Page 1 of 11 Twyman Portfolio Project
Portfolio Project Financial Analysis and Management Ashley V Twyman
Presented in partial fulfillment for Financial Analysis & Management 565 8/17/2009 – 9/27/2009 Dr. Joel Light
Page 2 of 11 Twyman Portfolio Project • Time Value of Money Principle: If you own money, you can rent it or loan it to another party. The recipient of the money must pay interest on the money borrowed. FV = PV + r (PV) = PV (1 + r) Where FV = Future Value PV = Present Value r = rate • Balance Sheet Assets are productive resources used in its operations Assets = Liabilities + Stockholder’s equity • Liquidity Ratios: Measure a firm’s liquidity. Measures a firm’s ability to meet its short term obligations as they come due. Working Capital Working Capital = Current assets – Current liabilities Current Ratio Current ratio = Current assets Current liabilities Quick Ratio Quick Ratio = Current assets – Inventories Current liabilities Cash Ratio Cash Ratio = Cash and Equivalents Total assets • Asset Activity Ratios: Designed to measure how effectively a firm manages its assets. Receivables turnover ratio: Receivables turnover = Annual credit sales Accounts receivable Days’ sales outstanding ratio: Day’s sales outstanding = 365 = Accounts receivable Receivables turnover Annual Credit Sales/365 Inventory turn over ratio: The inventory turn over ratio is a good estimate of how many times in a year the inventory is physically turning over. Inventory turn over = Cost of goods sold Inventory Day’s sales inventory =
365 Inventory Turnover
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Fixed Asset and Total Asset turnover ratios: These ratios show the sales generated per book-value dollar of fixed assets and total assets, respectively. Fixed asset turnover = Sales Net Fixed Sales Total asset turnover =
Sales Total assets
• Leverage Ratios: Measure the amount of financial leverage. Debt ratio: The debt ratio is the proportion of debt financing. Debt ratio = Total debt Total assets Debt/equity ratio: Expresses the same information as the debt ratio but on a different scale Debt/equity ratio = Total debt Stockholder’s equity Equity Multiplier: Shows how much total assets the firm has for each dollar of equity. Equity multiplier = Total assets Stockholder’s equity • Coverage Ratios: Show the number of times a firm and cover or meet financial obligations Interest coverage ratio or times-interest-earned ratio: Measures the coverage of the firm’s interest expense. Times-interest-earned ratio = interest coverage ratio = EBIT Interest expense Fixed-charge coverage ratio: Used when fixed charges consist of interest expense plus rental payments Fixed-charge coverage ratio = EBIT + Rental Payments Interest expense + Rental Payments Cash flow coverage ratio: The firm’s operating cash flows divided by its payment obligations for interest, principal, preferred stock dividends, and rent. Cash flow coverage ratio = EBIT + Rental Payments + Depreciation Preferred Stock Debt Rental Payments + Interest expense + dividends + repayment 1–T 1–T
Page 4 of 11 Twyman Portfolio Project • Profitability Ratios: Measure how effectively a firm is able to generate profits. Gross profit margin: Represents the amount of money remaining to pay operating costs, financing costs, and taxes and to provide for a profit. Gross profit margin = Gross profit = Sales – Cost of good sold Sales Sales Net profit margin: Measures the profit that is available from each dollar of sales after all expenses have been paid. Net profit margin = Net income before extraordinary items Sales • Rate of Return Ratios: Express profitability in relation to various measures of investments in the firm. Return on Assets (ROA): ROA = Return on assets = Net income Total assets Earning Power: Earning Power = EBIT Total assets Return on Equity (ROE): Shows the residual profits of the firm as a proportion of the book value of common stockholder’s equity. ROE = Earnings available for common stock before extraordinary items Common shareholder’s equity • Market Value Ratios These rations relate the market value of the firm’s common stock to earnings per share (EPS), dividends per share (DPS), and book value per share, which is total common equity divided by the number of common shares outstanding. Market value leverage ratio: Uses the firm’s market value of equity (market cap.) in place of book value of equity in the debt ratio. Market value leverage ratio = Book value of debt Book value of debt + Market value of equity Price/earnings ratio (P/E): P/E = price/earnings ratio = Market price per share Earnings per share Earnings yield: The reciprocal of the P/E value. Earnings yield = Earnings per share Market price per share Dividend yield: Dividend yield = Dividend per share Market price per share
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Market-to-book ratio: Is a very rough index of a firm’s historical performance. Market-to-book ratio = Market price per share Book value per share • Rates of Return The rate of return is the amount of return acquired from an investment. Return = Rate of return = Cash flow + (Ending value – Beginning value) Beginning Value • Net Present Value (NPV) Projects the cumulative present value of a firm. A positive NPV would create value because an asset is worth more than it cost. NPV = present value of expected future cash flows – Cost • Future Values A future value is a value at the end of a given time period. FVn = PV(1 + r)ⁿ =PV(FVFr,n) • Present Values An amount invested today at r per period that would provide a given future value at time n.
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PV = FVn
1 = FVn (PVF r,n) (1 + r)ⁿ • The Future Value of an Annuity The total value that will have accumulated at the end of the annuity if the annuity payments are all invested at r per period. n-1 FVAn = PMT
Σ (1 + r)t = PMT [(1 = r)ⁿ - 1] = PMT (FVAF r,n) t=0
r
• The Present Value of an Annuity The amount that, if invested today at r per period, could exactly provide equal payments every period for n periods. PVAn = PMT 1 + 1 + + PMT 1 (1 + r)1 (1 + r) 2 (1 + r)ⁿ •
Calculating Annuity Payments
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]
PMT = PVAn r(1 + r)ⁿ = PVAn (1 + r)ⁿ - 1 PVAF r,n
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• Perpetuities An annuity that continues indefinitely is t perpetuity. They can be used as a simple and fairly accurate approximation of a long-term annuity. PVAn = PMT
[ (1 + r)ⁿ - 1 ] = PMT [ (1 + r)ⁿ ] – PMT [ r (1 + r)ⁿ
[
] [
r (1 + r)ⁿ
1 r(1 + r)ⁿ
]
]
PVAn = PMT - PMT r r(1+ r) ⁿ Therefore the present value of a perpetuity is PVAperpetuity = PMT r • Annual Percentage Rate (APR) The APY is the periodic rate times the number of periods in a year. The APR is a nominal rate. The true annual rate may be different from the APR because of compounding frequency. APR = (m)(r) • Annual Percentage Yield This is the true annual rate of return.
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APY = 1 + APR m – 1 M • Compounding frequency effects on future value APY = Annual interest Principle • APY and APR with continuous compounding APY = e APR - 1 • Bond Valuation Formula For a bond with semiannual coupon payments B0 = PV(coupon payments) + PV (par value)
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B0 = CPN (1+r/2)2N - 1 + 1000 2 (r/2)(1+r/2)2N (1+r/2)2N • The Fair Price of a Share of Common Stock Use this to estimate the future fair price of an owned stock. P0 = D1 + D2 + ….+ Dn + Pn (1+r)1(1+r)2 (1+r)ⁿ(1+r)ⁿ • Payout ratio Expresses the firm’s cash dividend as a proportion of its earnings Payout ratio = Dividends Earnings
Page 7 of 11 Twyman Portfolio Project • Consistent Growth Model Dt = D t-1 (1+g) = D t-2 (1+g)2 = …= D0(1+g)t • Rearranging Equation Provides a model for computing a stock’s expected return. Pt = D t-1 (r-g) • Estimating a stock’s required return using Consistent Growth Model The income component is also called the dividend yield, which is the dividend divided by the price. The capital gains is g. The total return is simply the sum of the two. r = D1 + g P0 • Dividend Growth The firm’s payout ratio (POR) is the proportion of earnings it pays out in dividends. Let i represent the expected return on the money retained. g = (1 – POR)i • Measuring the expected NPV of growth opportunities This provides a way to compare the difference between the required return and expected return and to measure how that difference affects the stock value.
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)
r = (POR) EPS1 = (1 – POR)r P0 Solving this for P0 we get: P0 = EPS1 r • Estimating NPVGO P0 can be expressed as the value of the firm’s current operations plus NPVGO, the expected NPV of the firm’s future growth opportunities. P0 = EPS1 + NPVGO r • Holding period realized return For an N-year holding-period, we can compound the APY for N years to compute the holdingperiod realized return: 1 + r = (1 + realized APY)N • The mean The mean of any random variable is its long run average. N Xbar =
Σ PnXn n=1
• Variance and Standard Deviation The variance is the measure of the dispersion of all possible outcomes around the mean. The Standard Deviation is the square root of the variance. N
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Σ Pn (x
n
– xbar)2
n=1
• Covariance Covariance is the measure of how two random variable vary together, or “covary”. N
Σ Pn (x
Covariance = Cov(X,Y) =
n
– xbar) (yn – ybar)
n=1
• Correlation Coefficient Correlation Coefficient removes the sensitivity that covariance has to the particular unit of measurement. It can take on any value but only be between minus 1 and plus 1. Corr(X,Y) = Cov(X,Y) Sigma square x sigma squaredy
• Risk and Return in Two-Asset Portfolios This can be used to assess how the risks and expected returns of individual assets combine to create a portfolio’s risk and expected return. rp – w1r1 + (1 – w1)r2 • Capital Market Line Use this when figuring the slope of the CML. The capital market line is the line that links the possible investment contributions when you can borrow at the riskless return. CML slope = rM – rf Sigma squared M
• Diversifiable risk and Nondiversifiable risk premium Nondiversifiable risk (systematic risk) is risk that cannot be eliminated by diversification. Diversifiable risk (unsystematic risk) is risk that can be eliminated by diversification. Specific risk = Diversifiable risk – Nondiversifiable risk Nondiversifiable risk of security j r= [Corr(j,M)]σ j −r Risk premium = [Corr ( j , M )]σ j M f ÷ σM The beta is a measure of its market – or nondiversifiable risk. βj =
Corr ( j , M )σ j
σM
=
Corr ( j , M )σ jσ M
σ Mσ M
=
Cov ( j , M ) σ M2
• Security market line A security market line is when the capital market is in equilibrium. The SML also identifies the required return for security j that is implied by the CML.
ri = r f + βi ( RM − r f )
• Estimating and Using the CAPM This can measure how stock returns vary with respect to the market portfolio’s return by applying a statistical method called linear regression. Rj = rf = Betaj (RM – rf) Or Required Market portfolio' s = Riskless return + Beta − Riskless return return expected return
•
Arbitrage Pricing Theory
Page 9 of 11 Twyman Portfolio Project The APT is more general than the CAPM and relies on the principle of Capital Market Efficiency.
r j = r f + β j1 ( r f 1 − r f ) + β j 2 ( r f 2 − r f ) + + β jK ( r fK − r f )
• Capital Asset Pricing Model This can be used to obtain the cost of capital for a capital budgeting project. rj = rf + bj(rm – rf) where rj = cost of capital for project j, rf = riskless return rm = required return on the market portfolio bj = beta of project j • WACC Calculation The WACC is the weighted average cost of capital. It represents the weighted average rate of return required by the suppliers of return required by the suppliers of capital for a firm’s investment project. WACC = (1 −L) re + L(1 −T ) rd
• Financial leverage and Beta Financial leverage increases a firm’s beta. It does not increase the risk of assets, instead it increases the financial risk.
• Internal Rate of Return (IRR) The IRR is like the NPV and is used to evaluate capital budgeting projects in the fact that it calculates a project’s expected return. CF0 + CF1 + CF2 + … + CFn (1+IRR) (1+IRR)2 (1+IRR)ⁿ • Profitability Index (PI) The profitability index is another time-value-of-money-adjusted method that may be used to evaluate capital budgeting projects. It is also called the benefit-cost ratio. Profitability Index = PI = PV(future cash flows) = 1 + NPV Initial investment Initial Investment • Modified Internal Rate of Return (MIRR) This calculates the present value of all the cash outflows and the future value of all the cash inflows using the cost of capital. It was designed to provide a better measure of relative profitability than the IRR calculation. PV(cash flows) = FV(cash flows)
Page 10 of 11 Twyman Portfolio Project (1+MISS)N • Cash Expenditure Cash expenditure = – I0 – E0 + T E0 = – I0 – (1 – T) E0 • Net Cash Flow from Sale of Old Asset S0 - T (S0 – B0)
• Net Initial Outlay A calculation for incremental cash flows. The net initial outlay can be broken down into cash expenditures for the new capital assets, changes in net working capital, cash flow from the sale of old equipment, and the tax impact of the sale of old equipment. C0 = – I0 – DW – (1 – T) E0 + S0 – T(S0 – B0) + Ic • Net Operating Cash Flow After the initial investment, a project generates future cash inflows and outflows. This can be expressed as: CFAT = DR - DE - Tax liability = DR - DE - T(DR - DE - DD) CFAT = (1 - T)(DR - DE) + TDD CFAT = after-tax operating income Then we can rewrite CFAT as: CFAT = (1 - T)(DR - DE - DD) + DD = after-tax net income + depreciation • Net Salvage Value This can calculate how much fiscal value a salvaged item can hold, even though it also has a depreciation value. Net salvage value = = S - T(S - B) - (1 - T)REX + DW • Equivalent Annual Cost This is the equivalent cost per year of owning an asset over its entire life. n C TC =C0 +∑ t t r) t= 1 (1+
r(1+r )n EAC = TC n 1 (1+r ) −
• Real options When the option on a project is costless, it simply adds to the project’s value. A project’s NPV can be expressed as its “basic” NPV from discounted cash flows (DCF-NPV) plus the value of
Page 11 of 11 Twyman Portfolio Project all options associated with the project minus any costs connected with getting or maintaining those options. NPV = DCF – NPV + Value of options – Cost of options
References: Emery, D. R., Finnerty, J. D., & Stowe, J. D. (2007). Corporate Financial Management (3rd ed.). Upper Saddle River: Pearson Education, Inc.