finance cheat sheet

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Corporate finance: Capital budgeting decision (longterm investment) (fixed A) Capital structure decision (longterm financing) (L+E) Working capital management (everyday financial activity) (CACL) Investors provide financing Firm generates income Distributed to investors Investment decision: increase size of pie Capital structure(financing decision): how to slice pie Primary goal: shareholder wealth maximization 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 + ΔLongterm 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 how quickly inv produced and sold Receivables Turnover = Sales/Receivables Days’ Sales Outstanding = 365/Rec turnover Average no of days before receiving cash Fixed Assets turnover = Sales/net fixed A Total Assets turnover = Sales/total assets Longterm Solvency Ratios: Extent firm relies on debt financing rather than equity ability to fulfill contractual obligations Variations DebtEquity Ratio = Total Debt/Total E Equity Multiplier = Total A/ Total E = 1 + DebtEquity 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 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 liquidity, asset management, debt on operating results Profit margin = Net Income/Sales Basic Earning Power = EBIT/Total Assets ROA = Net income/Total Assets Lowered by debt (interest exp lower net income) but debt lower equity. ROE may increase ROE = Net Income/ Total common E Doesn’t consider risk and capital invested DUPONT IDENTITY ROE = Profit Margin*TATurnover*EM operating 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 how much willing to pay for $1 of earnings MB ratio = mkt price per share/book value per share how much willing to pay for $1 of book value E PVFV: Compounding FVPV: Discounting Annuity: 1 st CF one period from now (end of P1) Annuity due: First cash flow now (start of period 1) Perpetuity: equal payment paid forever Growing perpetuity: Growing at constant rate Money today preferred due to lost earnings (can invested) and loss of purchasing power (inflation) FV n = PV(1 + i) n FV interest factor = (1 + i) n r= ( !" !" ) ! ! 1 t= !" ( !" !" ) !" (!!!) PV Annuity = PMT * [ !!!" !"#$%& ! ] PV factor = (!) PV Annuity Due = PV Annuity * (1+r) PV Growing Annuity = C* ! * ( ! ! ) FV Annuity = PMT*[ ! ! [(1+r) n 1] ] FV Annuity Due = FV Annuity * (1+r) PV perpetuity = PV growing perpetuity = ! 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, ! = ! ! ! ! !! Arithmetic mean, ! = ! Standard deviation, σ = = !( ! ) ! Total risk of investment Estimated σ = ! ( ! !) ! ! CV = Standard deviation/expected rate of return = !̂ risk per unit of return (lower=better) Risk premium = return – riskfree rate Portofoio returns, ! = ! ̂ ! ! !!! To find portfolio volatility, : Find expected returns for each scenario expected returns of portfolio SD using each return for each portfolio ! = ! ! ! σ ! ! + (1 ! ) ! σ ! ! + 2 ! (1 ! ) !" ! ! If = 1 riskless portfolio If =1 risk not reduced E(R) of risky asset only depends on systematic risks Total risk = companyspecific 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. = ! ! ! ! ! = !"#(! ! ,! ! ) ! ! ! High higher return when market doing well and vice versa high risk, high return When <0 move in opposite direction from the market When =0 riskfree asset When <1 asset less systematic risk than market (less E(R)) When =1 same systematic risk as market (same E(R)) When >1 more systematic risk than market (more E(R)) SML: R i =R f + (R M –R f ) CAPM Slope = R M –R f = market risk premium R f pure time value of money Fairly priced on SML Underpriced above SML Overpriced under SML Inflation parallel upward shift Risk aversion change change in slope Diversification get rid of the unsystematic risk.

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Transcript of finance cheat sheet

Page 1: 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.  

Page 2: finance cheat sheet

 

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  

Page 3: finance cheat sheet

   

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