finance cheat sheet
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Transcript of finance cheat sheet
Corporate finance: Capital budgeting decision (long-‐term investment) (fixed A) Capital structure decision (long-‐term financing) (L+E) Working capital management (everyday financial activity) (CA-‐CL)
Investors provide financing à Firm generates income à Distributed to investors
Investment decision: increase size of pie Capital structure(financing decision): how to slice pie
Primary goal: shareholder wealth maximization à maximize stock price (maximize value of firm, wealth of owners, price of stock, contribution to economy) Market value of shareholders’ equity = Market capitalization = Share price x
no. of outstanding shares *compare mkt value with mkt value, book value with book value* ASSETS = LIABILITIES + EQUITY
ENTERPRISE VALUE = MARKET VALUE OF EQUITY + DEBT -‐ CASH
Income Statement Revenue COGS Operating Expense Depreciation EBIT Interest Expense Taxable Income Taxes Net Income
Retained earning, beg + Net Income – Dividend = Retained earnings, end
Profits subtract depreciation, ignore expenditure on new fixed assets, record income and expense at time of sale and do not consider changes in net working capital ΔCash = ΔRetained Earnings + ΔCL – ΔCA other than cash – ΔNet Fixed A + ΔLong-‐term Debt + ΔCommon Stock Cash Flow from Assets = Operating Cash Flow (OCF) – Net Capital Spending (NCS) – ΔNWC = CF to Creditors + CF to Stockholders OCF = EBIT + depreciation – taxes NCS = End Fixed A + depreciation – Beg Fixed A ΔNWC = End NWC – Beg NWC CF to Creditors = Interest paid – Net new borrowing CF to Stockholders = Dividends paid – Net new equity raised
Asset Management Ratios: How effectively assets are being managed Inventory Turnover = COGS/Inv Days’ Sales in inv = 365/Inv turnover à how quickly inv produced and sold Receivables Turnover = Sales/Receivables Days’ Sales Outstanding = 365/Rec turnover à Average no of days before receiving cash Fixed Assets turnover = Sales/net fixed A Total Assets turnover = Sales/total assets
Long-‐term Solvency Ratios: Extent firm relies on debt financing rather than equity à ability to fulfill contractual obligations Variations Debt-‐Equity Ratio = Total Debt/Total E Equity Multiplier = Total A/ Total E = 1 + Debt-‐Equity Ratio LT Debt Ratio = LT Debt / (LT debt + Total E) Coverage Times interest earned ratio = EBIT/interest Cash coverage ratio = (EBIT + depreciation)/interest
Liquidity Ratios: Ability to convert A to cash w/o significant loss in value à ability to meet ST obligations Current Ratio = CA/CL Quick Ratio = (CA – Inv)/CL Cash Ratio = Cash/CL NWC to Total A = NWC/TA Interval Measure = CA/Average daily operating cost
Profitability Ratios: Ability to earn a return on investment à liquidity, asset management, debt on operating results Profit margin = Net Income/Sales Basic Earning Power = EBIT/Total Assets ROA = Net income/Total Assets à Lowered by debt (interest exp lower net income) but debt lower equity. ROE may increase ROE = Net Income/ Total common E à Doesn’t consider risk and capital invested DUPONT IDENTITY ROE = Profit Margin*TATurnover*EM àoperating efficiency, asset use efficiency, financial leverage
Market value ratio: Stock price to earnings, cash flow and book value per share PE ratio = price/earnings per share àhow much willing to pay for $1 of earnings MB ratio = mkt price per share/book value per share àhow much willing to pay for $1 of book value E
PVàFV: Compounding FVàPV: Discounting
Annuity: 1st CF one period from now (end of P1) Annuity due: First cash flow now (start of period 1) Perpetuity: equal payment paid forever Growing perpetuity: Growing at constant rate
Money today preferred due to lost earnings (can invested) and loss of purchasing power (inflation)
FVn = PV(1 + i)n
FV interest factor = (1 + i)n
r = (!"!")!! -‐ 1 t =
!" (!"!")
!" (!!!)
PV Annuity = PMT * [!!!" !"#$%&!
]
PV factor = 𝟏(𝟏!𝒓)𝒕
PV Annuity Due = PV Annuity * (1+r) PV Growing Annuity = C* 𝟏
𝒓!𝒈 * (𝟏!𝒈
𝟏!𝒓)𝒕
FV Annuity = PMT*[ !!∗ [(1+r)n -‐ 1] ]
FV Annuity Due = FV Annuity * (1+r) PV perpetuity = 𝑪
𝒓
PV growing perpetuity = 𝑪𝟏𝒓!𝒈
APR = period rate*no of periods/year
EAR = [1 + !"#!
]m -‐ 1
Investment returns = amt received – amt invested = [(amt received – amt invested)/ amt invested] * 100% Total dollar return = div income + capital gain/loss Dividend yield = Dividend/Initial Share Price Capital gain yield = Capital gain/initial share price Total percentage return = dividend yield + capital gain yield
1 + Real Return = !!!"#$%&' !"#$%&!!!"#$%&'(" !"#$
Expected returns, 𝒓! = ∑ 𝑟!𝑝!!!!!
Arithmetic mean, 𝒓! = ∑ 𝒓𝒕𝑻𝒕!𝟏
𝑻
Standard deviation, σ = √𝑽𝒂𝒓𝒊𝒂𝒏𝒄𝒆 = !∑ (𝒓𝒊 − 𝒓!)𝟐𝒏
𝒊!𝟏 ∗ 𝒑𝒊 à Total risk of investment
Estimated σ = !∑ (𝒓𝒊!𝒓!)𝟐𝒏𝒊!𝟏
𝒏!𝟏
CV = Standard deviation/expected rate of return = 𝛔
!̂
àrisk per unit of return (lower=better) Risk premium = return – risk-‐free rate
Portofoio returns, 𝑹!𝒑= ∑ 𝑤!�̂�!!!!!
To find portfolio volatility, 𝛔𝒑: Find expected returns for each scenario à expected returns of portfolio à SD using each return for each portfolio 𝛔! = !𝑤!!σ!! + (1 − 𝑤!)!σ!! + 2𝑤!(1 − 𝑤!)𝜌!"𝜎!𝜎! If 𝜌 = -‐1 à riskless portfolio If 𝜌 = 1 à risk not reduced E(R) of risky asset only depends on systematic risks
Total risk = company-‐specific risk (unsystematic) + market risk (systematic) = SD
Beta: measure of responsiveness of security to movement in the market portfolio; risk investor exposed to by holding particular stock compared to market as a whole. 𝛽 = !!
!!𝜌! =
!"#(!!,!!)!!!
High 𝛽 à higher return when market doing well and vice versa à high risk, high return When 𝛽 < 0 à move in opposite direction from the market When 𝛽 = 0 à risk-‐free asset When 𝛽 < 1 à asset less systematic risk than market (less E(R)) When 𝛽 = 1 à same systematic risk as market (same E(R)) When 𝛽 > 1 à more systematic risk than market (more E(R))
SML: Ri = Rf + 𝜷𝒋(RM – Rf) àCAPM Slope = RM – Rf = market risk premium Rf à pure time value of money Fairly priced à on SML Underpriced à above SML Overpriced à under SML Inflation à parallel upward shift Risk aversion change à change in slope
Diversification get rid of the unsystematic risk.
Bond: Long-‐term debt instrument sold to raise money Coupon: Actual period payment made to bond holder Coupon rate: Annual interest rate of coupon Coupon payment: (Stated annual coupon rate*par value)/no of coupon payment Par value: amount repaid at the end of the term Maturity: date par is paid back Term: time remaining until principal repayment date Callability: Able to redeem bond before it matures Senority: preference in lender position Debenture: bond backed by issuer’s general credit and ability to pay rather than assets Basis points: 0.01% = 0.0001 Convertibility: option to exchange bond for stocks Protective covenants: terms of loan that limit certain actions during term of the loan Sinking fund: fund set aside to repay bond Zero-‐coupon bond: pay no interest till maturity date àyield also expressed as YTM (par – purchase) Floaters: coupon rate depend on some index value
Bond value = PV of coupons + PV of par = PV annuity + PV of lump sum
= Coupon*!𝟏! 𝟏
(𝟏! 𝒓𝒅)𝟐
𝒓𝒅! + 𝑭𝒂𝒄𝒆 𝑽𝒂𝒍𝒖𝒆
(𝟏! 𝒓𝒅)𝑵
Overall rate of return = (annual coupon + (current bond price – beg bond price))/beg bond price
Current yield = i/ paid by bond/current market price (not as relevant as YTM ∵ don’t consider K gain/loss)
Yield-‐to-‐maturity: rate of return if held to maturity; PV of all cash flow from bond to price of bond à rate for discounting à compare bond with same risk level Same risk & maturity; same R & YTM (regardless coupon rate) Interest ↑à bond PV ↓, so YTM ↑ à bond price ↓
Bond selling at: Discount: Coupon Rate< CY< YTM Premium: CR >Current Yield >YTM Par value: CR = CY = YTM
T-‐bills: pure discount bond -‐ maturity ≤1 yr T-‐notes: coupon debt w/ maturity 1-‐10 yrs T-‐bonds: coupon debt w/ maturity >10 yrs
Term structure: relationship between time to maturity and yield; same risk and holding all else equal Normal: upward; LT yield > ST yield
Intrinsic value: PV of expected future value Discount rate = required rate of return (CAPM)
Constant dividend: P0 = 𝑫𝟏𝑹𝑬 = 𝑷𝑴𝑻
𝒊
Constant dividend growth: P0 = 𝑫𝟎(𝟏!𝒈)𝑹𝑬!𝒈
= 𝑫𝟏𝑹𝑬!𝒈
à cannot use model if RE < g & RE = g Dividend yield = 𝑫𝟏
𝑷𝟎
Capital gains yield = 𝑷𝟏!𝑷𝟎𝑷𝟎
In equilibrium, Expected returns = Required returns Intrinsic value = Market price RE = Rf + 𝜷𝒋(RM – Rf)
𝑹!𝑬= 𝑫𝟏𝑷𝟎 + g
à 𝑅!!> RE = bargain (undervalued) à Buy > Sell à Above SML RE changes w/ inflation g changes w/ macroecons & firm-‐specific events
Preferred stock: -‐ cumulative -‐ fixed dividends
VP = 𝑫𝑹𝑷
Corporate value model: à CFFA = OCF – NCS – ΔNWC Find MV of firm (PV of future CFFA) à minus debt & preferred stock = MV common stock à Divide by no of share outstanding to get intrinsic value per share To find stock price of firm that don’t pay dividend à Terminal value (growth constant)
Capital budgeting considerations: Time value of money, adjustment for risk; creating value
NPV RULE: Accept if NPV > 0 NPV = intrinsic value – cost
= ∑ !"!(!!!)!
!!!! -‐ CF0
PV(cash inflow) > PV(cash outflow) à increase value of firm àCF reinvested at weighted average cost of capital (opp cost of capital)
Payback period rule: Accept if period < preset limit Add year on year till it becomes (+) Year X: -‐Y + Z = (+) à Payback period = X!
! years
Discount payback rule: Accept if period < preset limit Same as payback period rule just that add discounted returns to cost BOTH BIASED AGAINST LT PROJECT
Average accounting return rule: Accept if AAR > preset rate AAR = !"#$%&# !"# !"#$%&
!"#$%&# !""# !"#$%
INTERNAL RATE OF RETURN RULE: Accept if IRR > required rate IRR: return that makes NPV = 0 à CF reinvested at IRR MIRR à invested at WAAC PV outflow = !" !"#$%&
(!! !"##)!
NPV and IRR generally give the same results EXCEPT: 1. Initial I substantially different 2. Timing of cash flow substantially different 3. Nonconventional cash flow à Cash flow sign change more than once à More than 2 points of intersection à In this case, to find the crossover point: (A-‐B) then find IRR
CF must be after-‐tax and incremental basis. à w/ project – w/o project (incremental) Relevant: opp cost, ΔNWC, taxes Irrelevant: sunk cost, interest exp & dividends (in discount rate) NPV = -‐C0 +
!!(!!!)
+ !!(!!!)!
+ ⋯ + !!(!!!)!
WACC = rD * (1 – Tc) * !! + RE *
!!
OCF = EBIT + Depreciation – taxes NOPAT = EBIT – taxes ∴ OCF = NOPAT + depreciation NCF = OCF – NCS – ΔNWC NCS = end net FA – beg net FA + depreciation
Depreciation: tax purpose Depreciation tax shield = D*T
Net savage value = S – T(S – B) If S > B: Gain If S < B: Loss 2 Cases 1. Fully depreciated 2. Take into consideration salvage value
3 ways to calculate OCF 1. No interest rate (bottom-‐up) OCF = NI + Depreciation OCF = Sales – cost – tax rate*(Sales – cost – depreciation) 2. Top-‐down OCF = sales – cost – taxes 3. Tax shield OCF = (sales – cost)(1 – T) + Depreciation*T
Unequal life projects 1. Calculate NPV [Find CF] à If not replaced, stop here 2. Calculate equivalent annual annuities [Find PMT] 3. Apply appropriate decision rule
Bid price = Selling price à After finding NPV, use it as PV to get PMT for per time period
Additional Funds Needed (AFN) = 𝑨∗
𝑺𝟎(𝑺𝟏 − 𝑺𝟎) −
𝑳∗
𝑺𝟎(𝑺𝟏 − 𝑺𝟎) −𝑴(𝑺𝟏)(𝑹𝑹)
A* = assets linked to sales L* = liabilities linked to sales M = profit margin = NY/Sales S0 = past year sales S1 = projected sales RR = b =
!"# !"#$%&!!"#"$%&$'!"# !"#$%!
ASSUMPTIONS 1. Firm is operating at full capacity 2. Constant profit margin 3. Payout ratio ( !"#"$%&$' !"# !"!!"
!"#$%$&' !"# !!!"#= !"#"$%&$'
!"# !"#$%& ) and Retention ratio (RR) are constant
Internal growth rate = 𝑹𝑶𝑨 𝑿 𝒃𝟏!𝑹𝑶𝑨 𝑿 𝒃
where ROA = !"# !"#$%&!""#$"
à Retained earnings only form of financing
Sustainable growth rate = 𝑹𝑶𝑬 𝑿 𝒃
𝟏!𝑹𝑶𝑬 𝑿 𝒃 where ROE = !"# !"#$%&
!"#$%&
àFinance by internally generated funds & issuing debt àDebt-‐equity ratio constant
Pro Forma Income Statement Sales Variable cost Gross profits Fixed costs Depreciation EBIT Taxes Net income Dividends Additions to retained earnings
Gross working capital = current A Net working capital = CA – CL Net operating working capital = op CA – op CL = Cash + inv + acct receivables – (accurals + acct payable)
Inventory period = Inventory/(COGS/365) Acct receivable period = Receivables/(Sales/365) Acct payable period = Total purchases/Average payable = 𝑪𝑶𝑮𝑺!𝑬𝒏𝒅 𝒊𝒏𝒗!𝑩𝒆𝒈 𝒊𝒏𝒗
𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝒑𝒂𝒚𝒂𝒃𝒍𝒆
Lockbox: PV of adopting = total gain
NPV = gain – cost = gain -‐ !"#$ !"# !"#$!"#$%$&# !" !"#$ !"#$
= 𝐍𝐂𝐅 𝐩𝐞𝐫 𝐝𝐚𝐲𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭
Float: Difference between book and bank accounts Float (value) = 𝑪𝒐𝒔𝒕 𝒕𝒐 𝒆𝒍𝒊𝒎𝒊𝒏𝒂𝒕𝒆 𝒄𝒐𝒎𝒑𝒍𝒆𝒕𝒆𝒍𝒚
𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒆𝒓 𝒕𝒊𝒎𝒆
Bank > Book: Disbursement float (bank write check) Bank < Book: Collection float (Received before bank credit) Credit policy Credit period: 3/15, net 40 (3% discount if pay in 15 days) To find: Interest rate early discount not taken up Period rate = 3/97 Period = 40 – 15 = 25 No of periods = 365/25 EAR = (1 + 3/97)365/25 – 1
Evaluating proposed policy: 1. Find incremental cash flow à (P – V)*(Q’ – Q) 2. Find PV of incremental cash flow 3. Find cost of switching à V(Q’ – Q) + (P * Q) 4. NPV = (2) – (3) à Accept if NPV>0 Buildup of receivables: à P*Q’*amt of time
Carrying cost: ↑ w/ ↑ levels of current assets Shortage cost: ↓ w/ ↑ levels of current assets
Exchange-‐traded derivatives: Standardized Over-‐the-‐counter: Customized contracts Call: give owner right to PURCHASE given asset on given date for a predetermined px Put: give owner right to SELL given asset on given date for a predetermined price
S – price of underlying asset S0 – price of underlying asset today ST – Price of asset at expiry date X – Exercise or strike price r – interest rate (risk-‐free rate) C0 – price of call option today CT – price of call option at expiry date
Payoff of call at maturity: CT = Max {ST – X, 0} Profit to call/put holder = payoff – premium Profit to put writer = Payoff + premium
Imagine situation when maturity was today: In-‐the-‐money option: would exercise option àS > X (call), X > S (put) At-‐the-‐money option: indifferent àS = X Out-‐of-‐the-‐money option: would not exercise option à S < X (call), X < S (put)
Stock + put: S < X à Exercise put and receive X S ≥ X à Let put expire and have S Call + PV(X) (treasury bills w/ face value = X): S < X à Let call expire & have investment, X S ≥ X à Exercise call using I and have S Put Call Parity: Px of underlying stock + Px of put = Px of call + PV of Exercise Price (zero-‐coupon bond w/ face value = X)
S + P = C + PV(X)
Intrinsic value: profit if option was immediately exercise àCall: stock price – exercise price àPut: exercise price – stock price Time (volatility) value – Diff between option price and the intrinsic value
Max {S0 – X, 0} ≤ C0 ≤ S0 If violated à arbitrage opportunity