Exam 1 Formula Sheet

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University of Alabama, Birmingham *

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621

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Finance

Date

Feb 20, 2024

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2

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Definitions: Current Assets : Assets that can be easily converted to cash within 1 year ie. Marketable securities,A/R,Inventory,Work-in-Progress,Finished Goods Long-term Assets : Net property,Plant, and Equipment, Intangible assets/Goodwill, Property not used in primary business operations Current Liabilities : Liabilities that will come due within 1 year ie. Accounts payable, short-term debt, current maturities of long-term debt, salary, taxes owed but not yet paid, unearned revenue Stockholder’s equity = Book value of Equity = Assets – liabilities Net Working Capital = Current Assets – Current Liabilities Market Value = # shares outstanding x $ market share price Market-to-book ratio = Price-to-book ratio = Market cap / Book value Ie.P/B >1 for most successful firms, low P/B = value, High P/B = growth Total Enterprise Value = Market cap + Debt – Cash Gross Profit = sales revenue – costs of sales Operating Income = Gross Profit – Operating expenses EBIT = Operating income + Addl revenue – Addl expenses Pretax Income = EBIT – Interests expense Net income = Pretax income – Corporate taxes EPS = Net income / #shares Dilution = Growth in number of shares while maintaining the same earnings Stmnt Cash Flows = contains cash outflows not reported on P&L ie. Investments in property/plant/equipment/inventory Operating activity = starts with net income adds back non-cash entries ie. Depreciation, deferred taxes, stock based compensation, A/R increases are decuted from cash flows = reduces cash available to firm A/P increases are added to cash flows = increases cash available to firm Inv. Increases are deducted from cash flows Inv. Activity Capital expenditures = cash flow for purchases of new property, plant, equipment, amount of depreciation realized can be deducted Financing Activity = dividends paid are cash flows out and are deducted Retained earnings = net income – dividends Cash from stock sales or spent on buybacks is calculated here Increases in cash flows does not always equal a healthy business, increases In financing that outweigh negative operating activities can be of concern Profitability ratios: Gross Margin = Gross profit/sales, Operating Margin = Op. income/sales EBIT Margin = EBIT/sales, Net Profit Margin = Net income/sales Liquidity Ratios : Current Ratio = Current assets/current liabilities Quick Ratio = (Cash+Short-term investments+A/R)/Current liabilities Cash Ratio = Cash/current liabilities Working Capital Ratios: A/R days = A/R /Avg Daily Sales A/P days = A/P /Avg daily cost of sales Inv days = Inv/Avg daily cost of sales Inv turnover = Annual cost of sales/inv Interest Coverage Ratios : EBIT/interest, EBITDA/interest Leverage Ratios : Debt/equity = total debt/total equity Debt/capital ratio = Total debt/Total equity+Total debt Use market value of equity/Book value of debt Valuation Ratios: P/E ratio = Market cap/Net income=Share price/EPS Ent.Val to EBIT = Mrkt Val Equity+debt-cash/EBIT Ent.Val to Sales = Mrkt Val Equity+debt-cash/sales Return Analysis: ROE = Net income/Book Val equity ROA = Net income+Interest/Total Assets ROIC=EBIT(1-TaxRate)/Book val. Equity + net debt Dupont = NetIncome/Sales*Sales/TotalAssets*TotalAssets/BookValEquity = Net income/BookValEquity Asset Turnover = Sales/Total Assets = Reflect Firms efficiency Equity Multiplier = Total Assets/BookValEquity Net Present Value & Stand Alone Projects: NPV = PV BENEFITS -PV COSTS , PV PERPETUITY = C/r, PV FINITE = C/(1+r) n IRR is discount rate where NPV = zero Only applied to single stand alone projects Gives same result as NPV when cash flows are conventional ie. All Negative Cash flows precede positive cash flows IRR Rule says take investment if IRR > cost of capital When IRR Fails: Delayed investments – NPV only positive when r >IRR, when IRR >r larger difference = more confidence Multiple IRRs – If r is within upper and lower limits = more confidence, multiple IRRs when sign of cash flows changes more than once Nonexistent IRR – absence of IRR does not always equal positive NPV Mutually Exclusive Projects: Step1: Calculate NPV for each Step2: Rank high to low NPV Step3: Choose highest IRR Rule & Mutually Exclusive Projects: When projects differ in scale of investment,timing,or riskiness IRR cannot be meaningfully compared Scale: compare 500% return on $1 to 20% return on $1M Timing: Longer return horizon > shorter Risk: Compare cost of capital Forecasting Earnings: Investments in PPE are cash flows but not included when calculating earnings,Depreciation are realized annually less salvage Interest expenses are not considered when evaluating capital budgeting Unlevered Net Income = EBIT(1-TaxRate)=(Rev-Costs-Depreciation)(1-TaxRate) Corporate Income Tax = EBIT*TaxRate Indirect Effects on Incremental Earnings Opportunity Costs : Resources owned are not free, cost is the value it could have provided to the next best alternative; add to selling/gen/admin exp Using a warehouse vs Renting it out $200k rental rev*Tax Rate = incremental earnings Project Externalities = indirect effects of a project; cannibalism Sunk Costs : Unrecoverable costs paid regardless of decision to proceed Not included in capital budgeting decisions Ie. Spending $300k on a feasibility study to determine if a project is viable, Fixed overhead expenses, Past R&D expenses, Unavoidable competitive Effects Sunk Cost Fallacy = Concorde Effect = Being influenced by sunk costs to continue a negative NPV project due to large investment incurred Free Cash Flow and NPV: Increases in NWC is effectively a cash outflow=increasing assets Increases in assets/decrease in liabilities = cash outflow FCF = (rev-costs-depreciation)+depreciation-CapEx-ΔNWC Depreciation is non-cash expense must be added back CapEx are cash expenses they are deducted Depreciation Tax Shield = τ C *depreciation Capital Gain = sale Price – Book value Book Value = Purchase price – accumulated depreciation After-tax cash flow from asset sale = Sale price – (τ*Capital Gain) Terminal Value Example : Base hardware is opening stores, after year 4 sales are expected to grow at 5% per year. The continuation value in year 4 of the free cash flow for year 5 and beyond is: Present Value of constant Growth Perpetuity = C/ r – g Reminder: (perpetuity = start at t=1 not t=0) Terminal Value at Year 4 = FCF 4 (1+g)/r -g = 1.3x1.05/.1-.05 = $27.3M Continuation Value = $27.3M at year end 4 Continuation value can be added to year end 4 FCF Thus NPV of the investment for Base Hardware is = -10500 – 5500/1.1 + 800/1.1 2 + 1200/1.1 3 + 28600/1.1 4 = $5.597M Probability Distribution and Expected Return: E[R] = Σ R (Probability*Return) Variance: squared deviation from the mean Var(R) = Σ R *(P R (R-E[R]) 2 ) StdDev = SqrRt(Var(R)) Qrtrly StdDev = Sum of squared deviations/#samples less 1 Comparing Historical Return: Realized Return is the return that actually occurs during period R T+1 = (Div T+1 +P T+1 /P T )-1; Div = dividend, P T+1 = end price, P T = start price Dividend Yield = Div T+1 /P T , Capital Gain Rate = (P T+1 -P T )/P T Assumption = All dividends are immediately reinvested Annual Realized Return = 1+R annual = (1+R Q1 )(1+R Q2 )…(1+R Q4 ) Empirical Distribution of Annual Returns: Average Annual Return = R bar = (1/T)ΣR T Var(R) = (ΣR T -R bar ) 2 /T-1
Excess Return = Risk Premium = R bar – risk free proxy return, return in excess of risk-free return No precise relationship between volatility and R bar Larger stocks tend to have lower volatility than smaller All individual stocks have higher risk/lower returns than a larger portfolio Total Risk = Firm specific risk + Systematic risk Firm specific/unsystematic/diversifiable/idiosyncratic risk can be eliminated Systematic risk = market risk, undiversifiable Large portfolios average out unsystematic risk Risk premium is determined only by systematic risk Competitive financial markets do not reward unnecessary risk ie. Diversifiable risk Capital Asset Pricing Model (CAPM): CAPM prices risk E[R i ] = r i = r f + β i Mrkt (E[R Mrkt ]-r f ) Risk Premium = β i Mrkt (E[R Mrkt ]-r f ) β = expected return in excess of 1% change in market portfolio Related to how sensitive a firms underlying cashflows are to market Conditions Cost of Equity Capital = E[R i ] = r i = r f + β i Mrkt (E[R Mrkt ]-r f ) Historical Risk Premium = R Mrkt = Div yield + g Cost of Debt Capital = Estimated using YTM of firms bond traded in market Weighted Average Cost of Capital: Firms pretax WACC r WACC = Equity/debt+equity*r E + Debt/Debt+Equity*R D R E = cost of equity capital = r f + β i Mrkt (E[R Mrkt ]-r f ); R D =cost of debt capital=YTM Unlevered cost of capital = E/E+D * r E + D/E+D * r D = 100/125 *10% + 25/125 *6% = 9.2% Thus WACC is = E/E+D * r E + D/E+D * r D (1-τ C ) = 100/125 *10% + 25/125 *6%(1-40%) = 8.72% In capital budgeting, the WACC is used as the discount rate to compute NPV or the required rate of return in applying the IRR decision Discounting: FV n = C*(1+i) n ; PV = C/(1+r) n PV PERPETUITY = C/r, payments start at n=1 When payments start at n=0 PV = (C/r)+C Annuity PV = C/r(1-(1/(1+r) n )), start at n=1 Lottery prize = annuity + C FV ANNUITY = C/r((1+r) n -1); Growing perpetuity = C/(r-g) if g>r Loan Payment = P/((1/r)(1-(1/(1+r n ))) Missed Questions: Q: Which of the following is a way that the operating activity section of the statement of cash flows adjusts Net Income from the balance sheet? A: It adds all non-cash entries related to a firm's operating activities. Q: Allen Company bought a new copy machine to be depreciated straight line for three years for use by sales personnel. Where would this purchase be reflected on the Statement of Cash Flows? A: It would be an addition to property, plant and equipment so it would be an investing activity. Q: Company A has current assets of $42 billion and current liabilities of $41 billion. Company B has current assets of $2.7 billion and current liabilities of $1.8 billion. Which of the following statements is correct, based on this information? A: Company A is less likely than Company B to have sufficient working capital to meet its short-term needs. Q: Which of the following is NOT a diversifiable risk? A: the risk that oil prices rise, increasing production costs Review: 1.The above diagram shows a balance sheet for a certain company. If the company pays back all of its accounts payable today using cash, what will its net working capital be? $45 million 2. A company has a share price of $22.15 and 118 million shares outstanding. Its market-to-book ratio for equity is 4.2, its book debt-equity ratio is 3.2, and it has cash of $800 million. How much would it cost to take over this business assuming you pay its enterprise value? $3.805 billion 3. Consider the above Income Statement for CharmCorp. All values are in millions of dollars. If CharmCorp. has 4 million shares outstanding, and its managers and employees have stock options for 2 million shares, what is its diluted EPS in 2018? $1.67 4. Which of the following is NOT an operating expense? interest expense 5. Refer to the income statement above. Luther's earnings before interest, taxes, depreciation, and amortization (EBITDA) for the year ending December 31, 2015 is closest to? $135.9 million 6. The balance sheet and income statement of a particular firm are shown above. What does the account receivable days ratio tell you about this company ? It takes on average about 4 weeks to collect payment from its customers . 7. Manufacturer A has a profit margin of 2.2%, an asset turnover of 1.7 and an equity multiplier of 5.0. Manufacturer B has a profit margin of 2.5%, an asset turnover of 1.2 and an equity multiplier of 4.7. How much asset turnover should manufacturer B have to match manufacturer A's ROE? 1.59 8. A software company acquires a smaller company in order to acquire the patents that it holds. Where will the cost of this acquisition be recorded on the statement of cash flows ? as an outflow under investment activities 9. The expected return for Alpha Corporation is closest to: 5.00% 10. The standard deviation of the return on Alpha Corporation is closest to 21.8% 11. Historically, stocks have delivered a _ return on average compared to Treasury bills but have experienced _ fluctuations in values. higher, higher 12. Which of the following investments offered the lowest overall return over the past eighty years? Treasury bills 13. Suppose you invested $59 in the Ishares Dividend Stock Fund (DVY) a month ago. It paid a dividend of 0.38 today and then you sold it for $66. What was your return on the investment? 12.51% 14. Suppose you invested $100 in the Ishares High Yield Fund (HYG) a month ago. It paid a dividend of $2 today and then you sold it for $100. What was your dividend yield and capital gains yield on the investment? 2%, 0% 15. Ford Motor Company had realized returns of 10%, 20%, -10%, and -10% over four quarters. What is the quarterly standard deviation of returns for Ford? 15.00% 16. The standard deviation of returns of _. I. small stocks is higher than that of large stocks II. large stocks is lower than that of corporate bonds III. corporate bonds is higher than that of Treasury bills Which statement(s) is/are true? I and III 17. Big Cure and Little Cure are both pharmaceutical companies. Big Cure presently has a potential "blockbuster" drug before the Food and Drug Administration (FDA) waiting for approval. If approved, Big Cure's blockbuster drug will produce $1 billion in net income for Big Cure. Little Cure has ten separate, less important drugs before the FDA waiting for approval. If approved, each of Little Cure's drugs would produce $50 million in net income. The probability of the FDA approving a drug is 50%. What is the expected payoff for Little Cure's ten drugs? $250 million 18. Taggart Transcontinental is considering adding a trucking division to expand the coverage of its existing rail lines. The trucking division will cost $1,000,000 and is expected to generate free cash flows of $100,000 for each of the next five years. Taggart Transcontinental forecasts that future free cash flows after year 5 will grow at 2% per year, forever. Taggart Transcontinental's cost of capital is 10%. The continuation value for the trucking division in year five is closest to: 1,275,000 19. The NPV profile: shows the internal rate of return the point at which NPV is zero. c. shows the NPV over a range of discount rates. d. B and C are correct . 20. Which of the following statements is FALSE? Since the IRR rule is based upon the rate at which the NPV equals zero, like the NPV decision rule, the IRR decision rule will always identify the correct investment decisions 21. Which of the following statements is/are FALSE? I) When evaluating a capital budgeting decision, we generally include interest expense. II) Only include as incremental expenses in your capital budgeting analysis the additional overhead expenses that arise because of the decision to take on the project. III) As a practical matter, to derive the forecasted cash flows of a project, financial managers often begin by forecasting earnings . I only 22. Taggart Corp has an expanding project, and as a results expects additional operating cash flows of $26,000 a year for 4 years. This expansion requires $39,000 in new fixed assets. These assets will be worthless at the end of the project. The project also requires an additional $3,000 of net working capital at the start of the project and remains $3,000 throughout the life of the project; Sol expects to recover this amount at the end of the project. What is the NPV of this expansion project at a 16% required rate of return? $32,410 23. Below is the key information concerning TM Industry: Yield-to-Maturity on long-term government bonds 3.4% Yield-to-Maturity on TM industry's long-term bonds 8.1% Market risk premium 6.0% Estimated company equity beta 1.4 Stock price per share $30.00 Number of share outstanding 60 million TM industry's debt value $1.2 billion tax rate 25% Its cost of equity capital is: 11.80% 24. Below is the key information concerning TM Industry: Yield-to-Maturity on long-term government bonds 3.4% Yield- to-Maturity on TM industry's long-term bonds 8.1% Market risk premium 6.0% Estimated company equity beta 1.4 Stock price per share $30.00 Number of share outstanding 60 million TM industry's debt value $1.2 billion tax rate 25% Its WACC is 9.51% 25. Which of the following statements concerning risk are correct? I. Systematic risk is measured by beta. II. The risk premium increases as unsystematic increases. III Systematic risk is the only part of total risk that affects asset prices and returns. IV Diversifiable risk is the market risk you cannot avoid : I and III only
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