MGT 181 Formula Sheet PDF

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Download MGT 181 Formula Sheet PDF

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Net Working Capital = Current Assets - Current Liabilities Tax Bill (Liability) = (First $$)*Rate + (Second $$)*Rate + ... (Progressive Tax System) Average Tax Rate = Tax Bill/Taxable Income Net Income = Sales - Cash Costs (COGS) - Depreciation (Non-Cash Costs) - Interest - Taxes EBIT = Sales - Cash Costs (COGS) - Depreciation (Non-Cash Costs) Operating Cash Flow = Sales - Cash Costs (COGS) - Taxes (Top Down Method) = EBIT + Depreciation - Taxes (Base Method) = Net Income + Depreciation + Interest (Bottom Up Method) Current Ratio = Current Assets/Current Liabilities Quick Ratio = (Current Assets - Inventory)/Current Liabilities Debt/Equity = Total Debt/Total Equity Times Interest Earned = EBIT/Interest ROA = Net Income/Total Assets ROE = Net Income/Total Equity Market-to-Book Ratio = Market Value/Book Value Market Value = Number of Outstanding Shares * Market Price per Share Book Value = Total Assets - Total Liabilities = Total Equity

FV = P(1+rt), where P is the initial deposit, r is the rate, and t is the number of periods (Simple Interest) FV = PV(1+r)^t and PV = FV/(1+r)^t (Compound Interest) 72 = Number of Periods * Rate of Return (Rule of 72 for doubling money) Amount of Compound Interest = FV (Compound) - PV - Amount of Simple Interest PV(Ordinary Annuity) = C[(1-(1/(1+r)^t))/r], where C is the constant amount per period FV(Ordinary Annuity) = C[(((1+r)^t)-1)/r] Annuity-Due = Ordinary Annuity * (1+r) PV(Level Perpetuity) = C/r PV(Increasing Annuity) = C[(1-(((1+g)/(1+r))^t))/(r-g)] PV(Increasing Perpetuity) = C/(r-g) EAR = (1+Quoted Rate/m)^m - 1 = (1+APR/m)^m - 1, where m is the number of compounding periods per year APR = Interest rate per period (known as period rate) * Number of periods EAR = e^q - 1 when the number of compounding periods gets to infinity (q is the quoted rate) for continuous compounding Principal at end of t-1 = Principal at beginning of t = Principal at beginning of t-1 - Principal Repaid in t-1 Payment = Interest + Principal Repaid = (Principal at start of period * interest rate) + Principal Repaid PV(Bond) = PV(Annuity of Coupons) + PV(Face Value at maturity) Current Yield = Annual Coupon/Price Call Premium = Call Price - Stated Value Clean Price = Dirty Price - Accrued Interest Nominal Rate = Real Rate + Inflation Rate

P0 = D/R (Level Perpetuity with constant dividends) Pt = D(t+1)/(R-g) = Dt(1+g)/(R-g) (Constant Growth, Dividend Growth Model) P0 = (D1/(R-g1))*(1-((1+g1)/(1+R))^t) + Pt/(1+R)^t (Supernormal Growth) R = (D1/P0) + g (Total Return = Dividend Yield + Capital Gains Yield) Pt = Benchmark PE Ratio * EPSt Investment Decision Making Technique

Rule

Net Present Value (NPV)

Accept if NPV>0

Payback

Accept if periodrequired return (fixed)

Profitability Index (PI)

Accept if PI>1 (NPV>0)

Discounting Approach: Change future negative CFs into a CF at t=0 and keep positive CFs as is Reinvestment Approach: Accumulate all future CFs (except t=0) to the last date Combination Approach: Discount negative CFs to t=0 and accumulate all other CFs to the end Project CF = Project OCF - Project change in NWC - Project capital spending OCF = EBIT + Depreciation - Taxes = NI + Depreciation = Sales - Costs - Taxes = (Sales Costs)(1-T) + Depreciation(T) = [(Sales/unit-VC/unit)(Units)] - Fixed Costs Depreciation Tax Shield = Depreciation Expense * Marginal Tax Rate Net Income = (Sales - Costs - Depreciation)(1-T) (Obtain NI to help with OCF calculation) Straight-Line Depreciation = (Initial cost - salvage)/Number of years MACRS- Multiply cost by percentages in MACRS table to get the annual depreciation expense Book Value = Initial Cost - Accumulated Depreciation (Sum of MACRS) After-tax salvage = Salvage - T(Salvage - Book Value) (SalvageBV, gain)

Scenario Analysis

Base Case

Worst Case

Best Case

Sales Price

Pre-determined

Lowest

Highest

Units

Pre-determined

Lowest

Highest

Costs (VC and FC)

Pre-determined

Highest

Lowest

Sensitivity Analysis: Apply the same process, but freeze all variables except one of them and use the base case values of the freezed variables for all three cases Total Cost = Variable Cost + Fixed Cost (VC = variable cost/unit * number of units) Average Cost = Total Cost/Number of units Marginal Cost = Variable Cost/Unit CM/Unit = Sales/Unit - Variable Cost/Unit NI = 0 = Sales - Costs - Depreciation (Accounting Break-Even) Q = (FC+D)/(P-v) (Accounting Break-Even) Q = FC/(P-v) (Cash Break-Even, OCF = 0) Q = (OCF+FC)/(P-v) (Financial Break-Even, OCF = PMT on HP calculator TVM, what OCF makes NPV = 0 (able to recover entire investment)) DOL = 1 + (FC/OCF) % Change in OCF = DOL * % Change in Units Sold

Total Dollar Return = Income from Investment + Capital Gain (Loss) due to price change Total % Return = Dividend Yield + Capital Gains Yield = Income/Start Price + Growth Rate Risk Premium = Expected Return - Risk-Free Rate (General Formula) Historical (Sample) Variance = [(R1-R)^2 + ... + (Rn-R)^2]/(n-1) (R = Expected return/Arithmetic Average (Mean), Ri = ith return) Sample Standard Deviation = [Historical Variance]^0.5 (square root of variance) Arithmetic Average = (R1 + ... + Rn)/n Geometric Average = [(1+R1)...(1+Rn)]^(1/n) - 1 Total Return = Expected Return + Unexpected Return = Expected Return + Systematic Portion + Unsystematic Portion Reward-to-Risk Ratio = (E(Ri) - Rf)/Bi = (E(Rm) - Rf)/Bm = E(Rm) - Rf (Market Risk Premium) E(Ri) = Rf + Bi(E(Rm) - Rf) (CAPM, all assets plot on same SML (same reward-to-risk ratio)) Unexpected Return = Systematic Portion + Unsystematic Portion E(Rp) = w1*E(R1) + ... + wn*E(Rn) (Portfolio expected return, wi = weight of ith security = pi = probability of occurrence) Total Risk = Systematic Risk + Unsystematic Risk Bp = w1*B1 + ... + wn*Bn (Portfolio Beta, same meaning for wi) Re = D1/P0 + g (Cost of Equity, Dividend Growth Model) Re = Rf + Be(E(Rm) - Rf) (Cost of Equity, SML) Rd = YTM for Bond (Use Bond Pricing TVM from Chapter 7) (Cost of Debt, Pre-Tax) Rp = D/P0 (Cost of Preferred Stock) After-Tax Cost of Debt = Rd(1 - TC) (Tax deductible for debt only, not equity of any kind) WACC = (E/V)Re + (P/V)Rp + (D/V)Rd(1-TC) (Weighted Average Cost of Capital) V = E + P + D (Total Market Value as sum of market values for equity, preferred stock, debt)

Pre-Money Valuation = Post-Money Valuation - Investment Post-Money Valuation = Investment/(% ownership by potential investor) New Shares = Funds/Subscription Price Ownership Position = Number of owned shares/(Outstanding shares + New shares) Value of Right = Old Share Price - “New” Share Price Number of Rights to buy stock = Old Shares/New Shares Forward Rate > Spot Rate

Foreign currency is selling at a premium relative to dollar

Forward Rate < Spot Rate

Foreign currency is selling at a discount relative to dollar

Note: “1.00 USD” refers to foreign currency/1 USD, and “inv 1.00 USD” refers to USD/1 foreign currency Triangle Arbitrage Process (Currency X, Y, $)

1. Start with $ 2. Convert to Currency X by its exchange rate (X/$) 3. Convert to Currency Y by its quoted rate (Y/X), not cross rate ((Y/$)/(X/$)) 4. Convert back to $ by its exchange rate ($/Y)

Covered Interest Arbitrage Process

1. Use the risk-free US nominal rate to accumulate the starting amount (in $) over the time period 2. Convert the starting amount to the foreign currency by its spot rate (happens at start) 3. Accumulate the converted amount by the foreign currency’s risk-free nominal rate over the time period 4. Convert back to $ by the forward rate (happens at end) 5. Subtract beginning accumulated $ amount (pre-arbitrage) from the ending $ amount (post-arbitrage)

Absolute Purchasing Power Parity (APPP)

Pfc = S0*Pus (Pi is current i-country’s price) (S0 is spot exchange rate between foreign country and US)

Relative Purchasing Power Parity (RPPP)

E(S1) = S0*[1+(hFC-hUS)] E(St) = S0*[1+(hFC-hUS)]^t (General Form) (E(St) is expected exchange rate in t periods) (S0 is current spot exchange rate) (hI is inflation rate for country I)

Interest Rate Parity (IRP)

F1/S0 = (1+Rfc)/(1+Rus) Ft = S0*[1+(Rfc-Rus)]^t (General Form) (Ft is forward exchange rate at time t) (S0 is current spot exchange rate) (Ri is nominal risk-free rate for country i)

Unbiased Forward Rates (UFR)

F1 = E(S1) Ft = E(St) (General Form) (Ft is forward exchange rate at time t) (E(St) is expected exchange rate in t periods)

Uncovered Interest Parity (UIP)

E(S1) = S0*[1+(Rfc-Rus)] E(St) = S0*[1+(Rfc-Rus)]^t (General Form) (E(St) is expected exchange rate in t periods) (S0 is current spot exchange rate) (Ri is nominal risk-free rate for country i)

International Fisher Effect (IFE)

Rus - hUS = Rfc - hFC (Ri is nominal risk-free rate for country i) (hI is inflation rate for country I)...