across time can yield multiple IRRs. To accept a project, IRR < hurdle rate. IRR can cause problems in multiple-period CF investments that require a different discount rate for each cash flow. YTM of security with same risk and CF patterns as the investment would have to be found. Mutually Exclusive Investment Decisions NPV is best where multiple investment options compared and subsequently ranked. If IRR must be used, incremental cash flow analysis should be used. Take any two projects out of the group. Find the one that has the highest positive cash flow total. Investment with highest CF is defender, the other challenger. Subtract CF of challenger from the defender. Results are incremental cash flows. Find the IRR of the incremental cash flows. If the IRR > hurdle rate, keep defender and throw out challenger and visa versa. Pick next project from group and repeat process-using winner of #5 until only one investment remains. Calculate the IRR of the winner. If it is greater than the hurdle rate, accept it, if not then reject all the projects. Never use if; More than one change of sign across time. Projects differ in risk or financing and require different hurdle rates. Cost-Benefit Ratio CBR = ? inflowst / (1+rv*)t / ? outflowst / (1+rv*)t Accept if CBR is >1 = positive NPV Reject if CBR is <1 = negative NPV Profitability Index Ratio of accumulated PV of FCF to the present CF of an investment. PI = PV of Cash Flows / Total Investment PI > 1 OK PI < 1 Reject Capital Rationing Used to choose group of projects that will maximise shareholder wealth with limited funds. Investments accepted in order of PI, until budget exhausted. Inflation Real rate of return = nominal rate - influence of inflation for time in the future. Inflation occurs, costs of assets will increase across time faster than the rate of inflation. Results in FCF increasing at a slower rate than inflation. Accelerating depreciation schedules have been put in place to help offset this effect: double-declining balance, or sum-of-the-years digits methods. Real rate of return = (1 + nominal rate) / (1 + inflation rate) Renewable Investments – when two investments have different time durations: Calculate NPV of both investments. Divide by annuity factor from PV for t periods tables (% and t) Result = constant annuity outlay per period. Choose the investment with lowest outlay per period. Leasing Contractual agreement between asset owner (lessor) and asset user (lessee). Financial or capital lease. Advantages Higher tax benefits. Information asymmetries exist on certain types of assets, leasing can lower the costs. Economies of scale in the management of specialised asset leasing. Misconceptions Leasing saves money because does not have to make large outlay to purchase. Lessee debt capacity is higher since they do not need to borrow money to buy asset. Evaluating Leases CF used would include: Cost of purchasing Lost depreciation tax shields Lease payments Lease payment tax shields. Correct discount rate for performing NPV is the after tax interest rate (rd*). Important to know which lease rate would allow for positive NPV when negotiating lease. Module 7 – Investment Risk 777240128270Return Risk 00Return Risk Security market line (SML) - relationship between risk and return as being positive. Higher the risk, the higher the required return. Capital supplier risk = standard deviation of rates on return on entire portfolio of assets. Risk of set of securities quote probabilities of various rates of return or the probability distributions of returns, for example; Mean of probabilities; 0.085 x 0.35 = 0.02975 + 0.11 x 0.10 = 0.01100 + 0.135 x 0.30 = 0.04050 + 0.16 x 0.25 = 0.04000 Mean = 12.125 % Standard deviation; (0.085-0.12125)2 x 0.35 = 0.00045992 (0.110-0.12125)2 x 0.10 = 0.00001266 (0.135-0.12125)2 x 0.30 = 0.00005672 (0.160-0.12125)2 x 0.25 = 0.00037539 = 0.00090469 ?0.00090469 = 0.03008 = 3.008% Result = risk inherent in a portfolio. Morowitz - shareholders are risk-averse and require higher returns for higher risks. Positive relationship between return and standard deviation of return only true for the entire portfolio and not for the individual assets within. Part of standard deviation of return for individual assets is diversified away when included in a portfolio with others. Average Return of two investments. Average Standard Deviation of two investments. Portfolios return probability distribution = must know how individual asset returns interact from joint probability distribution; Asset 'B' Returns 7% 12% Probability Asset 'A' Returns 10% 0.35 0.1 0.45 20% 0.3 0.25 0.55 Probability 0.65 0.35 1 Each cell describes the probability of a particular set of returns being simultaneously earned by both assets A and B. Joint (interior) probabilities must sum in rows and columns to equal the original probabilities of the individual security returns while the sum of all cells = 100% (1.0). Portfolio Events and Probabilities Asset A Asset B Portfolio Probability Event 1 10.0% 7.0% 8.5% 0.35 Event 2 10.0% 12.0% 11.0% 0.1 Event 3 20.0% 7.0% 13.5% 0.3 Event 4 20.0% 12.0% 16.0% 0.25 Whole portfolio has less risk than the average risk of the securities due to diversification. Method for figuring out risk of a portfolio is using the correlation coefficient. Market Model and Individual Asset Risk Sharpe and Lentner = only relevant risk in a market where everyone understands the benefits of diversification is the undiversifiable or systematic risk of an asset. 1148715116840Risk of average Portfolio # of securities in portfolio 00Risk of average Portfolio # of securities in portfolio Riskm Common factor is called the market factor (Riskm). Systematic risk of securities is based upon the extent to which the market influences their returns. Measure of undiversifiable risk of a security (j): Systematic Riskj = Std. Deviation of return(j) x Correlation of (j) with the market. Correlation = 1 = systematic risk = standard deviation = not diversifiable. Low correlation to the market will have much of its risk diversified away when held in a portfolio with other securities = low systematic risk. Std deviation of returnj x Correlation of j with the market Betaj (?j) = --------------------------------------------------------------------------------- Std deviation of market return ?jm ?j = ------ ?2m ?j is the beta coefficient for j; ?jm is the covariance of j and the market; ?2m is the variance of the market. Regression coefficient - provides same information as previous systematic risk measure, but scaled to the risk of the market as a whole. Example: ? of 1.0 indicates that an x percent increase or decrease in the return on the market is associated with an x percent increase or decrease in the return on that security. ? of 1.5 indicates an x percent increase or decrease in the market will result in a 1.5x return. 1423035109220Return of security j Slope ? Line of best fit Return of the market 00Return of security j Slope ? Line of best fit Return of the market Steeper the slope (?), greater returns on security j gear upward (or downward) the returns on the market portfolio. Security Market Line If the financial market sets securities returns based upon their risks when held in well diversified portfolios, systematic risk will be an appropriate measure of risk for individual assets and securities, and the SML will dictate the set of risk-adjusted returns: 18745202540?j rf m Erj E(rm) SML 00?j rf m Erj E(rm) SML Above relates the amount of systematic risk inherent in the returns of a security ? to the return required on that security by the market. Relationship is positive where higher systematic risk of j, the higher its expected return. SML is located with repect to two important points, the risk-free rate (rf) and the market portfolios risk-return location (m). m = return of E(rm) and ? of 1.0 E(rj) = rf + [E(rm) – rf] ?j Investments must have returns > capital suppliers opportunity costs to be acceptable. Capital Asset Pricing Model (CAPM) System that generates required rates of return based on risk of assets. 123444046355Erj ?A RISKWACC ?B ReturnB WACC SML ?j 00Erj ?A RISKWACC ?B ReturnB WACC SML ?j 114300028575ReturnA 00ReturnA WACC = average of risk-adjusted rates of return of various endeavours, including asset types and FCF expectations. Acceptable = investment expected return > return on SML investments systematic risk level. Good investments would plot above the SML, perpendicularly above their systematic risk. Investment A is above the WACC = acceptable but below the SML = does not offer return high enough to compensate for its risk. Investment B has the opposite problem. E(re) = Risk Free Rate + (Beta equity x Market Risk Premium) E(rd) = Risk Free Rate + (Beta debt x Market Risk Premium) Tax Adjusted Debt Cost = E(rd) x (1 – Corp Tax Rate) WACC = E(re) x Equity financed + TADC x Debt financed Total E&D Total E&D Estimating Systematic Risk Use SML for estimating required returns the amount of systematic risk of a project. If project is same risk as company, and shares are traded on stock market, look up ? coefficient of the company’s shares in financial reporting services that supply data. If risk differs from company average, investment may be similar to another company. ? coefficient of other company can be used. Also valuable when the shares of the investing company are not traded, but those of a similar company are, and the investment is simply a scale change. If market ? coefficients are unavailable, systematic risk measure must be constructed. Begin with ? coefficient for company thinking of undertaking project, and adjusting coefficient for differences between the project and company. Considerations Volatile projects revenues are volatile in to overall market relative to company average, adjustment to ? coefficient must be made. Fixed costs of project is high proportion of total cost, ? coefficient must be adjusted upward for operational gearing. Beta(project/ungeared) = Beta (equity) x (% equity) + Beta (debt) x (% debt financed) ?v = ?e E/V + ?d D/V ?e and ?d are observed equity and debt ? coefficients E and D are their observed market values V is the sum of E and D. Revenue risk differential adjustment: Project revenue volatility Revenue-adjusted ? = ?v X ------------------------------------ Company revenue volatility Operational gearing adjustment: (1 + project fixed cost %) Project ?y = Revenue adjusted ? X ------------------------------------- (1 + company fixed cost %) Estimating the WACC of an Investment Return required on the equity of the project. E (rj) = rf + [E(rm) – rf] ?j ? is determined as above rf = government bond interest rates (YTMs) for comparable investments bonds. E(rm) = function of risk-free rate and estimate the difference between E(rm) and rf. Historical average market (i.e. LSE, NYSE) return above the risk-free rate. Once the equity required return is determined - find after tax cost of capital. Find the WACC of the project = WACC = rv* = D/V (rd*) + E/V (re) Certainty Equivalents Possible to adjust downward expected FCF for risk characteristics creating a certainty-equivalent CF, and to DCF at risk-free rate. CF – E(rm) – rf CFce = --------------------- X Covariance (CF,rm) Variance (rm) CFce = expected risky cash flow (CF) - adjustment for systematic risk. Variance (rm) is the standard deviation2 of market return Covariance (CF, rm) is the ? coefficient of the CF x variance of the market return of the cash flow with the overall market. Risk Resolution across Time Risk of investment can change as time passes. Common error = treat the investments entire cash flow set as having the same risk. Basic question is whether to undertake an initial outlay, where the desirability of that outlay depends upon the outcome of the test. Module 8 – Dividend Policy Residual cash not paid as dividends is still owned by shareholders. Retained cash is reinvested in the company on behalf of shareholders. Cash-retention or reinvestment decision. Dividend Irrelevancy Net result of changing a company’s dividend is substitutability of capital gains (i.e. share value increases) as the dividend is reduced for cash when it is paid. Increased dividends = decreased market value, and vise-versa. Increase in dividends would be shown as a widening of the dividend pipe and a narrowing of the retention pipe resulting in a smaller investment amount. Increase in dividends = increase in new equity (more shares issued) Decrease in dividends = decrease in new equity (less shares issued) Taxation of Dividends From shareholders perspective, it is after-tax dividends that are of interest. Dividend substitute for capital gains are liable for taxation. Dividends are taxed more heavily than capital gains. Dividends paid are taxed at the shareholder level. Imputation systems = amount of company taxes to shareholders based upon the dividends paid and give shareholders a credit on their taxes for that amount. Double payment effect = personal income tax liabilities of shareholders = the tax credit. Transactions Costs Shareholders may prefer one dividend policy to another depending on preferences for consuming wealth across time and costs paid to achieve the desired consumption pattern. Flotation Costs Companies incur costs in raising money from capital markets when they pay dividends so high as to require new shares to be issued. Combined Friction Optimal dividend policy: find all investments with +NPV & retain cash to undertake. Cash left over, dividend could be paid – passive residual dividend policy. Dividend Clientele Irrelevancy Differing groups of shareholders become known as clienteles in finance. Groups that would be willing to pay extra to get the type of dividend policy that is best suited to their own tax and consumption benefits must pay change premium. Switching policies can be costly to shareholders and is likely non-optimal. Signaling Interests of managers and shareholders to have share prices reflect new information (good or bad) as quickly as possible. Alterations in dividend policy are subtle way to communicate this information. Share Repurchase Cash dividend to shareholders. Money received in share repurchases is taxed more lightly. Signs of signal attempts that receive a positive response from holders. Not so positive for shareholders is a targeted share repurchase. Repurchase only particular shares usually held by potential buyers. Repurchase price = significant premium over the market price. Bird-in-hand - Passive Residual - Perfect Market – Traditional - Dividend Signalling Module 9 - Capital Structure Capital Structure, Risk and Capital Costs Debt is not cheaper than equity. Assurance of debt increases the ROE - implicit cost of borrowing. EBIT-EPS chart. Differences in level of steepness in EPS ranges are described as gearing or leverage. Irrelevancy: Modigliani & Miller Makes no difference to shareholder wealth whether the company borrows money or not. Shareholders can borrow and lend on the same basis as companies and any benefit/loss residing in company borrowing can be duplicated/canceled by shareholders borrowing or lending transactions in their own personal portfolios. Wealth increase is impossible since identical FCF expectations can be achieved in a different manner, and less expensively. Debt is more risky than its capital claims. Gains from issueing low interest debt offset by increases in the risk and attendant returns required by shareholders. Debt in the capital structure increases risk. Risk is related to beta. Beta is related to the variation in return. Since debt is first in line, debt amplifies the variability of return. Gearing or leverage is description of amplification of variability idea. Ungeared Company EBIT outcome EPS outcome Probability 15000 1.5 .1 120000 12.00 .55 150000 15.00 .35 Geared Company EBIT outcome Interest outcome Equity outcome EPS outcome Probability 15000 40000 -25000 -5 .1 120000 40000 80000 16 .55 150000 40000 110000 22 .35 Arbitrage and Prices Arbitrage is a transaction where an instantaneous risk-free profit is realized. Market prices adjust to cause all equivalent FCF to sell for the same price. Forces of demand and supply. Summation of Capital Structure Irrelevancy The M & M ideas make clear that the total value of the company must be unaffected by a change in its capital structure. Company Values without taxes 868680286385rv re 25% 20% 15% 10% 5% 0% 0 16.67% 33.33% 50.00% 66.67% 83.33% 100.00% 12.0% 00rv re 25% 20% 15% 10% 5% 0% 0 16.67% 33.33% 50.00% 66.67% 83.33% 100.00% 12.0% Behavior of required rates of return and overall capital cost of the company; it alters the company’s capital structure. 124650516764000 2947035121285rd 00rd Weighted average relationships determining rv we can imply; rv = D/V (rd) + (1 - D/V) (re) Higher proportion of lower-cost debt offsets lower proportion of higher cost - equity such that their weighted average is unchanged. Capital Structure and Taxes Companies are taxed on the amount of income or profit that they make. Income tax shields. Deductibility of interest payments cause a bias in capital structure towards the use of borrowing instead of equity capital. Debt is cheaper in that total of taxes paid by companies and shareholders will be lower than if the companies were to issue equity. Capital Structure Relevance with Taxes Because of the tax advantage in borrowing, a company with debt in its structure will be more valuable than an otherwise identical company that does not borrow. Value of tax benefit: VITS = ITS / rd Valued of debt plus equity or APV type situation: V = VU + VITS 4343400394335rv 00rv WACC steadily declines as the company substitutes debt for equity in its capital structure. As company value is increasing, ungeared FCF must stay the same as D/V increases. If V = FCF* / rv*, rv* must be declining as D/V increases. Cost of capital is therefore lower, the higher its proportion of debt. Capital Structure Irrelevancy - Taxes Miller: companies in economies with progressive personal taxes undertake more borrowing. Interest rates necessary to sell bonds to high personal-tax investors will cause the benefits of company borrowing to disappear. Tax benefits of company borrowing compete with other mechanisms used to reduce taxes (depreciation, credits) that tends to reduce debts advantages, particularly when the amounts of income that require shelter from taxes is uncertain. Agency Problems Agency deals with situations where the decision-making authority of a principal shareholder or bondholder is delegated to an agent such as managers of a company. Conflicts of interest may arise among principals and agents. To resolve conflicts of interest is by complex debt contracts. Debt claims carry a convertibility provision; under certain conditions, at the option of the lender, a bond can be exchanged for common shares. Agency conflict occurs when a company in financial distress is unwilling to undertake a profitable investment because the resulting effect would benefit bondholders, not shareholders. Agency Costs Costs of bankruptcy or financial distress are: Legal process of realigning the claims on assets from those specified in the original borrowing contract. Implicit and opportunity costs incurred relative to what would have happened had the company financed instead by equity capital. Agency Considerations Perk consumption beyond the point where management productivity is efficiently enhanced. Conglomeration to increase the size and reduce the CF risk of the company. Company Borrowing Decision Importance to optimal amount of borrowing is tax considerations. Net tax benefits of borrowing. Risky business should borrow less (or be lent less) than companies that are not so risky. Rule probably works due to agency costs – risk is likely to make agency costs higher. Book Values and Borrowing Practitioners prefer Book values used for measuring the extent of company borrowing. Academic prefer that market values. Book values in the real world make sense. BV is a good measure of the extent of which values will not be upset by financial distress when engaged in borrowing. Deciding on Capital Structure Use simulation to forecast CF and financial statements across the foreseeable future under the various alternative proposals for financing. If significant chance of conflict with borrowing contracts in ways that would damage the operational aspects of the firm, borrowing should be avoided. If tax benefits of borrowing simply replace other tax benefits there is little reason to borrow. If company value is largely based in tangible assets, more borrowing is sustainable. Industry gearing ratios are useful to see what other companies have been able to sustain. If potential lenders fear company action to the detriment of bondholders, the company should attach covenants to the bonds to alleviate some of that concern - convertibility provisions. Reasons to avoid new equity issuance such as loss of ownership control and considerations may outweigh the negative aspects of borrowing. Once a tentative conclusion has been made, see if the result would be inconsistent with the capital structures of other companies in the same line of business. If so, it should be determined whether this is an improvement over the usual practice or a signal that something has been left out of the analysis. Module 10 – Working Capital Management WCM = current assets & current liabilities. Risk, Return, and Term on Investments Short-term finance tends to be risky in requiring the firm to frequently renew the principal amounts of financing outstanding. Interest rates are not the reason for return or cost differences between short and long terms. Costs depend on reversibility differences between the types of finance. Where companies find themselves with unforeseen reductions in the need for financing, short-term finance is dispensed with quickly at the end of its term. Short-term finance is less costly than long-term finance and because lower costs mean higher return, it also exhibits a higher return. Exactly opposite of the risk return characteristic of its assets. Combining Risk and Rates of Return on Assets and Financing Finance short-term assets with short-term liabilities and long-term with long-term. Maturity matching. Optimisation and Short-term Investment Balance costs and benefits to produce highest net benefit or lowest net cost. Asset Type Benefit Cost Cash Highest liquidity Forgone interest Marketable Securities Liquidity Zero NPV Accounts Receivable Increased revenue Delayed, uncertain cash receipts Inventories More efficient production schedule, sales flexibility Capital costs, transaction costs Efficient management of asset investments 108013540640Total Cost Max. net benefit Optimum usage Total benefit Amount of short-term assets used Total benefit and total cost 00Total Cost Max. net benefit Optimum usage Total benefit Amount of short-term assets used Total benefit and total cost Management of Cash Balances Cash and near cash assets offer the high liquidity benefit. Transaction balances – debts must eventually be paid in cash. Precautionary/anticipatory reserves – events that cannot be anticipated which require cash, as well as anticipated future cash needs of major dimensions. Compensating balances – cash amounts contractually left on deposit with banks. Costs of cash balances are the transactions costs of switching between higher and lower interest-bearing securities and accounts, and the differential interest rate earned. 1325880125095Time Minimum Replenishment Usage Maximum Cash Balances 00Time Minimum Replenishment Usage Maximum Cash Balances Cash usage model: Interest penalty of i percent (interest foregone) in holding cash balances j. Fixed transaction cost of $T for cash replenishment. Optimising of cash replenishment amounts: $r = [(2 x $D x $T)/ i ]1/2 $r is the optimal amount of cash replenishment, $D is the total annual amount of cash spent by the firm – economic order quantity. Seasonal or cyclic cash requirements = specify a probability distribution of potential cash balance changes. 132588065405Time $U $R $M Cash Balances 00Time $U $R $M Cash Balances $M is the lower bound, the minimum amount of cash on hand. $U is the upper bound. $R is a return point. Cash falls to $M, interest bearing securities are cashed to return the balance to $R. Cash balances increase $U, securities are bought with excess cash to bring the balance to $R. If $U and $R are well chosen, the costs of maintaining the cash balance are minimised. The formula below chooses $R; $R = [(3 x $T x s2) / 4I]1/3 + $M $T and i are as above s2 is the variance of the changes in cash balances – if the amount of increase / decrease in cash balances is expected, by the probability distribution, to be $c for each of the number of times (t) cash balances can change per day, s2 = $C2 x t. $U is part of this solution; $U = $M +3 ($R - $M) Management of Receivables Necessary to hold accounts receivable and inventory stocks. Inventories are handled similarly to cash but with the cost of shortages considered. Higher level of receivables = more credit sales and more customers willing to purchase = longer waits for actual receipt of cash = increase likelihood of bad debt. Discerning who should receive credit: Credit-reporting agencies supply information. History of customer accounts can yield information of a customer paying. Sophisticated statistical analysis (i.e. discriminant analysis). Accepts everybody: Expected Profit = (# good customers x profit per customer) + (# bad customers x loss per customer) If company performs a credit analysis: Above + (- the cost of the credit analysis) Calculate NPV associated with a proposed change in credit terms for a company; NPV = Change PV of sales receipts – change variable costs – change WCM Management of Short-term Financing Maturity matching. Short-term financing as required with short-term investments, for balance of risk and return. Takes advantage of credit extended by a vendor. Payment terms are described such as 2/10 net 30 which states 2% discount for payment within 10 days and payment beyond that is at full market price and is due in 30 days. Interest cost is composed of an annualised discount percentage given for early payment. i = (1 + [discount % / (1 – discount %)]365/discount days Working capital management involves two levels of activity: Application of management techniques to specific asset and financing decisions. Policies for decisions, so that the company automatically determines each of these small decisions well considered policy. Financial Ratio Analysis = L + P + CS + E Liquidity = CR + QR Current Ratio = Current Assets / Current Liabilities Quick Ratio = Current Assets – Inventory / Current Liabilities Profitability = PM + ROTA + ROSA + ROE + PS Profit Margin = Net Profit after Taxes / Sales Return on Total Assets = Net Profit after Taxes / Total Assets Return on Specific Assets (e.g. Inventory) = Net Profits after Taxes / Specific Asset Return on Owners Equity = Net Profit after Taxes / Owners Equity Percentage of Sales = Item chosen / Sales at 100% Capital Structure = FCAR + DR + TIE Fixed to Current Asset Ratio = Fixed Assets / Current Assets Gearing ratios (leverage) = contributions of shareholders with the financing provided by the company’s creditors and other providers of loan capital. Low gearing ratios = less risk when the economy goes into a recession, but also lower returns when the economy recovers. High gearing ratios experience the opposite. Debt Ratio = Total Debt / Total Assets Times Interest Earned = Profit before Taxes + Interest Charges / Interest Charges Efficiency = IT + ACP + FAT Inventory Turnover = Sales / Inventory Average Collection Period = Debtors / Sales per Day Fixed Asset Turnover = Sales / Fixed Assets O/S AP = Days O/S x AP Amount x (Rate Finance – Rate Return) Days Example: O/S AP = (20/30) x 700,000 x (20% - 8%) Module 11 – International Financial Management Exchange Rates and the Law of One Price Law states that the same thing cannot sell for different prices at the same time. Purchasing power parity across countries. Frictions to purchasing power equilibrium = transaction and information costs, positive and negative impediments to free trade imposed by governments. Spot and Forward Exchange Rates Spot rate = rate for given currency to be exchanged for another on that day. Forward rate = going price for exchanging between currencies at some future time. Forward exchange contract = commitment to purchase or sell currency at a fixed price and time in the future. Avoid the risk of exchange rate fluctuations or to hedge such transactions. Forward exchange market can be used to speculate in exchange rates = commitment to purchase a currency but has no future dollar inflow expectations. If currency is selling at a higher forward rate than spot rate = forward premium If lower = forward discount. Exchange Rates and Interest Rates Same as hedging through borrowing funds in the required currency at an existing interest rate, and exchange those funds for the local currency at the existing exchange rate. The amount of dollars required to pay off loan with cash expected from collecting receivables at a future time point; Amount borrowed = $ receivable / (1 + existing interest rate). Loan amount is then switched to local currency at the spot rate. Local currency is then invested for the duration of the loan at the local interest rate. Receivables, when received, are used to pay off the original loan. Cash proceeds = same as purchasing foreign funds in the forward exchange market. Necessity of foreign exchange and interest rate markets, due to interest rate parity. Interest rate parity = borrowing/lending in one currency at applied interest rate will produce the same final wealth as borrowing/lending in other currency at its interest rate. Interest rates must adjust to ensure such parity or there will be arbitrage opportunities. Relative interest rate = Relative forward exchange discount / premium. Forward Exchange, Interest Rates, and Inflation Inflation, differential inflation, influences exchange and interest rate markets. Inflation affects the future purchasing power of that currency. Forward exchange rate two currencies = expectation of differential inflation rates. If inflation is expected to exist during the loan period, the real (in terms of purchasing power) return is expected to be less than the nominal return. Nominal interest rate = real interest rate + effect of inflation (1+ nominal rate)n = (1+ real rate)n x (1+ inflation rate)n where n is the number of periods in question Ratio forward exchange rate to spot exchange rate = ratio expected inflation rates of two currencies. Interest rate differentials = caused by inflation differentials = cause of observed discount or premium on forward exchange. International Financial Management: Hedging International Cash Flow Arguments to hedging exchange exposure: Real assets in other countries will experience nominal increases in value as inflation increases and exchange rates move down in that currency. Significant transaction costs to hedging. Foreign exchange option. Allows holder to buy/sell foreign currency in the future. Cost of options is usually higher than forward contract. Forward contract to sell cash hedges exchange risk. Investing in Foreign Real Assets Deciding financial viability of foreign investment. Estimate expected DCF and discount at the investment’s cost of capital. When currency translation should be done in the evaluation of an investment. Use interest rate structure of foreign currency to estimate risk-adjusted foreign currency discount rate. Find foreign currency NPV. Translate foreign currency NPV at spot exchange rate to find domestic value. Diversification – if a shareholders are not well diversified across international borders, a foreign investment may deserve lower risk profile than a pure domestic one assuming the foreign investments CF are not well correlated with a comparable domestic one. Relative uncertainties of the investment – alterations in foreign trade laws, exchange restrictions, asset confiscation, and friction repatriation can increase the risk of a foreign investment. Financial Sources for Foreign Investment Exchange rate changes due to inflation in the foreign country. Domestic currency value of a real asset in foreign currency will not necessarily change, because the Forex rate effect upon value will be offset by the inflationary effect. Foreign real assets tend to experience increases in value as inflation increases, where as monetary assets do not and are serious candidates for the hedging of exchange risk. International capital market: long-term funds are called eurobonds; Short-term borrowings are called Eurocurrency. Borrowing rates are lower in eurobond/currency markets = lower regulatory costs. Repatriation of funds = problem for companies whose shareholders are foreigners. Some countries have significant measures in place that seek to keep profits earned by foreign firms within their borders. Management fees, royalties, loan interest and principal repayments, and transfer payments are used to repatriate funds to the domestic parent company. Financial Solutions to other International Investment Risks Moral hazard risks = dealing with foreign authorities. Management of this risk = agency theory. Anticipate potential situations where the host country would be likely to take action, and build automatic and irreversible counter-incentive into the original agreement. Involves a third party who the host country must appease (i.e. World Bank, IMF). Module 12 – Options, Agency, Derivatives, and Financial Engineering Options Call option = allows purchase another security or asset at fixed price and time period. Strike or exercise price - price of option allows you to purchase the shares. Expiration date - final date you can exercise the option. European - can only be exercised at expiration. American - can be exercised any time before or at expiration. In the money - option can be exercised profitable. Out of the money – option can be exercised in a loss. Option writer - issuer of the option is often termed the. Covered option or call - if the writer actually owns the underlying securities. Put option - allows the holder to sell at a fixed price for a fixed period of time. Spreads, strips, straddles, hedges, butterflies. Option Valuation As long as there is some chance that an option could have some exercise value prior to expiration, the at the money option would sell for a price > zero. Out of the money options - market price is lower since security must increase more in value. In the money options also sell for more than their exercise value as the holder stands to gain at exercising the benefit of possible interim increases in underlying asset or security value, but is not at risk for all possible reductions in underlying asset value. Option market value is always above exercise value = option premium. Calculating the Value of a Simple Option Assume price changes are binomial; they can take only one of two values. Example: stock trading at $1.50 has a 60% chance of increasing to $2.40, and a 40% chance of decreasing to $0.90: 141732032385q = 0.6 1-q = 0.4 0.6 So = $1.50 dSo = 0.6 x $1.50 = $0.90 uSo = 1.6 x $1.50 = $2.40 00q = 0.6 1-q = 0.4 0.6 So = $1.50 dSo = 0.6 x $1.50 = $0.90 uSo = 1.6 x $1.50 = $2.40 So = current price of underlying security X = strike price u = upward multiplier d = downward multiplier uSo = underlying security increased price result dSd = underlying security decreased price result Cu = option payoff at expiration if underlying security price is up = uSo - X Cd = option payoff at expiration if underlying security price is down = dSo – X Y = shares to purchase = (Cu – Cd) / (So (u-d)) Z = amount to lend at RFR = (uCd – dCu) / (u-d)(1+rf) Co = current market value of the option = Yso + Z Second: invoke law of one price we can discover Co by calculating the value of another investment that offers the same FCF or call equivalent portfolio. Payoff if underlying shares increase becomes; YoSo + Z(1 + rf) = Cu If shares decrease it becomes; YdSo + Z(1 + rf) = Cd Value of the option is equal to the cost of the call equivalent portfolio, YSo + Z Hedge Ratio = m = So (u-d) / (Cu – Cd) uSo – mCu = dSo - mCd Valuing Realistic Options Any realistic model must allow for multiple prices. Black-Scholes option model is essentially the same as the many short period binomial models, except the time-periods are continuous. Co = SoN(d1) – Xe-rfT N(d2) d1 = [ln(So/X) + rfT]/?(T1/2) + 0.5?(T1/2) d2 = d1 – ?(T1/2) SoN(d1) = value of the cumulative normal unit distribution at the point d1. Xe-rfT = exercise price multiplied by e-rfT, which is a continuously compounded interest or discount rate with e = base of a natural logarithm, rf = risk-free rate, and T = time remaining until option expiry. N(d2) = cumulative normal distribution value. ln = natural log of the bracketed expression. ? = standard deviation of the price of the underlying security. Five variables for determining option value; So, X, rf, ?, and T. So = Security price X = Strike price rf = Risk free rate of interest = Standard deviation of underlying security price (volatility,) T = Time until expiration So and X identifies the exercise value of the option, and how far in or out of the money. rf determines how much money must be set aside to exercise the option at expiration; as interest rates increase, the PV of future outlay to exercise declines and option value increases. ? is positively related to option value. Random movement in security price is likely to help than harm option value. As T increases, option value increases. If the So/X ratio is high = option is in the money = low proportion of debt in capital structure. If S/X ratio is low = company has lots of debt. Increase in ? means that the operating assets of the firm are more risky. Agency Efficient market for company take-overs is an important solution to the agency problem of manager-shareholder conflict. Any solution to an agency problem requires an overall gain in solving the problem, which is allocated in a way that the agent has an incentive to participate in the solution. Derivatives Financial security whose return or outcome is derived from other assets value or return. Most common type of transaction = hedging of risk. Types of Derivatives Interest Rate = forward contracts, futures contracts, options, and swaps. Stock Market = futures contracts on market indexes, options on market indexes. Mortgage = complex derivatives. Foreign Exchange = forward / future contracts, options, swaps. Real Asset = forward / future contracts, options contracts. Swaps = Derivatives designed to hedge risks of interest rate and foreign exchange. Hybrid and Exotic = formulated from combinations of other types of derivatives. Financial Engineering Designing a hybrid/exotic financial security to fit specific risk-shaping intentions of firm. All financial securities can have some combination of; Credit extension - loans, bonds, etc. Price fixing - futures / forward contracts Price Insurance - call / put options Invention of new hybrid financial securities to fit exactly some requirement of an individual financial market participant is a matter of combining these elements into a package that will produce a profile of cash flow expectations meeting this need. Summary Version 2 Chapter 1 Future Value = fv = CF0 (1+i) n ?100(1+.10)5 = 100(1.61051) = ?161.05 Present Value = PV = CF0 1/ (1+ i) n Cash Flow signs (-) Cash out (+) Cash in Multi Period NPV NPV = - CF0 + CF1 / (1+ i1) + CF2 / (1+ i2)2 + CF3/ (1+ i3) 3 + CFn / (1+ i n) n Perpetuity: A cash flow continuing forever (40+ periods) Perpetuity = CF/ i Perpetuity with growth rate g % = CF/ (i -g) Perpetuity with decay rate g % = CF / (i+g) (up to i = g) Financial Exchange Line Spending, Borrowing or Lending does not affect Wealth Only Shifting of the Financial Exchange Line Effects wealth Internal Rate of Return = IRR The point on the discount line where NPV = 0 NPV = 0 = CF0 + CF1 / (1+IRR) + CF2 / (1+IRR)2 + CF3 / (1+IRR)3 NPV = 0 = -550 + 770 / (1+IRR) = (1+IRR) = 770/550 = 1.40 = IRR = 40 % Forward Interest Rates = Rates which begin in the future 0f1 = Spot Rate = (1+ i) 0 = Beginning Period; 1= end period 0f1 =(1+ i) 1f2 = (1+ i2)2 / (1+ 0f1) 2f3 = (1+ i3)3 / (1+1f2 )(1+ 0f1) Compounding Interest: CF2 = CF0 (i1)2 CF2 = CF0 + [CF0 (i1)] + [CF0 (i2)] + [CF0 (i1)(i2)] €121 = €100 (1.10)2 €121 = €100+ [100 (1.10)] + [100 (1.10)] + [100 (1.10)(1.10)] 21717002362200017145002362200011430002362200068580023622000€121 = €100+ [10] + [10] + [1] (Amount Invested interest) (earned per period) (interest on interest) Compounding periods increase- Interest compounds more quickly CF0 [1+ (i/m)]mt I = interest rate m =compounding periods t = number of periods ?100 note compounds twice per period for two periods at 10% ?100 [1+ (0.10/2)](2)(2) = ?100 [1+ 0.05](4) = ?121.55 Continuous Compounding FV CF0 (eit) e is the base of the natural log= 2.718 ?100, at 10 % for five years = ?100(2.718)(0.10)(5) =?100(2.718)(0.5) =?100(1.6487) =?164.87 Continuous Compounding PV Present Value of a =?100/(2.718)(0.5)= ?60.53 Interest rate futures- Future rate based upon available information, future rates will vary as additional information appears. Futures are selling a commitment to transact in a financial security at prices fixed in the present. t1 futures price to transact in t2= ?1000 / (1+ 1f2) discounted to t0. Need ytm, effective rate, apr Duration – the number of periods in the future where a bond’s value is generated. The longer the number of periods the greater the risk on variable CF coupons, high coupons, further away in time have greater duration. NPV = C1 / (1+i1) /$ + C2/ (1+i2)2 / $ + C3/ (1+i3)3 / $ NPV = $80 / (1+0.08) /$1000 + 90 / (1+0.09)2 / $1000 + $1080 / (1+ 0.10)3 / $1000 Chapter 2 Capital suppliers- equity & debt Equity is a residual claim; officers & directors are agents tasked with increasing shareholder wealth. Equity has limited liability and is last in line for claims for assets, however gets everything remaining. The market value of the common share is the discounted value of all future dividends expected. Value0 = Dividend1 + Value1 V0 = DIV1 + V1 (1 + Equity discount rate) 1+ re Et = Equity value at time t1 re = equity discount rate DIVt = Expected Dividend at t1 E0 = the sales value of the shares at t1 The purchasers of the shares at t1 expect V1 = DIV2 + V2 1+ re The change in shareholder wealth by an investment occurs regardless of the source of cash. If it comes from new investors or dividends not paid, both NPVs are equal. Value change increases by the NPVs + the cost to under take. Investment Decisions in a Borrowing Corporation Borrowing does not affect negatively or positively the NPV of an investment decision. Share Values and P/E Ratios P/E may be the reciprocal of re: 1/re. Hence, re = 20% P/E = 5 This rule of thumb is a blunt instrument where the correct relationship is more complex. P/E is in effect a discount rate where lower multiples indicate higher risk, Higher multiples indicate lower discount rates and lower risk. Payout Ratio (PR): the proportion of company’s earnings it pays as a dividend. (EPS)(PR) = DIV P/E is a complex number in terms of what can influence it; PR risk and re. Earnings, Profit & Cash flow Corporations should attempt to: 1) Maximise the shareholders wealth. 2) NPVs is ? wealth which occurs 3) Corporate NPV is the ? between the increase in market value and the cost of the investment. Cash flows are NOT accounting numbers! Financial ‘Customers’ are not Sales as in Accounting Sales; they are the CFs, cash into corporation. Likewise, Operations are not expenses, they are cash outlays. Operations include hard cash outlays, labour, fuel, and materials. Criteria: 1- paid in cash that period 2-Deductible for taxes that period 3- not a payment to a Capital supplier (dividend, interest) Everything in operations is an expense, however, not all expenses are in operations. (Depreciation, Depletion, etc.) t0 t1 t2 Customers 0 +17,500 +23,500 Operations 0 - 7,000 - 3,830 Assets -10,000 - 4,000 - 2,000 Govt 0 - 4,000 - 8,085 Capital FCF -10,000 + 2,500 + 9,585 Capital: the amount of cash left over after all cash amounts are paid, the bottom line. Free Cash Flow. FCF. Cash Flow and Profits Cash flows differ from profits in the timing of the cash received. Total expenses exceed total cash out lay by the amount of depreciation. Tax cash flows are on revenue less expenses called taxable income. Notes: Project evaluations are viewed from the affects on the company as a whole. Negative tax cash flows, as evaluated by a project analysis seek to encompass the benefits transferred to the company as a whole. A tax loss on this project can offset income in a different area of the company. Investment or project NPV is calculated by discounting to present all of the resultant cash flow of the whole corporation FCF is the residual cash flow, which can be extracted without disturbing the investment. Chapter 4 Cash Flows Variables and Formulas FCFt = Free Cash Flow- Net amount of cash It = Interest Cash Flow Tc = Corporate Tax rate ITS = Interest Tax Shields FCF*t = Un-leveraged FCF, not including ITS Et = Expected Market Value of equity investment at t Market Values Dt = MV of Debt at t Vt = MV of Et + Dt re = required return on equity investment Required Returns rd = required return on debt investment rd* = net cost of debt [rd (1- tc)] rv= weighted average return on capital WACC rv = D/E (rd) + E/V (re) rv* = D/V (rd* ) + E/V (re) ru = Unleveraged, all equity cost of capital WACC-NPV Investment Evaluation NPV0 = ? FCF* APV0 = ? [ FCF*t +ITS ] (1+rv*)t (1+ru)t (1+rd)t WACC NPV = - CF0 + FCF1 / (1+ rv*) + FCF2 / (1+ rv*)2 + FCF3/ (1+ rv*) 3 + FCFn / (1+ rv*) n Chapter 5 Estimating CFs 1-Include all economic opportunity costs (a) Using existing resources 2- Relevant CFs interactions with other investment activities of the corporation 3- Sunk costs are to be ignored 4-Caution in interpolating of overhead numbers, incremental increases caused are to be included, arbitrary allocations are to be scrutinised. Remember: Accounting Numbers are very different from CFs and incremental CFs. These may be included erroneously: MGMT salaries, depreciation, inventory allocations. May be overlooked: Interactions with existing lines, incremental increases in cash balances. Operating CFs Change in Net Working Capital Remember Revenues are not CFs! Net working capital is the change, which occurs, in total current assets & total current liabilities between the periods. t0 t1 t2 t3 Total Current Assets 1,100 + 1,750 +1,320 150 Total Current Liabilities 0 - 300 - 800 150 Net Working Capital (NWC) 1,100 + 1,450 520 0 Change in NWC 350 -930 -520 [*Change in NWC is the difference between t1 – t0 t2 – t1 t3 – t2] (1,750-1,100) (520-1,450) (0-520) Changes in NWC reduce or enhance CF in the opposite direction; a (+) change in NWC means more cash is tied up, a (-) means cash freed. NWC often includes changes in Cash balances or Inventory. Net cash from Sales t0 t1 t2 t3 t4 Operating Profit 0 750 620 400 -60 Less Change in NWC -1,100 - 350 930 520 0 Plus Overhead 0 70 80 80 0 Operating CF -1,100 +470 +1630 +1,000 -60 Operating CF is the actual cash received from sales activities, Debtors or Accounts Receivable is not included. Allowance for Bad Debts is a ‘set aside’ and negative adjustment must be made shown in t4. Fixed Asset CFs t0 t1 t2 t3 Fixed Asset Purchases 1,300 200 0 0 Fixed Asset Sales 0 0 0 950 -1,300 0 0 +950 Fixed asset CFs are straightforward when depreciation is clearly indicated, a nightmare if it is not. Income Tax CFs Net Income after Deductible items times the tax rate. Deductions include Depreciation, Interest expense, depletion, credits etc. Summary CFs t0 t1 t2 t3 t4 Operating CF -1,100 +470 1,630 1000 -60 Fixed Asset CF -1,300 - 350 0 950 0 Tax CF 0 70 110 185 -30 F CF -2,400 +110 +1,520 +1,765 -30 Cash Flows for end of period analysis are “0” Use revenue figures to determine income, taxes Adjust cash flow with cash flow analysis, If asked for WACC, do not subtract interest. Procedure for Cash Flow Analysis The goal is to evaluate the investment in terms of its wealth increasing prospects or NPV The FCF will be evaluated at the appropriate discount rate, most likely rv*. FCF is the net cash flow derived from the investment, which is CF from operations (CFO). (Customers less taxes, plus change in NWC). To Find CFO, you must subtract Operations from Customers then, subtract taxes. To find Taxable income you must consider depreciation. Hence the steps for Investment analysis: Calculate depreciation over time for tax purposes, Residual depreciation captured at sale, Income from sale is attached to revenue item: OtherIncome. Calculate Taxes over time, Taxable income = Total revenue less Direct expenses, less Depreciation multiplied by tax rate. When calculating expenses be careful, attributing actual expenses promulgated by, or incrementally increased by the investment. Do not include expenses that will be paid regardless of the investment decision. Do not include ‘Sunk Costs’. Interest Charges (and consequential income reduction) are not included when using rv* or WACC, compensation is with rate adjustment. Calculate Net Working Capital Sales does not equal cash received, working capital items purchased does not mean they have been paid with cash. Cash balances and inventories may increase or decrease with investment. These calculations set to adjust for these phenomenons. Setting a table to calculate actual AR - AP +/- ? Cash & inventories for each period. It is the period to period change that is defined as NWC Summarise and find FCF for each period Sales Revenue less (Direct Expenses) less (?NWC) less (Fixed Asset CF) less (Taxes) . Equals FCF 5- Discount at appropriate rate = rv* = E/V(re) + D/V(rd*) rd* = rd(1-Tc) Chapter 6 Investment Analysis using Alternatives to NPV A fundamental premise of EBS Finance course is the superiority of the NPV to other analytical tools. Exploring alternatives: The Payback= the number of periods the in CFs equal the initial investment or out CFs. Problems: Payback ignores CFs beyond re-cooperation point, does not discount. Discounted Payback solves one of these problems. ROI: Return on Investment = Expected profits . Net book value of assets ROI is an accounting formula that in spite of its popularity does not accomplish what it hopes to, evaluate the performance of an investment. (1) It does not discount (2) It does not use the correct numbers (3) It does not correctly value timing of cash flows. t1 t2 t3 600 500 400 500 500 500 All CFs Are values the same! 400 500 600 NPV Weights CFs to Front Also, ROI Use depreciated asset over time. This is not what happens in CF patterns. IRR vs. NPV- NPV is superior. IRR is average per period rate returned on an amount invested. Calculating IRR is by the heuristic method, guessing various discount rates to bring NPV to 0. IRR is comparable to the hurdle rate rv* IRR is useful where early CFs are (-) and subsequent CFs are(+) Problems: (1) Cash flow sign changes affect answer, sometimes giving numerous disparate answers (2) IRR cannot accommodate changing interest rates over time. (3) IRR can produce ‘Cross over’ rates (4)IRR assumes reinvestment of CF at IRR, which seldom is the case. Improvements on IRR Incremental Cash Flow Analysis (ICFA): Can be used to overcome the obstacles inherent to IRR. ICFA can be used to choose between two investments Steps: (1) Pick two investments from the “pot” (2) Select the one with the highest ? of FCF*, discounted at 0%, this is called the Defender, The other the Challenger. (3) Subtract CFc from CFd to find the incremental cash flow ICF. (4) Calculate the IRR for the ICF (5) If the IRR for the ICF is greater than the hurdle rate rv*, then keep the challenge, throw out the defender, the winner becomes the defender. If lower than rv* toss the challenger. (6) Repeat the process for all competing investments. (7) Calculate IRR of the winner if greater than rv* accept, if less reject the whole pot. Never use ICF method if there is more than one change of sign or varying rv* Summary of IRR vs. NPV Both are discounting Methods IRR compares the average per period earn rate to rv*, NPV uses rv* as the discount to compare wealth increase. IRR & NPV will usually give the same answer. If comparing multiple projects, ICF method must be used. IRR has significant problems when multiple sign changes occur. IRR is not useful if there are changes in interest rate. Cost Benefit Ratio Sum of the discounted inflows Sum of the discounted outflows If the analysis yields answer > 1 investment is accepted if < 1 investment is rejected. Profitability Index Sum of the discounted FCF Cash out flow CBR & PI are a relative measure not an absolute wealth measure. They are bias to high differential ratios. Capital Rationing: There is not enough money available to undertake all desired profitable investments. Generally, there is virtually unlimited capital available for profitable investment; however, constraints are derivatives of the following themes (1) Inter-departmental decisions (2) Capital Markets disagree with the desirability of the investment. Capital rationing techniques the set of methods for dealing with access constraints, budgets and highest NPV. Capital rationing in the first place indicates inter-organisational communication problems or you have been unconvincing to the capital markets each is a failure in some respect. Capital Rationing Techniques: Rank Investment by PI and choose to the limit of capital budget using care for both quantitative factors and qualitative attributes. Investment Interrelatedness: Acceptance or rejection of one investment affects the CF of some of the other investments. These are economic interrelated. Mutual exclusivity one investment or combination of investments excludes others. Positive / negative interrelatedness, a funeral parlour and a rock concert arena. Positive Neither Negative Purely Somewhat Independent Somewhat Mutually Contingent Exclusive Economic relatedness of Investment Cash Flows List all mutually exclusive combinations and choose one with highest NPV Renewable Investments- Assets where periodic replacement is essential appears least expensive 49149002476500Process: (1) Replacement lives must correspond: rv=10% Life Product t0 t1 t2 t3 t4 t5 t6 NPV Annuity factor 3 A -14 -3 -3 -17 -3 -3 -3 -37,585 2.4869 2 B -7 -5 -12 -5 -12 -5 -5 -39,343 1.7355 Convert single cycle at discount rate to NPV. Find annuity factor for number of periods in each cycle at appropriate discount rate. Example: Product ‘A’, life 3 years, rv is discount rate 10%, NPV= -21,241 / 2.4869= -8,629 (-14, -3, -3, -3) Product ‘B’, life 3 years, rv is discount rate 10%, NPV= -15,687 / 1.7355 = -9,029 (-7, -5, -5) As a cost minimising strategy, Choose A for long lived assets. Economics of Leasing: Misconceptions: Leasing saves money because lessor is paying for the asset and lessee does not have large capital out lay. WRONG! A contract for payment is a debt obligation analogous to a loan. Balance sheet and cash flow statements will look the same. Debt capacity and company risk will be the same Benefits: (1) Leasing allows for higher tax benefits than alternative forms of borrowing and purchasing asset. If the leasee has low or uncertain taxable income, they can swap valuable depreciation and credits for lower implicit rate of borrowing. (2) Information Asymmetries exist and leasing can lower these costs. Asset obsolescence can be factored into encompass “latest & greatest”. (3) There are economies of scale in leasing. Specialisation creates expertise and efficiency. Evaluating Leases: Is it better to purchase or to lease? Airplane Lease vs. Purchase: Cost ?1,000,000; Depreciation SL 4 years; Residual ?0; Lease 5 years ?270,000, Tax rate 40%, thus Leasing tax credit ?108,000 Depreciation Tax credit is lost ?1,000,000 / 5 yrs. = ?100,000. Discount rate 14% ?(000) t0 t1 t2 t3 t4 Cost 1000 Lost depreciation Tax Credit (100) (100) (100) (100) Lease Payment (270) (270) (270) (270) (270) Lease Tax credit 108 108 108 108 108 Lease Cash Flow 838 (262) (262) (262) (262) Analysis: Consumer Gains ?838,000 by avoiding ?1M cash outlay and looses ?100,000 annual depreciation, and has to make ?270,000 annual lease payments of which ?108,000 is deductible. What is the best? Of course, check with NPV calculations. The interest rate appropriate is the after tax discount rate rd* calculated as 0.14(1-.40)=0.084 Lease NPV: 838,000 -(262) / (1.084)-(262) / (1.084)2- (262) / (1.084)3 -(262) / (1.084)4 =?-22,106.68 Therefore; if NPV is> 0 leasing is better; if NPV is<0 then purchase: Inflation & Company Investment Decisions: Do we use Real or Nominal rates when measuring returns? Real Return = Inflation free rate of return. Nominal Rate of Return = return adjusted for inflation Example: Nominal Rate = Real Rate + Inflation rate (1+ nominal rate) = (1 + real rate)(1 + Inflation Rate) (1 + 15.5%) = (1 + 10%) (1 + 5%) If cash flows are adjusted for inflation and rates are then NPVs will be the same. Caution! Do not mix real and nominal in same equation or analysis. Chapter 7 Risk and Company Investment Decisions: Capital Asset Pricing Mode l (CAPM): The market relationship between the relevant risk of an individual asset and the rates of return or discount applied to the cash flows of the asset. Risk is best measured by the ? of the rates of return on the entire portfolio of assets Portfolio probability distribution Rates of Return Probability Calculation 0.085 0.35 0.02975 0.110 0.10 0.01100 0.135 0.30 0.04050 0.25 0.04000 ? 0.12125 Mean Expected return = 12.125% Standard Deviation (0.085 -0.12125)2 times (0.35) = 0.00045992 (0.110 0.12125)2 times (0.10) = 0.00001266 (0.135 0.12125)2 times (0.30) = 0.00005672 (0.160 0.12125)2 times (0.25) = 0.00037539 ? 0.0009046 ?2 = 0.0009046 ?= 0.03008 The standard deviation of the return is 3.008%. Empirical Validity shows little evidence between ? actual returns. ? is an absolute value of dispersion and does not consider dispersion of outcomes in relation to an expected value. Risk, Return And Diversification: Risk is reduced by combining differing assets called diversification. The weighted average ? is not the correct way to calculate risk of a portfolio. This method produces a result that is too high by neglecting the benefits of diversification. The correct way is to calculate a joint probability table. Asset B Return 7% 12% Probability 10% 0.35 0.10 0.45 Asset A Returns 20% 0.30 0.25 0.55 0.65 0.35 1.00 Diversification Lowers risk. Hence, the joint risk of a well-diversified portfolio of stocks is lower than the weighted average ? of the stocks. Interrelatedness of two assets’ returns: Correlation Coefficient- Possess values from-1.0 to +1.0. Negative 1.0 is perfect negative correlation to positive 1.0 perfect positive correlation. Important points Individual Asset will not have the weighted average risks as a collection of individual stocks. Joint probability distributions detail the interaction of the assets. Risks of individual assets will be mitigated by diversification by a degree of covariance. The higher the correlation between assets in a portfolio the lower the benefits of diversification. The Market Model and Individual Asset Risk: The risk of a portfolio of securities decreases with the number of stocks. The un-diversifiable or systematic risk is the market risk. Un-diversifiable risk of a security j = ?j x (correlation of j with the market) Hence the ?eta = ?j x (correlation of j with the market) This is also called the regression coefficient. ?2m Beta corresponds to relative movements in the market The market influence on a security Beta, is measured on a scale of (-1.0) to (+1.0), where a given % movement in the market M, corresponds to the security moving Beta times that given %. Beta is the slope of the regression line. The steeper the slope the higher the Beta, the higher the Beta the higher the gearing to the market. Beta amplifies the effect of the underlying market. Security Market Line: Assumptions: Participants in the market understand the benefits of diversification. The prices of the securities reflect this. The only risks that will receive higher compensation are un-diversifiable or systematic risk. How much compensation is required? The higher the risk the higher the required return. Required Return = Risk Free Rate + [(return on market)-(risk free rate)] Beta E(r)j = E(r)rf + [E(r)m + E(r)rf ]B Risk is of types diversifiable and Market Market risk is common to all assets and a common correlating limit to risk reduction. Systematic risk is Beta Securities returns are based upon risks when held in well diversified portfolios SML returns are opportunity cost of capital markets. Capital Asset Pricing Model (CAPM) = SML generates risk rated returns on assets. A company should not generally apply its WACC as its sole investment criterion. The WACC will give the correct answer only when investment risks do not differ. Investments above the WACC but below the SML do not compensate for the riskiness Investments above the SML but below the WACC require special risk adjusted return evaluation particularly if they are a cost savings investment. Cost savings investments are granted an x% reduction in discount, Scale increasing investments are considered equivalent risk uses the WACC, scope expanding, new ventures or riskier investments need augmented discount. Estimating Systematic Risks of Company Investments: If the project is simply an extension of scale the normal Beta is used. If it is a new investment, the Beta does not apply. If there is a similar company in the new business using its Beta as a benchmark is a good measure. For non-publicly traded companies selecting a Beta from a similar publicly traded company and adjusting therefore. Beta amplifies the effect of the underlying market. Operational Gearing: Adjusting the Beta upwards for high fixed to total costs. Financial Gearing: Adjusting Beta for borrowed money Bu = Be E/V + Bd D/V E = Market Value of Equity =250 D = Market Value of Debt = 100 V = E+D = 350 U = un-leveraged B =1.6 .rf = 10% Adjusting Beta for Project variance: Purify RV for financial gearing = B Bu = Be E/V + Bd D/V Bu will be less than Bru Bu = (1.6) (250/350) + (0.44) (100/350) =1.27 17145005334000 Adjust for Revenue Volatility Proposed Revenue is Numerator Times Beta = B Present revenue is base denominator 102870012319000(1.27)(0.95 / 1.2) =1.01 Adjust for operational gearing (1 + % of CF fixed Proposed) Times Beta = B (1+ % of CF fixed Present) (1.01)(1.15 / 1.25) =0.93 10287001587500 Restructure Beta for any proposed financial gearing: Bu = Be E/V + Bd D/V 0.93= Be (0.80) + (0.22)(0.20) Be =1.11 102870013652500 Find Project WACC= Be E/V + Bd D/V .rf =0.10 rm =0.091 Bd =0.22 E=80% D=20% Tc=50% Extract E(re) = rf + = Be (M-rf) Equity E(re) = 0.10 + (0.091)(1.11) E(re) = 0.201= 20.1% E(rd) = rf + = Bd (M-rf) Debt E(rd) = 0.10 + (0.22)(0.091) E(rd) = 0.12 = 12% Adjust for Taxes rd* rv*= Be E/V + Bd D/V rd*=(1-Tc) .rv* =(0.20)[(0.12)(1-0.50)] + (0.201)(0.80) = 0.173 =17.3% Construct NPV Run Certainty equivalents. CFce = Cash Flow Certainty Equivalents: How much would you exchange in the future “for Certain” For the derived CF and associated risks? CFce = CF – Erm –rf / variance(rm) [ Covariance(CF, rm) ] E(rm) =0.18 Var(rm) =0.01 Covar(CF1, rm) =?2400 rf =0.10 CFce =?150 000 – [(0.18-0.10) / (0.01)] ?2400 = 130 800 This is a t1 value this needs to be discounted to t0 at the rf rate, as certainty is risk free ?130 800 = ?118 909 (1+0.10) Revenue Adjusting: Bu (Project Revenue Volatility / Company Revenue Volatility) Operational adjustment: Project Compare with present WACC Chapter 8 Company Dividend Policy: How much should a company pay shareholders over time? Dividends are the amount of cash a company distributes to shareholders to service capital. Any residual cash after debt claims is owned by shareholders. The dividend decision is the mirror image of the cash retention or reinvestment decision. Dividend Irrelevancy The substitutability of capital gains for dividends. Paying dividends lowers future capital claims by increasing the number of shares sold. Withholding dividends increases future capital claims of existing shareholders. Paying dividends lowers the market value while retaining earning increases it. Hence there is no change in shareholder wealth only composition. Dividends and Market Frictions: Taxation, floatation & transaction costs are considered market frictions. Taxation of dividends varies by country; most often are after corporation taxation and passed to shareholders where taxation occurs again. Transaction Costs of Dividend Payments: Shifting from shares to cash is not without costs. Sale of shares is recognition of capital gains. If shareholders wish to use cash to increase wealth in corporation, they must repurchase shares with cash. Floatation Costs: Investment or Merchant bankers fees for issuance of new shares. Passive Residual Dividend Policy: Find investments with positive NPV retain as much cash as necessary to undertake investment, if a surfeit exists, return to shareholders, if insufficient, raise funds. Share Repurchase: “ Investing in ones’ self” is a bogus concept. Share repurchase is simply a transfer of cash to shareholders. A large dividend Signalling Value of Dividends: Changes in dividend policy are means of communicating information that cannot be explicitly broadcast. A pattern of dividends over time creates an expectation. A change in dividend policy signals positive or negative expectations, which would not be possible if dividends where random. Share dividends & Splits: These maintain proportional ownership, no reason other than signalling justifies. Dividend & Share Repurchase: Repurchases are a cash dividend or in the extreme a liquidation of the company. Share repurchases often receive a positive response from shareholders. This is not necessarily rational. Targeted share repurchases: These are offers to purchase only specified groups shares, usually at a significant premium. The non-targeted shares usually decline more than the rise of the targeted. Dividend policies exist to the preference of the individual shareholders consumption patterns of wealth, without market advantage to competitors. In aggregate companies dividend policies clears the market of potential share premiums of any particular policy. Price/share= Dividend1 / re-g = ?10 / 0.15-0.05 =?100 Chapter 9 Company Capital Structure: Capital structure decisions are the mix of Debt & Equity and the corresponding effects upon the shareholders wealth. Capital structure risk and costs Plausible, but incorrect notions: Equity requires no scheduled payments to contributors, this is ridiculous, as capital gains and dividends both costs. The notion the capital contributors require nothing for their capital contribution is preposterous. When adding debt, Equity’s residual claim is more risky with debt, via the SML and must always be more costly. D pushes up U to E creating a WACC which is higher than U. Hence, D’s low costs are offset by E’s higher ones. Capital Structure and Risk “EBIT-EPS’: Debt commits a company’s earnings EBIT outcome Interest outcome Equity outcome EPS outcome Probability ? 15 000 ?40 000 -? 25 000 -? 5.00 0.10 ?120 000 ?40 000 ? 80 000 ?16.00 0.55 ?180 000 ?40 000 ?110 000 ?22.00 0.35 . Debt in the capital structure increases earnings volatility for a given range of probabilities- Volatility in earnings increases Beta, with increased Beta comes increased Risk, and required return. Hence, for any two companies identical in every respect except capital structure, the one with the higher Beta will have a higher required return associated with it. The Beta of a stock is the slope of the line. Gearing of a company affects the steepness of the EBIT / EPS graph. D pushes up U to E creating a WACC that is higher than U called financial risk. Capital Structure Irrelevance: Miller & Modigliani clearly state opportunities with the market place do not allow for instantaneous risk free profits called arbitrage’. Market prices quickly adjust and cause all expectations of future cash flows to sell at the same price. The effects of demand & supply quickly dismantle arbitrage’ opportunities. Hence, the value of the company is unaffected by the structure. Every ? of debt is offset by a ? less of equity and therefore V is constant. Capital Structure and Taxes: Can an individual profit by personally borrowing and purchasing a debt free security? Debt No Debt Cash Flow ?120 000 ? 120 000 Interest Payment 40 000 0 Profit 80 000 120 000 Tax (50%) 40 000 60 000 Net Cash 40 000 60 000 Personal Interest 0 40 000 Net to Investor 40 000 20 000 It is decidedly better for the individual to borrow at the corporate vs. the personal level. Therefore, the transformation of the cash flows is different depending on the capital structure. The advancing idea is a company that borrows is more valuable than one financed with equity as it pays lower taxes and possess better cash flows and that cash flow is worth something call interest tax shields ITS. ITS =Tc (i) or the tax rate times the interest, hence, VITS = ITS/rd V = Vu + VITS. V is max when D = 100% . rv* decreases as D increase as FCF* remains constant rv* must decline V = FCF*/ rv*, therefore a companies cost of capital is increasingly lower by using more D where V approaches V of tax-free rate. Capital Structure and Irrelevancy: Miller asserts the benefits of corporate borrowing are erased by increases in taxes of debt holders and therefore higher and higher rates of interest are required as incentives. Summary: Capital Structure is unimportant in a tax-less world. However, when companies can deduct interest payments debt becomes a cheaper source of capital. In real world economies, progressive income taxes appear and cause the benefits of company borrowing to disappear. Additionally, above a certain level, borrowing competes with other tax leverage mechanisms (depreciation, depleation) to over ‘tax leverage’ a company. Tax reductions do create higher FCF, however, substituting another cost for taxes does not increase wealth or NPV! Capital Structure & Agency Problems: Conflicts of interest arise and issues of agency need to address them. Bondholders prefer the safest most predictable Cash Flows, shareholders prefer the highest NPV and conflicts ensue. Bonds are issued with certain expectations; shareholders may seek to switch to potentially higher NPV projects with greater risk to Cash Flow to the detriment of bondholders. Restrictive covenants and monitoring are costs built into issued rate. Convertible bonds enhance safety concerns of Bondholders and negate any incentives for stockholders to play games. Default & Agency Costs: Yes, it is true a company can only go bankrupt if it has creditors. Two things must be in mind (1) Circumstances of bankruptcy are not dependant on capital structure (2) Bankruptcy simply switches control from shareholders to bond holders. The determinants of bankruptcy are the frictions, (law suits, time in court, legal fees) operational constraints, and opportunity costs. Bankruptcy costs are not the costs that precipitate the decline in assets. Conclusion to Agency Considerations: Agency costs are therefore those of potential inefficiencies operating or investing in assets caused by default. The assumption is managers will seek to advance the interests of shareholders at the expense of bondholders, all of which is priced into the deal and all other deals in an efficient market. Convertible bonds, call options, complex securities are designed to lower costs. However at some point continuing to add debt to structure raises agency costs, the greater the leverage of debt to equity, the greater the leverage and incentive for managers to shift wealth to equity holders. Other Agency Issues Agency issues exist between managers and shareholders as well. As each party proclives to each best interest, conflict opposed to congruence ensues. Managers augment their wealth to the detriment of shareholders. Perquisites and conglomeration of companies, reduces cash flow stabilises manager remuneration with out corresponding benefit to shareholders. Similar to bondholders vs. Shareholders vs. managers produces agency costs, albeit higher as bondholders have first claim on assets and are less likely to be damaged via manager perk consumption. Making the company borrowing Decision: There is no rigorous quantitative formula to drop variables into to derive precise D/V. There are however guidelines. Tax consideration Are tax benefits certain? Is income high enough and stable enough to utilise obligations? Other non cash means of Tax write downs: Credits, depreciation, depletion Agency Costs: Risk is likely to make agency costs higher. Book values and borrowing; Academic view Debt/ Market Value Practitioner view: Debt/Book Value As a practical matter, lenders need to be concerned about the ownership of the assets and book value may be a better indicator of real value. Example: Goldmine vs. Software company: tangible assets present fewer problems than intangible ones in borrowing Techniques of Deciding upon Company Capital Structure: Low- tech solution: Ratio analysis, through industry trade journals and publications comparing to similar companies,” if they are doing it and surviving then it must be ok”. However, this Darwinian rule of thumb speaks more to survival than of optimisation. High-Tech solution: Financial Planning a detail examination of the future cash flow expectations, under a variety of “what ifs” scenarios and economic conditions. The hope is one alternative will present itself as superior. How is one gauged as superior? 1- Commodity Businesses with durable cash flows and tangible assets should look to debt. 2- Service or specialty products which experience highly volatile cash flows will find high agency costs on debt and should seek lower D/V and higher E/ V. 3- High Fixed asset companies with volatile cash flows and extensive depreciation and depletion allowances, negate tax benefits and increase risk due to volatile cash flows, should avoid borrowings and seek creative financing mechanisms. 4- Conglomerate Organisations with far-flung endeavours find debentures expensive. Amorphous structure is agency complex, with lenders. Inventive, creative securities may lower agency costs and produce favourable terms. Suggestions for Capital Structure: Using a simulation model forecast alternative structures under a variety of conditions. If simulators indicate significant chances for coming into conflict with borrowing covenants, which could damage operational aspects of the firm, borrowing should be avoided. If simulations indicate significant chance of tax benefits of borrowing not adding value, borrowing should be avoided. If companies value is largely in tangible assets borrowing is more sustainable. Industry gearing ratios are useful. Call provisions, convertibility appease lenders fearing companies will take action to the detriment of the bondholders Remember equity issuance dilutes ownership and may out weigh negative aspects of borrowing When a tentative capital structure is decided benchmark with other in the industry. The characteristic of company capital structure at the onset seems to be a rigorous quantitative process, however, in its practical application it is not. Project Evaluations: Conclusion of Chapter 9 1- Out line Goal: Make shareholders as wealthy as possible by highest NPV or Lowest cost relative to risk. Can the benefits of Debt be exploited? Are earnings at a point where tax shields are useful? Are earning stable? Are there other mechanisms reducing tax outflows? Depreciation? Credits? What is the status of any other debt? Earnings volatility? Covenants of debt. Do they significantly hinder the operational fluidity? Do the covenants redirect strategic imperatives? What constraints are placed on future borrowing? Existing collateral? How does borrowing change expected use of EBIT? Rate can tighten or restrict options. Benchmarking with other industry ratios. What do deviations mean? How do project goals align with ratios and other constraints? If needed what changes can be made? What capital structures are typical for industry? Equity EBIT-EPS, present vs. proposed. Floatation costs vs. lenders points. New issuance dilutes ownership and shifting of control, not dissimilar to lender’s restrictive covenants. New owners may redirect strategic imperatives and creditors may restrict them. Merchant bankers who take down significant percentages of an issue are as restrictive as large bondholders are, therefore if equity concentrated in controlling amounts can be more dangerous (restrictive) than debt. Remember, qualitative factors can weigh as much or more than quantitative ones. Chapter 10 Working Capital Management: The capital structure decisions are episodic ‘working capital management’ WCM is likely to be a larger component of a financial managers time. WCM is the management of current assets and current liabilities with a short-term emphasis and the wealth effects of these decisions. Short-term assets are less risky than long tern ones, because of enhanced liquidity. Long-term assets are more industry or company specific and are more expensive. Short-term assets are a commodity in nature, where long-term are differentiated in to the uniqueness of the individual company. Short term assets Long Term Assets Cash, marketable securities, Capital equipment, buildings, Inventories, accounts receivable land, brands, Intellectual capital, Management expertise Technological expertise Risk and Rates of Return on Financing by Term: Short term financing requires frequent review, rate adjustments thus increasing risks Long-term financing- a single review Rates of Return: Financial markets are fiercely competitive and rates reflect the costs and risks of the financing. The reason the costs differ between Long-term and short-term financings is of the attribute known as reversibility. Reversibility is less costly to disconnect, easier to end the relationship quicker to cash, the counterpart to liquidity The lower costs create higher returns to the lender. The company borrowing short term has the mirror image of this equation and possess greater risks of cancellation. This is the opposite of the assets profile. The risk of financing (cancellation, terms changing) is highest with assets that are of lowest risk (highly liquid). The risk of financing (cancellation, terms changing) is lowest with assets that are of highest risk (highly tangible). The mixing of Short-term & Long-term financings and assets presents a continuous challenge. The objective of maturity matching is a mix of risk & returns that are survivable. The greater the amount of long term financings on short-term assets the higher the probability of unneeded financing. This excess facilitates net lending. Management of Short –term Assets & Financings: Opposed to episodic Long-term asset purchases encompassing NPV and analytical evaluations, Managers develop policies on Short-term assets, such as Highest net benefit at lowest net cost. Asset Benefit Cost Cash High Liquidity Lost interest, Negative NPV Marketable Securities Liquidity $0 NPV Debtors Revenues, Sales Collection Uncertainty Inventories Production planning, sales Capita costs, transaction costs Uncertain NPV Management of Cash Balances: Liquidity means use for transactions in facilitation of operations and settlement of debts for cash. Precautionary or anticipatory balances (reserves) are for unforeseen events. Compensating balances cash amounts contractually obligated to banks. Transaction costs of switching between securities and accounts. Proper Cash Balances: Interest is forgone by holding cash. There are transaction fees for converting securities into cash. What is the proper balance for meeting predictable cyclical balances? Interest rate =i%, transaction fee = $T, Point of replenishment = $r Total annual cash required= $D Formula: $r= [(2D)(T/i)]1/2 Cash requirements are less likely to be predictable cyclical amounts, but random amounts. U= upper limit of cash, L= lower limit of cash R = the return point s2 = the variance in the balance U=M+[(3T)(s2) / (4i)]1/3 As free instantaneous cash transfers become ubiquitous these formula become of less practical significance. Management of Receivables: Managing the trade off from enhanced credit sales vs. the chance of slow or no pay. The goal of course to these policies is to Maximise NPV. The use of discriminant analysis examination of various customers’ attributes and thereby make predictions on credit worthiness. This analysis has costs and at a point, the value fades. To compare the costs of credit analysis, to costs of none: No Credit analysis: Expected profits= (Number of goods sold)(profit per each) + (Number of defaults)(Loss per default) Example: Sales= 100 Profit =? 100 Cost= ?400 Defaults =5% = (100)(100)+ (5)(400)= ?7 500 With Credit analysis: Each costs ?25, however, eliminates all defaults. =(100)(100)+(0)(400)-(25)(100)= ? 7 000 Quantitatively it is better to proceed without the expense of the credit analysis, however, if this were to become known, the default rates might increase. Calculating NPV of a Change in Credit Policy: Will a change in credit policy increase NPV, Will the expansion of credit terms increase sales enough to compensate for additional defaults, extension in average credit received NPV= (the change in the PV of the sales receipts) (Daily rate of Interest) ?Number of days minus (the change in the variable costs) minus (the change in the working capital requirements) (Daily rate of Interest) ?Number of days Example: Present working capital 20% of sales sales 100 @?250 Variable costs = ?175 Average days to pay = 35 Bad debts= 3% daily rate 0 .04% Proposed working capital 20% of sales sales 125 @?250 Variable costs = ?175 Average days to pay = 40 Bad debts= 4% daily rate 0 .04% = {[(125)(250)(0.96)] - [(100)(250)(0.97)]} (1.004)40 (1.004)35 [(125)(175)]} - {[(100)(125)] – 0.20(25 000) - .0.20(31 250) + 0.20[{(125 x 250) / (1.004)40} – 0.20(100 x 250) / (1.004)35 =?1206.30 The answer in this case is yes. The new credit policy increases shareholder wealth. Management of Short–term Trade Credit: Logic the price of the item includes payment deferred until due. Often there is a discount for payment made in advance of the final date. To evaluate the value of the NPV of the credit period vs. the discount: i={(1+{?[discount %/ 1-discount%])365/discount days Example: Payment 2/10/30 365 day line of credit 12% Effective interest rate = 1= (0.02 / 1-0.02)365/20 –1= 44.6% If a company has on average ?250 000 in payable s the differential is ?54 300 (20/30)(250 000)(0.446-1.12) Financial manager must set guidelines for the comparison of implicit short-term financing costs. Cash Budgeting and Short-term Financial Management The setting forth of the company’s expectations for its inflows and out flows over the near term. Cash budget plc Quarter 1 2 3 4 Explanation 1 Receivables at Start of period £40.00 £26.00 £19.00 £22.00 2 Sales during Period £130.00 £95.00 £110.00 £250.00 3 Collections from: 4 Current period sales £104.00 £76.00 £88.00 £200.00 80% of 5 Prior period sales £40.00 £26.00 £19.00 £22.00 20% of prior period sales 6 Total Collections £144.00 £102.00 £107.00 £222.00 7 Receivables at End of period £26.00 £19.00 £22.00 £50.00 = 1 +2 –6 8 Cash in flows: 9 Total Collections £144.00 £102.00 £107.00 £222.00 = line 6 10 Other sources £16.00 £5.00 £5.00 £4.00 Estimated 11 Operating Cash InFlows £160.00 £107.00 £112.00 £226.00 9+ 10 12 Cash out flows 13 Payment of payables £100.00 £65.00 £45.00 £55.00 Estimated 14 Other operating costs £26.00 £19.00 £22.00 £50.00 Estimated 15 Capital Expenditures £0.00 £100.00 £0.00 £0.00 Estimated 16 Taxes £6.50 £4.75 £5.50 £12.50 Estimated 17 Interest £3.00 £3.00 £3.00 £3.00 Estimated 18 Dividends £0.30 £0.30 £0.30 £0.30 Estimated 19 Total Cash Outflow £135.80 £192.05 £75.80 £120.80 Sum of 12 - 17 20 Net operating Cash Flow £24.20 -£85.05 £36.20 £105.20 11-19 21 Cash at Beginning of period £10.00 £34.20 £8.00 £44.20 22 Net operating Cash Flow £24.20 -£85.05 £36.20 £105.20 20 23 Cash balance at end of period £34.20 -£50.85 £44.20 £149.40 21+22 24 Minimum cash balance required £8.00 £8.00 £8.00 £8.00 Estimated 25 Necessary Financing Required -£26.20 £58.85 -£36.20 -£141.40 Negative of 23-24 Conclusion: Working capital management involves two levels of activity Active application of management techniques for assets and financings. Setting of policies for such decisions so virtually all small decisions have clear guidelines All WC strategies must be developed in the confines of a real time cash budget. Chapter 11 International Financial Management Exchange rates predicated on purchasing power parity known as” the law of one price’. As examined earlier arbitrage opportunities do not exist for long. If an item sells for more in one market than another, then sellers will deluge that market to get higher prices, two things will happen: 1) sellers’ competition will force prices downward and 2) Buyers will move to the market where the item can be purchased more cheaply. Therefore, all the machinations will lead to a singularity of price points in time. Spot & Forward Rates: The spot rate is the immediate exchange rate between two currencies. The forward rate is the exchange rate fir future points in time Exchange rates and Interest Rates: A necessity of foreign exchange and interest rates is the concept called interest rate parity: Borrowing or lending in one currency at its interest rates will produce the same wealth as borrowing or lending in any other currency. There will seldom exist arbitrage opportunities. Hence, Relative interest rates = relative forward rates, either as a discount or a premium. $/ ? ?/ $ Rates Spot 1.5960 0.6266 (1.0894)1/2 (0.988)(Present) = Future 180 day 1.5780 0.6337 (1.0650)1/2 (1.011)(Future) = Present If parity did not exist, a skilled financier could turn markets into money pumps. Forward Exchange, Interest rates & Inflation Speculation: Differential inflation: Inflation in a currency affects the future purchase power of that currency, and as purchasing power parity holds true in the spot market it also holds true in forward. An important determinant of exchange rates is the expectation of differential inflation between them. Hence, relative inflation = relative forward exchange discount or premium. Remember the Nominal rate is equal to the Real interest rate + effect of Inflation (1 +Nominal Interest Rate) = (1+ Real Rate) n x (1 + Inflation Rate) n Therefore if the real rates of interest are 4% in both the US and UK then (1.0894) ½ / (1.04) ½ =(1 +I) ½ = 4.75% (1.0650) 1/2/ (1.04) ½ =(1 +I) ½ = 2.40% International Financial Management: Hedging international cash flows “Frictions & Restrictions” Operating without a hedge is speculating upon future exchange movements, magnitudes and directions, in essence proclaiming knowledge better than implied by the rate structure. Foreign Exchange Option: he rights but not the obligation to exercise an exchange contract. The risk of loss has been eliminated, but the chance of gain is still present. A perfect solution? The sellers of the option has surely calculated their risk and priced it accordingly. Therefore, the option is not a hedge in the true sense of the word it is a super hedge. The benefits are equal to the costs, of course. Investing in Foreign Assets- Analysis of financial viability of a foreign asset is similar to domestic evaluations. The analysis may be more complicated due to qualitative factors in addition to quantitative ones. Consistency in the analysis is paramount. Evaluate the investment in the foreign currency, using its variations of inflation and interest rates, then convert the NPV from foreign currency to the spot exchange rate. Forward rates are usually only extended to 365 days, therefore when analysing periods longer than one year A comparison between the currency and the incremental differences of long term interest rates. Two tenets of foreign investing: 1) Benefits of diversification 2) relative uncertainties of the investment frictions, tax laws confiscation, etc. Financial Sources for foreign investment: Do you raise the funds domestically, in the foreign location or somewhere else? It does not matter quantitatively. Examining the relationship between real and monetary assets brings some insights. The value of ‘Real Assets’, buildings, land, distribution channels, management expertise do not fluctuate with fluctuation in exchange rates. Example: Inflation pushes the price of real estate upwardly, the corresponding exchange rates drop, the increase (due to inflation) of the real estate is offset exactly by the decrease in the exchange rate. The real decreases in the currency are off set by the nominal increases in the fixed asset evaluation. In times of inflation Real asset increase in value, where monetary ones do not. Therefore the only serious candidates for hedging are monetary assets. International Capital Markets: can make Euro dollar loans and exist simply because of lower regulatory costs. Chapter 12 Derivatives, Options, Agency and Financial Engineering Options: Options are contingent claims as there value depends on the value outcomes of the underlying assets at a fixed price, for a fixed period of time based on expectation of future cash flows Call Option: The right but not the obligation to purchase an underlying asset for a fixed price of a fixed period of time. Expiration date: The date where the contract expires. Option Premium The amount the option’s market value exceeds its exercise value. What is the market price of an Option? The exercise value plus the value of the possible interim increases in value. Calculating the value of a simple option: The underlying price changes during the life are the binomial. The value is up or down. The amounts, however, are uncertain. (1.6)($1.50)=$2.40 22860007429500Diagram of Out comes q=1.6 22860004254500 Share ValueS0 = 1- q =0.4 Exercise Price X= $1.25 (1.0 –0.4)($1.5) = $0.90 (0.60) Value of in the money option: Exercise $1.25, Current value $1.50 .Is “In the Money”. Procedures: Value of Expected outcomes: Cu =$2.40 - $1.25 = $1.15 Cd =$0.90 - $1.25 = $0.00 (an option by definition rejects this outcome) Therefore Cu = max (0,uS0 – X) The Law of One Price in Option Evaluation: Arbitrage opportunities do not exist in efficient markets, and therefore, the law of parity or law of one price prevails. The call equivalent portfolio Analysis rf = Risk free rate Y = Number of underlying shares to purchase (+)(as call) or sell(-)(as put) Z= The amount of money to Lend (+) or borrow (-) at rf Cu = (Yu)(So) + Z (1+rf) Yu = Cu - Cd Z = uCd - dCu Cd = (Yd)(So) + Z (1+rf) S0(u - d) (u-d) (1 + rf) Continuing with above example: Yu = $1.15 – $0.00 = $1.15 = 0.7667 Shares Zu = (1.6)($0.00) – (0.6)($1.15) = $0.6273 ($1.50)(1.6 – 0.6) $1.50 (1.6 – 0.6) (1.10) Therefore, if you purchase 0.7667 shares and simultaneously borrow $0.6273 you have identical cash flow expectations as the call above. Thus if shares increase the future CF is (0.7667)($2.40) = $1.84 From this figure you would subtract the cost of the borrowing = ($0.6273)(1.10) = $0.69 This equals of course $1.15 If they decrease the future CF is (0.7667)($0.90) = $0.90 From this figure you would subtract the cost of the borrowing = ($0.6273)(1.10) = $0.69 This equals of course $0.00 So what is the value of the option? It is of course the cost of the call equivalent portfolio. The C0 = Y S0 + Z = ( 0.7667)(1.50) - $0.6273 = $0.5227 The premium over the exercise price is $0.2500 The value is of course the difference $0.2727 Facts Four factors causing NPV to be incorrect Incremental cash flows – sunk costs, depreciation, overhead, etc. Rate of return – correctly using proper rate. Future events – technology advances and investment obsolescence. Determine value of investment options. Investment Inter-relatedness Economically inter-related – positive and negative correlation. Mutually exclusive – NPV of investments and choose only one. Capital Rationing – NPV of investments and choose as many as possible to optimize limited available capital and maximizing combined NPV. Renewable Investments Real assets that wear from asset use. Useful asset life expectancy limited by available lifecycle. Salvage value and replaceable in future. Equivalent annuity cost method. NPV / PV annuity factor = annuity cost. Choose asset with the lowest annuity cost. Agency & Bankruptcy Bankruptcy is positive for BH. Negative situation for SH. Agency occurs with a conflict of interest between SH – Managers – BH. BH want maximized NPV for debt. SH prefer maximized NPV for dividends, investments, shares, and projects. NPV debt < > NPV shares negatively correlated. Managers must manage the business to keep share values attractive to the equity markets but also keep the debt/bond values high to keep BH satisfied. Agency Methods Covenants/KPI Convertible bond = converted to shares at option of holder. Call provision. = redeem bond for preset amount prior to maturity. Bankruptcy = legal transfer of assets from SH to BH because company could not meet their debt obligations. Costs: transaction, legal, opportunity, and implicit. Equity in geared company: Call option If bond defaults = BH owns assets. Assets sold provisionally to BH at debt issue and repurchased by interest & principal payments by company representing SH. Capital Structure Academics = market values Frictionless markets. No agency, transaction costs, and information asymmetries. Traditionalists or practitioners = book values Market has frictions in real world. Asset NBV is representative of asset value for lenders. Historical and depreciated values for lenders. Tangible assets – used for gearing with book value ratios. Intangible assets, intellectual capital, goodwill, etc – do not use for gearing. Capital Budgeting – Cash Flow Analysis Interest payments Not included in CF since factored into WACC. Include ITS either as a reduction or NPV when using APV. Opportunity costs Include in CF as a cost or gain based on market values. Working capital = Net change per year included in Operating CF calculation. Fixed overheads = Do not included unless generated by investment/project. Profits = Not used or included except for Operating Profits in the calculation of Operating CF. Taxation = Included in CF to determine FCF. Feasibility study = Sunk cost. Loan Interest on loan is cash outflow to calculate income tax but NOT for cash flow. Interest use for ITS and used in APV calculation. Buildings – opportunity costs. Increase in AP – used in calculation of net WC. Inflation – increase CF calculations by relevant inflation rates and discount WACC by dividing by inflation rate for capital. Problems with IRR No measure of wealth creation. Inconsistent NPV project rankings. Multiple solutions with multiple CF sign changes. Assumption of reinvestment of net cash flows at IRR. Leasing Advantages No upfront cash outlay. Fewer financing restrictions. No asset ownership and obsolescence. Disadvantages High long run cost if asset is purchased. Higher interest rate than borrowing. Asset reverts to lessor at contract expiration. Diversification & Debt Two companies merging. Reduce debt risk when combined. Co-insurance – 2 groups of SH, BH, debt, CF, etc. Merger: Debt value increases = BH benefits SH decreases = SH loses Shift SH wealth to BH. Diversification – should not do since SH can self-diversify to hedge investment risk. Debt factors: Tangible assets ITS CF volatility Agency problems Industry peers. Abandonment Value and NPV Projects Capital rationing. NPV – PI – CBR Mutual exclusive – Inter-dependence – Inter-relatedness – Opportunity costs – Abandon less NPV projects and reinvest funds to more NPV projects. Constructing Systematic Risk Beta co-efficient for company to measure systematic risk. Find market traded company similar in capital structure, operations, industry, etc. Adjust for financial and operational gearing. Financial Gearing = Bu x Project Revenue Volatility / Company Revenue Volatility Borrowing company have undertaken. Increased FG = increased income volatility. More borrowing = more risk. Operational Gearing = FG x Project Fixed Cost% / Company Fixed Cost% Increase OG = higher Fixed Cost %. Greater business risk. Different Levels of Gearing Industry risk Cash flow strength Cash flow variability Fixed operating costs Taxation Assets – tangible or intangible. Maturity Matching Asset Finance Term Short Long Short Long Risk Low High High Low Return Low High High Low STA <> LTF = low risk + low return LTA <> STF cash flow trap = high risk + high return Match Assets with Finance STA = STF low/high risk + high/low return LTA = LTF high/low risk + low/high return Liquidity/cash flow trap = failure to make efficient use of funds. Dividend Signalling & Passive Residual Policy Dividend Factors: Dividend sustainment. Need for cash. Signalling effects. Taxation. Floatation costs. Dividend Signalling – Stable Policy: Consistent, predictable and smooth dividends. Frictions: fees, taxes, information free-flow. Share price and dividend signalling. Share dividends and splits. Passive Residual Policy: Unstable, inconsistent, and erratic dividend payment. No signalling effect. NPV projects cash retention any excess to dividends. Not common practice. Dividend Irrelevancy: Perfect capital markets. No frictions: tax, info, transactions, and agency. Dividends have no effect to wealth. Invalid theory. P/E Ratio Compare same industry company, risk, and valuations. Share price – reliance of market factors. Pattern of dividends. Payout ratio. Risk factors. Equity discount rate. Cash flow. Relevance of Dividend Policy Frictionless capital markets. No agency or costs: floatation, transaction, tax, information = irrelevant dividends. Real world – frictions and costs exist. Signal effect of dividends. Smooth dividend policy. Build cash surplus = low cap-ex periods. Use surplus = high cap-ex periods. Agency and Dividend Payments Conflict of interest with cash dividends, share dividends, and share re-purchase. SH – Management – BH Asset shift and transfer of ownership from/to SH and BH. Risk and asset control changes as transfer occur. Methods: covenants/KPI, convertible, call provision. Dividend factors: Prudence SH/BH preference Future obligations and issues. Costs – floatation and transaction. Signal effort to capital markets. Debt obligation conflicts. Agency & Call Provision Agency problem = conflict of interests. SH – Management – BH Information asymmetries NPV Debt < > NPV shares Call provision – Assurance of project NPV to BH. NPV project increases = increase in bond. Call provision = allow company to repurchase bond at set price and time. Bond value low = call option under valued. Under value NPV project = low bond value. If NPV project increases = bond value increase. Company can repurchase bond by call provision and gain on bond value increase. Cash Surplus & Dividends Keep for future cap-exp requirements. Invest in short term. Repurchase of shares. Dividends – regular and special SH preferences. Future liquidity. Market reaction. SH tax liability. Restrictive covenants on Debt. Debt repayment. Tax shield. Debt rate uncertainty. Covenants. Market reaction. Common Shares Market Value Share value = PV dividends. SH returns = PV dividends and capital gains on share valuation. Value of claims against company future cash flow. Payment and dividend policies. Black-Scholes Option Model Volatility variability of cash flows = more variable = higher risk. Time to maturity – longer = riskier. Asset value = share price. Exercise price = interest and principal payments to creditors. Debt interest rate. Foreign Operation Risks Issue: Forex translation. Risk: Forex fluctuations. Risk: Currency devaluation. Risk: Repatriation – management fees, dividends, off-shore capital funds, investments. Risk: Political instability – war, terrorism, government intervention. Risk: Inflation and deflation. Interest Rate Parity – no reason to choose one location over another based on interest rate differences. All else being equal, foreign investments are equal regardless of their location but dependent if there are any special or preferential government subsidies and grants to attract foreign investments into the local economy, will off-balance the equality, and may favour a particular location. Real assets – do not hedge assets such as buildings, land, etc., because they are non-volatile and remain stable in valuations when compared to monetary assets. Monetary assets – hedge because of they above risks and volatility. Hedge: Swaps – CF stream, locked forex. Hedge: Options – no obligation and locks forex in defined future timeframe. Hedge: Forward Contracts – obligation and locked forex. Hedge = costly and difficult to manage. Law of averages = fluctuations will eventually average itself out.