Finance.pdf

FINE2000   Midterm  Notes        Jessica  Gahtan   Finance  Midterm  Notes  #iamsofucked   Table  of  Contents   Chapter  1  ..........................................................................................................................................  2   Chapter  2  ..........................................................................................................................................  4   Chapter  3  ..........................................................................................................................................  6   Chapter  4  ..........................................................................................................................................  8   Chapter  5  ........................................................................................................................................  12   Chapter  6  ........................................................................................................................................  16   Chapter  7  ........................................................................................................................................  20         Page  1  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   Chapter  1   -­‐ A  corporation  is  a  permanent  entity  that  is  legally  distinct  from  its  shareholders  (owners);  owners  have  limited   liability  (not  personally  accountable  for  corporation’s  debts   –  when  you  incorporate  you  (along  with  your  lawyer)   prepare  articles  of  incorporation  (=set  ou t  the  purpose  of  the  business  and  how  it  is  to  be  financed,  managed  and   governed)  –  You  can  incorporate  provincially  or  federally,  the  corporation  is  basically  considered  a  resident  of  the   jurisdiction  that  you  incorporate  under.   -­‐ Public  company  is  a  company  whose  shares  are  publically  listed  on  a  stock  exchange.     -­‐ Private  company  is  a  company  whose  shares  are  privately  owned   -­‐ Public  companies  offer  shares  for  sale  to  raise  $;  in  return,  they  provide  detailed  financial  info  in  their  annual  reports   and  make  timely  disclosure  of  significant  corporate  events;  private  companies  aren’t  required  to  do  either  of  these   things   -­‐ All  corporations  have  a  board  of  directors    -­‐>  selected  by  shareholders,  oversee  the  activities  of  the  corporation   -­‐ Because  there  is  a  separation   of  ownership  and  management,  corporations  have  permanence     -­‐ Not  all  companies  incorporate  because  of  time  and  $   -­‐ A  disadvantage  of  incorporating  is  double  taxation   –  taxed  on  profits  and  then  shareholders  get  taxed  on  their   dividends  or  if  they  sell  their  sh ares   -­‐ Public  corporations  also  need  to  pay  to  maintain  a  stock  listing,  to  comply  with  government  requirements,  securities   laws  and  to  share  info  with  the  public     -­‐ A  sole  proprietorship  is  owned,  operated  by  1  person;  unlimited  liability;  easy  to  establish,   few  regulations  that   govern  it;  taxed  only  on  the  personal  level   -­‐ A  partnership  is  a  business  owned  by  2+  people  who  have  unlimited  liability;  partnership  agreement  says  how   management  decisions  will  be  made,  the  proportion  of  profits  that  will  go  to  each  p artner;  partners  pay  tax  on   personal  level  for  their  share  of  profits   -­‐ Sole  proprietorships  and  partnerships  =  flow  through  entities  b/c  they  don’t  pay  income  tax  on  operating  profits  and   don’t  file  tax  returns  (corporations  not  the  same)   -­‐ Limited  partnership  partners  are  classified  as  general  or  limited   –  general  manage  the  business  and  have  unlimited   liability,  limited-­‐  liable  only  for  the  $  contributed  and  can’t  take  part  in  the  day -­‐to-­‐day  management  of  the   partnership   -­‐ LLP  (limited  liability  partnership)  is  where  both  partners  have  limited  liability     -­‐ A  Professional  corporation  (PC)  is  used  commonly  by  doctors,  lawyers,  accountants   –  limited  liability,  taxed  like  a   corporation,  still  can  be  sued  personally   -­‐ Income  trust  which  is  an  investment  fund     -­‐  called  mutual  fund  trust  –  they  sell  units  to  investors  to  raise  $  to  buy   shares  and  debts  of  operating  businesses;  flow -­‐through  entities;  income  trust  only  invests  in  1  company,  so  a  unit  of   one  is  similar  to  a  share;  this  is  a  smart  way  to   ↓  taxes  paid  by  the  underlying  business  enterprise;  it  allows  a   corporation  to  be  financed  by  a  ton  of  debt  which  lowers  the  amount  of  taxes  that  need  to  be  pay;  CDN  federal   government  changed  the  tax  rule  in  2006  because  they  feared  the  loss  of  tax  revenue  from  compa nies  using  this  to   pay  less  taxes   -­‐ Capital  budgeting  decision  or  investment  decision  is  the  decision  as  to  which  real  assets  the  firm  should  acquire -­‐   the  financial  manager  values  on  different  investment  opportunities  based  on  the  amounts,  timing  and  risk  of  the   future  cash  flows.  To  be  an  attractive  investment  the  opportunity’s  value  must  exceed  the  current  investment  it   requires.  An  investment  decision  can  literally  be  as  simple  as  buying  a  truck.   -­‐ Financing  decision  is  the  decision  about  how  the  $  to  pay  for  investments  will  be  raised.    It  can  happen  in  2  ways:  by   selling  shares  (equity  financing)  or  by  borrowing  (debt  financing).  Capital  structure  is  the  distribution  of  financing   between  these  two  different  methods  of  obtaining  $.  Capital  structure,  ‘raisin g  capital’  -­‐>  long  term  financing;      Financial  managers  also  need  to  manage  risk  against  things  like  a  drought     -­‐ $  Flows  from  investors  to  the  firm  and  then  back  to  investors  again   -­‐ First,  cash  is  raised  from  investors   -­‐ Then,  the  $  is  used  to  pay  for  the   investment  projects  needed  for  the  firm’s  operations   -­‐ Then,  the  profits  are  either  reinvested  into  the  company  or  returned  to   the  investors  via  dividends  **   need  to  remember  they  might  be  constrained  by  promises  that  they  made  to  those  that  provided  the  $   (i.e.  mandatory  dividends)   -­‐ Real  assets  are  used  to  produce  g/s     -­‐ Financial  assets  are  claims  to  the  income  generated  by  real  assets   Page  2  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   -­‐ Financial  manager  =  anyone  responsible  for  a  significant   corporate  investment  or  financing  decisions   -­‐ Treasurer  responsible  for  financing,  cash  management,  and  relationships  with  financial  markets  and  institutions ;  obtain   and  manage  the  firm’s  capital     -­‐ Controller  is  the  person  responsible  for  budgeting,  accounting,  auditing ;  makes  sure  the  $  is  used  efficiently   -­‐ CFO  overseas  the  controller  and  treasurer;  sets  overall  financial  strategy   -­‐ All  shareholders  want  to  maximize  the  current  value  of  their  investment   -­‐ For  public  companies  –  achieving  this  objective  means  that  you  want  to  maximize  the  value  of  today’s  stock  price s     -­‐ Reputation  is  important  in  finance -­‐  banks  and  firms  tend  to  protect  reputation  by  emphasizing  their  history  and   responsible  behavior  in  the  past  to  new  customers   –  irreparable  damage  if  reputation  is  tarnished   -­‐ Agency  problems  is  the  conflicting  interest  b/w  firm’s  owners  and  managers   –  managers  sometimes  act  in  a  way  that  isn’t   in  the  interest  of  the  owners     -­‐ Stakeholders  is  someone  with  an  interest  /  stake  in  the  firm   -­‐ Several  things  in  place  to  mitigate  agency  problems:    (1)  Compensation  plans  that  correlate  to  the  value  of  the  firm  –  i.e.   stock  options  (2)  board  of  directors   –  board  can  get  replaced  by  shareholders  if  they  feel  that  the  board  isn’t  managing   managers  well  (3)  takeovers   –  companies  that  perform  poorly  are  likely  to  be  taken  over  by  another  firm  (and  the  other   firm  will  likely  fire  the  management  team)  (4)  specialist  monitoring   –  analysts  monitor  the  behaviors  of  management  and   then  advise  investors  to  buy/sell/hold  shares;  also  reviewed  by  banks  who  have  loaned  $               Page  3  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   Chapter  2   -­‐ For  large  public  companies,  investors’  $  flows  through  financial  intermediaries  or  markets  or  both     -­‐ Financial  market  is  a  market  where  securities  are  issued  &  traded  –  most  important  =  stock  market   -­‐ IPO  (initial  public  offering)  –  when  a  company  goes  public ,  it’s  the  first  issue  of  shares  on  a  stock  exchange  (i.e.  the  TSX  or   NYSE)  –  it’s  usually  managed  by  investment  dealers  (i.e.  Steve  Madden  in  the  Wolf  of  Wall  Street)   -­‐ Seasoned  equity  offers  (SEO)  or  follow  up  offers  are  subsequent  public  stock  offerings   -­‐ When  there’s  a  new  issue,  the  stocks  are  sold  in  the   primary  market;  purchases  +  sales  of  existing  securities  b/w  investors   are  secondary  transactions  and  they  take  place  in  the   secondary  market   -­‐ Stock  markets  are  called  equity  markets   -­‐ Debt  securities  are  also  traded  in  financial  markets;  fixed-­‐income  market  is  the  market  for  debt  securities;  the  markets   for  long-­‐term  debt  and  equity  are  called  capital  markets;  short  term  securities  (<1  year)  are  traded  in  the  money  markets   -­‐ Other  markets  include:  Foreign -­‐exchange  market  (FOREX),  commodities  market,  markets  for  options  and  other   derivatives  (derivatives  are  securities  whose  payouts  are  contingent  on  the  price(s)  of  other  securities/  commodities   -­‐ A  financial  intermediary  is  an  organization  that  raises  $  from  investors  and  provides  financing  for  individuals,   corporations  or  other  organizations;  5  kinds:   1. Mutual  funds  and  ETFs:   mutual  funds  are  managed  investment  funds  that  pool  the  savings  of  many  investors  and   invest  the  $  in  a  portfolio  of  securities;  an  exchange  traded  fun  is  an  investment  fund  that’s  traded  on  a  stock   exchange-­‐  it  pools  the  savings  of  many  investors  and  invests  in  a  portfolio  of  securities  that  is  selected  to  replicate   am  established  securities  index;  Mutual  funds  =  actively  managed  (managers  try  to  like  beat  the  market   inefficiencies  that  exist  in  the  short  term);  ETFs  and  some  mutual  funds  are  passively  managed ;  fund  managers  get   commission  for  their  services;  mutual  funds  and  ETFs  allow  for  low  cost  diversification  and  professional   management   2. Hedge  funds  (like  mutual  funds)  get  $  from  investors  then  invest  in  a  portfolio  of  securities;  they  usually  use   untraditional  investment  strategies  (i.e.  short  positions,  arbitrage,  leverage,  options,  futures  and  other  financial   instruments  that  are  aimed  at  capitalizing  on  market  conditions);  some  are  only  opened  to  super  rich  and  smart   investors   3. Private  equity  funds  are  investment  funds  focused  on  investing  in  equity  of  privately  owned  businesses;  often  they   provide  financing  +  help  nurture  growing/troubl ed  companies  towards  stable  &  long  term  growth   4. Pension  fund  is  an  investment  plan  that  one’s  employer  sets  up  to  provide  for  his/her  employees’  retirements.   Defined  contribution  plan   –each  employee  owns  a  portion  of  the  pension  funds  and  accumulates  an  inv estment   balance  for  when  they  retire  (balance  depends  on  their  accumulated  contributions  +  the  performance  of  the  fund).   Defined  benefit  plan  –employer  promises  a  certain  level  of  benefits  when  the  employee  retires  and  the  employer   invests  in  the  pension  plan.  If  the  investment  value  <  promised  benefits  –  the  employer  must  contribute  more   -­‐ Financial  institutions  like  banks,  insurance  companies,  or  similar  financial  intermediaries;  they  d on’t  only  invest  in   securities-­‐  they  also  loan  $  directly  to  businesses,  individuals  and  other  organizations   -­‐ Functions  of  financial  markets  and  intermediaries :   -­‐ Transporting  $  across  time   -­‐ Risk  transfer  and  diversification   -­‐ Liquidity  (the  ability  to  sell  or  exchange  an  asset  for  cash  on  short  notice,  shares  of  public  companies  ar e  liquid   because  they’re  traded  more  or  less  continuously)   –  foreign-­‐exchange  markets,  government  securities  =  liquid   -­‐ The  payment  mechanism:  things  like  credit  cards  +  electronic  transfers  let  people  &  organizations  send  and  receive   payments  fast  and  over  long  distances   -­‐ Information  provided  by  financial  markets  –  for  example:   • A  CFO  can  find  commodity  prices  for  a  given  day  on  the  NYSE  and  budget  that  amount   • When  looking  for  financing   –  a  CFO  can  look  up  average  interest  rates  on  existing  Canada  bonds  traded  in   financial  markets   • To  value  the  entire  company,  or  the   enterprise  value,  add  the  value  of  the  company’s  debt  to  its  stock  value   – stock  prices  and  company  values  sum  up  the  collective  assessment  of  investors  about  how  well  a  company  is   doing  in  the  present  and  how  well  they  think  it’ll  do  in  the  future   -­‐ Value  maximization  →  there  are  always  those  investors  who  are  willing  to  take  on  the  risk  associated  with  risky   investments  (as  long  as  the  potential  upside  is  reasonable  to  them   –i.e.  the  interest  rate  they’ll  receive  is  high  enough)   -­‐ The  opportunity  cost  of  capital   Page  4  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   • Cost  of  capital  is  the  minimum  acceptable  rate  of  return  on  capital  investment   –  if  a  project  offers  a  higher  rate  of   return,  it  adds  value  to  the  firm;  a  ‘superior  rate  of  return’  refers  to  when  a  project  offers  a  better  rate  of  return   than  a  project  with  a  similar  amount  of  risk   • Expected  rates  of  return  determine  the  cost  of  capital  for  corporate  investments   • The  cost  of  capital  for  corporate  investment  is  set  by  the  rates  of  return  on  investment  opportunities  in  financial   markets.   • When  a  firm  invests  its  savings  i n  whatever,  the  shareholders  lose  the  opportunity  to  invest  in  something  else  (this   raises  the  cost  of  capital)   • The  riskier  an  investment  is,  the  higher  the  interest  rate/  expected  return           Page  5  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   Chapter  3   -­‐ The  Balance  Sheet  is  a  f/s  that  shows  the  value  of  a  firm’s  assets  and  liabilities  at  a  given  point  in  time   • Current  assets  are  those  which  are  likely  to  be  converted  into  cash  within  1  year   • Long-­‐term  assets  can  be  things  like  tangible  capital  assets/fixed  assets  (i.e.  buildings,  equipment)  or  investments  in   other  companies  (ownership  of  another  business)  or  goodwill  &  other  intangibles  →  on  the  other  side  of  the  b/s   there  are  liabilities.  Whatever  amount  is  leftover  when  you  subtract  liabilities  from  assets  is   your  shareholders’   equity   ' Shareholders equity=total  assets-­‐total  liabilities   -­‐ Book  v.  Market  Value   • GAAP  has  rules  that  relate  to  the  way  you  should  prepare  your  financial  statements   • Book  value  is  the  net  worth  of  the  firm  according  to  the  B/S  →  Based  on  historical  cost  →  market  values  ≠  book   values  →  Market  values  measure  current  values  of  assets  +  liabilities.   • Shareholders’  equity  is  likely  to  demonstrate  the  largest  difference  in  terms  of  comparing  book  and  market  value   • ‘Market-­‐value  balance  sheet’  is  forward  looking  and  it  depends  on  the  benefits  that  sh areholders  expect  the  assets   to  have   • The  stock  price  is  the  market  value  of  the  shareholders’  equity  divided  by  the  #  of  outstanding  shares     Note:  Usually  shares  of  stock  sell  for  more  than  the  book  value   -­‐ Income  Statement  is  the  f/s  that  shows  revenues,  expenses,  net  income  of  a  firm  over  a  period  of  time  (usually  1  year)   -­‐ Three  reasons  why  profits  ≠  cash  flow:   1. To  calculate  the  cash  produced  by  the  business,  you  need  to  add  the  depreciation  expense  (which  isn’t  a  cash   payment)  and  subtract  the  expenditure   on  capital  equipment  (which  is  a  capital  payment)   2. The  cash  that  the  company  receives  is  equal  to  the  sales  shown  in  the  I/S  minus  the   ↑  in  unpaid  bills  (A/R)   3. The  cash  outflow  =  COGS,  which  is  shown  in  the  I/S  +  the   ∆  in  inventories   -­‐ Statement  of  cash  flows  (Shows  the  firm’s  cash  inflows  +  outflows  from  operations,  financing  and  investment  activities)   • Cash  from  operating  activities   • Cash  from  investing  activities  (includes  purchases  of  new  capital  equipment,  investments)   • Cash  from  financing  activities  (includes  debt  payments,  new  debt,  selling  of  stock,  dividend  payments)     Cash  flow  from  operating  activities=   Net  earnings+  depreciation+  cash  from  other  income  statement  adjustments+  cash  from  non -­‐cash  working  capital     Cash  flow  from  assets  (free  cash  flow)=  cash  provided  by  operating  activities+  cash  flow  from  investments     Increase  (decrease)  in  cash  in  the  bank  =  cash  flow  from  assets+  cash  flow  from  financing  activities       -­‐ Fundamental  cash  flow  identity:     Cash  flow  from  assets  =  Increase  (decrease)  in  cash  in  the  bank  +  cash  flow  from  financing  activities   “Free  cash  flow”  b/c  the  $  is  available  for  payouts  to  bondholders  and  shareholders     -­‐ Financing  flow   • Cash  flow  to  bondholders  and  stockholders  plus  increas es  in  cash  balances,  also  equals  cash  flow  to  assets   • Interest  expense  should  be  considered  financing  activity  so  that  you  have  a  better  idea  of  cash  flows  generated  by   the  assets  rather  than  including  the  way  that  a  firm  chooses  to  finance  itself   Cash  flow  from  assets  (adjusted)  =  cash  flow  from  assets  +  interest  expense   • Free  cash  flow  is  useful  when  you’re  doing  a  valuation  of  the  company’s  assets   -­‐ Accounting  (mal)  practice   • Can  alter  statements  i.e.  through  revenue  recognition,  allowance  for  bad  debts   • Sarbanes  Oxley  Act  in  2002  –  aimed  at  making  sure  statements  are  presented  accurately   • Foreign  firms  need  to  make  their  statements  in  accordance  with  Canadian  GAAP  before  they  can  be  listed  on  a   Canadian  stock  exchange   -­‐ Taxes   • Corporate  tax   Page  6  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan    The  cost  of  depreciation  for  tax  purposes  is  found  in  the  income  tax  act   –  called  the  capital  cost  allowance   (CCA)      Company  can  deduct  interest  paid  to  debt  holders  when  calculating  taxable  income   –  but  dividends  aren’t   deductible    Losses  can  be  carried  forward  and  deducted  from   taxable  income  in  the  future   • Personal  tax    Marginal  tax  rate  is  the  additional  taxes  owed  per  dollar  of  additional  income      Most  provinces  –  progressive  tax  system  –  higher  income  =  higher  tax  rate  (Alberta  =  exception,  10%  for   all)    E.g.  of  progressive  system  –  15%  on  first  (for  example)  10$  then  22%  on  the  next  10$    Taxpayers  calculate  their  taxes  twice   –  once  for  federal  and  once  for  provincial    Average  tax  rate  is  the  total  taxes  owed  divided  by  total  income  –  differs  from  marginal  tax  rate    Tax  rates  are  relevant  for  financial  managers  b/c  if  their  share/bond  payments  are  heavily  taxed,   individuals  might  be  hesitant  to  buy  bonds  or  shares  or  w.e.    In  2006,  rules  categorized  dividends  as  eligible  and  non -­‐eligible    -­‐  effective  tax  rate  on  non-­‐eligible   dividends  =  higher  than  the  applicable  rate  on  eligible  dividends     Capital  gains  =  taxable  at  50%     →  capital  losses  can  be  used  to  reduce  your  capital  gains   →  if  you  don’t   have  capital  gains  to  offset  it,  you  can  carry  it  back  3  years  or  forward  indefinitely   to  reduce  capital  gains   in  another  year         Page  7  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   Chapter  4   Measuring  Market  Value  and  Market  Value  Added   • Market  capitalization:  total  market  value  of  equity,  equal  to  share  price  times  number  of  shares  outstanding     • Book  value  of  equity  =  sum  of  the  funds  invested  by  shareholders  plus  earnings  reinvested  in  the  company   o Cumulative  investment  in  the  firm   • Market  value  added:  market  capitalization  minus  book  value  of  equity     • Market-­‐to-­‐book  ratio:  ratio  of  market  value  to  book  value  of  equity   o = 𝒎𝒂𝒓𝒌𝒆𝒕  𝒗𝒂𝒍𝒖𝒆  𝒐𝒇  𝒆𝒒𝒖   𝒃𝒐𝒐𝒌  𝒗𝒂𝒍𝒖𝒆  𝒐𝒇  𝒆𝒒𝒖𝒊𝒕𝒚 • Market-­‐value  performance  measures  have  three  drawbacks   o Market-­‐value  of  the  company’s  share  reflects  investors’  expectation  about  future  performance   o Market  value  fluctuate  because  of  many  risks  and  events  that  are  outside  the  fi  ial  manager’s  control o Can’t  look  up  the  market  value  of  privately  owned  companies   whose  shares  are  not  publicly  traded   Economic  Value  Added  and  Accounting  Rates  of  Return   • Necessary  to  measure  whether  a  firm  has  earned  a  profit  after  deducting  all  costs,  including  costs  of  capital   • Economic  value  added  (EVA):  operating  profit  minus  charge s  for  the  cost  of  capital  employed.  Also  called  residual   income   o Total  capitalization  is  the  sum  of  the  firm’s  debts  and  shareholders’  equity   EVA=  Net  income  +  after-­‐tax  finance  expense  –  (cost  of  capital  *  total  capitalization)   • Net  operating  profit  after  t ax  (NOPAT):  the  after-­‐tax  profits  from  operations,  as  if  the  firm  had  no  debt.  Equals  net   income  (or  net  earnings  or  profit)  plus  after-­‐tax  net  finance  (or  interest)  expense   𝐸𝑉𝐴 = 𝑁𝑂𝑃𝐴𝑇 − 𝑐𝑜𝑠𝑡  𝑜𝑓  𝑐𝑎𝑝𝑖𝑡𝑎𝑙×𝑡𝑜𝑡𝑎𝑙  𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛   o Using  NOPAT  removes  the  effect  of  interest  tax  deductions     • Return  on  capital  (ROC):   net  operating  profit  after  taxes  (NOPAT)  as  a  percentage  of  invested  capital  (debt  plus   equity)   𝑁𝑂𝑃𝐴𝑇 𝑅𝑂𝐶 =   𝑡𝑜𝑡𝑎𝑙  𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 o The  return  that  shareholders  are  giving  up  by  keeping  their  money  in  the  company  is  called  their  cost  of   equity,  which  is  included  in  the  calculation  of  the  cost  of  capital   • Return  on  assets  (ROA):  net  operating  profit  after  taxes  (NOPAT)  as  a  percentage  of  total  asse ts   𝑁𝑂𝑃𝐴𝑇 𝑅𝑂𝐴 = 𝑡𝑜𝑡𝑎𝑙  𝑎𝑠𝑠𝑒𝑡𝑠   o Helpful  to  use  NOPAT  when  comparing  the  profitability  of  companies  with  different  capital  structures     • Return  on  equity  (ROE):  net  income  as  a  percentage  of  shareholders’  equity   𝑛𝑒𝑡  𝑖𝑛𝑐𝑜𝑚𝑒 𝑅𝑂𝐸 = 𝑒𝑞𝑢𝑖𝑡𝑦   o Necessary  to  decide  whether  to  use  net  profit  or  total  comprehensive  income   • Problems  with  EVA  and  accounting  rates  of  return   o Based  on  book  value  of  assets,  debt,  and  equity,  which  is  not  always  reported  on  SFP   Measuring  Efficiency   • Asset  turnover  ratio:  or  sales-­‐to-­‐assets,  shows  how  much  sales  are  generated  by  each  dollar  of  total  assets   o Measures  how  hard  the  firm’s  assets  are  working   𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠 𝐴𝑠𝑠𝑒𝑡  𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟 = 𝑡𝑜𝑡𝑎𝑙  𝑎𝑠𝑠𝑒𝑡𝑠  𝑎𝑡  𝑠𝑡𝑎𝑟𝑡  𝑜𝑓  𝑦𝑒𝑎𝑟   • Inventory  turnover:  how  quickly  inventories  sell   o Efficient  firms  don’t  tie  up  more  capital  than  they  need  in  raw  materials  and  finished  goods   Page  8  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   𝑐𝑜𝑠𝑡  𝑜𝑓  𝑠𝑎𝑙𝑒𝑠 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦  𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟 =   𝑎𝑣𝑒𝑟𝑎𝑔𝑒  𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑖𝑒𝑠 𝑎𝑣𝑒𝑟𝑎𝑔𝑒  𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑖𝑒𝑠 365 𝑎𝑣𝑒𝑟𝑎𝑔𝑒  𝑑𝑎𝑦𝑠  𝑖𝑛  𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑖𝑒𝑠 = =   𝑐𝑜𝑠𝑡  𝑜𝑓  𝑠𝑎𝑙𝑒𝑠 365 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦  𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟 • Receivables  turnover:  measure  efficiency  of  collection   o High  ratio  can  either  mean  credit  department  is  quick  to  follow  up  on  late  pay ers  or  an  unduly  restrictive   credit  policy   𝑟𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠  𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟 = 𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠   𝑎𝑣𝑒𝑟𝑎𝑔𝑒  𝑡𝑟𝑎𝑑𝑒  𝑟𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠 𝑎𝑣𝑒𝑟𝑎𝑔𝑒  𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛  𝑝𝑒𝑟𝑖𝑜𝑑 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒  𝑡𝑟𝑎𝑑𝑒  𝑟𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠   𝑎𝑣𝑒𝑟𝑎𝑔𝑒  𝑑𝑎𝑖𝑙𝑦  𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠 Analyzing  the  Return  on  Assets:  The  Du  Pont  System   • Profit  margin:  measure  the  proportion  of  sales  that  finds  its  way  into  profits   𝒏𝒆𝒕  𝒊𝒏𝒄𝒐𝒎𝒆 o 𝒑𝒓𝒐𝒇𝒊𝒕  𝒎𝒂𝒓𝒈𝒊𝒏 =   𝒔𝒂𝒍𝒆𝒔 o When  companies  are  financed  by  debt,  a  portion  of  the  revenue  produced  by  sales  must  be  paid  as  interest   to  the  firm’s  lenders    Profits  divided  between  the  debt  holders  and  the  shareholders    Operating  profit  margin:  net  operating  profit  after  taxes  (NOPAT)  as  a  percentage  of  sales   𝑁𝑂𝑃𝐴𝑇 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔  𝑝𝑟𝑜𝑓𝑖𝑡  𝑚𝑎𝑟𝑔𝑖𝑛 =   𝑠𝑎𝑙𝑒𝑠 • Du  Pont  formula:  ROA  equals  the  product  of  the  asset  turnover  and  operating  profit  margin   𝑁𝑂𝑃𝐴𝑇 𝑠𝑎𝑙𝑒𝑠 𝑁𝑂𝑃𝐴𝑇 𝑅𝑂𝐴 = = ×   𝑡𝑜𝑡𝑎𝑙  𝑎𝑠𝑠𝑒𝑡𝑠 𝑡𝑜𝑡𝑎𝑙  𝑎𝑠𝑠𝑒𝑡𝑠 𝑠𝑎𝑙𝑒𝑠 o Useful  way  to  think  about  a  company’s  strategy    Tradeoff  between  high  volume  (high  asset  turnover)  or  high  profit  per  unit  (high  operating  profit   margin)   Measuring  Financial  Leverage   • Debt  increases  returns  to  shareholders  in  good  times  and  reduces  them  in  bad  time   • Debt  ratio:  measures  the  percentage  debt  is  used  in  financing  a  company   o Long-­‐term  debt  should  include  not  just  bonds  or  other  borrowing  but  also  financing  from  long -­‐term  leases,   and  current  portion  of  long-­‐term  debt   𝑙𝑜𝑛𝑔  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡 + 𝑣𝑎𝑙𝑢𝑒  𝑜𝑓  𝑙𝑒𝑎𝑠𝑒𝑠 𝐿𝑜𝑛𝑔  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡  𝑟𝑎𝑡𝑖𝑜 = 𝑙𝑜𝑛𝑔  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡 + 𝑣𝑎𝑙𝑢𝑒  𝑜𝑓  𝑙𝑒𝑎𝑠𝑒𝑠 + 𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑  𝑒𝑞𝑢𝑖𝑡𝑦 + 𝑐𝑜𝑚𝑚𝑜𝑛  𝑒𝑞𝑢𝑖𝑡𝑦   𝑙𝑜𝑛𝑔  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡 + 𝑣𝑎𝑙𝑢𝑒  𝑜𝑓  𝑙𝑒𝑎𝑠𝑒𝑠 𝑙𝑜𝑛𝑔  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡  𝑡𝑜  𝑒𝑞𝑢𝑖𝑡𝑦  𝑟𝑎𝑡𝑖𝑜 = 𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑  𝑎𝑛𝑑  𝑐𝑜𝑚𝑚𝑜𝑛  𝑒𝑞𝑢𝑖𝑡𝑦   o Firms  acquired  in  a  leveraged  buyout  (LBO)  usually  issue  large  amounts  of  debt   o Debt-­‐equity  ratios  use  book  values  rather  than  market  values    Lenders  should  be  more  interested  in  market   values   𝑠ℎ𝑜𝑟𝑡  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡 + 𝑙𝑜𝑛𝑔  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡 + 𝑣𝑎𝑙𝑢𝑒  𝑜𝑓  𝑙𝑒𝑎𝑠𝑒𝑠 𝑡𝑜𝑡𝑎𝑙  𝑑𝑒𝑏𝑡  𝑟𝑎𝑡𝑖𝑜 =   𝑠ℎ𝑜𝑟𝑡  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡 + 𝑙𝑜𝑛𝑔  𝑡𝑒𝑟𝑚  𝑑𝑒𝑏𝑡 + 𝑣𝑎𝑙𝑢𝑒  𝑜𝑓  𝑙𝑒𝑎𝑠𝑒𝑠 + 𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑  𝑒𝑞𝑢𝑖𝑡𝑦 + 𝑐𝑜𝑚𝑚𝑜𝑛  𝑒𝑞𝑢𝑖𝑡𝑦 𝑡𝑜𝑡𝑎𝑙  𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑑𝑒𝑏𝑡  𝑡𝑜  𝑎𝑠𝑠𝑒𝑡  𝑟𝑎𝑡𝑖𝑜 = 𝑡𝑜𝑡𝑎𝑙  𝑎𝑠𝑠𝑒𝑡𝑠   • Times  interest  earned  (TIE)  ratio:  extent  to  which  interest  obligations  are  covered  by  earnings  or  operating  profits   𝐸𝐵𝐼𝑇 𝑇𝐼𝐸 =   𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡  𝑒𝑥𝑝𝑒𝑛𝑠𝑒 • Cash  coverage  ratio:  extent  to  which  interest  obligations  are  covered  by  cash   𝐸𝐵𝐼𝑇𝐷𝐴 𝑐𝑎𝑠ℎ  𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒  𝑟𝑎𝑡𝑖𝑜 = 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡  𝑒𝑥𝑝𝑒𝑛𝑠𝑒   Page  9  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   o EBITDA  is  earnings  before  interest,  depreciation,  and  amortization    Used  as  a  measure  of  true  operating  performance   • Removing  any  effect  of  depreciation  and  amortization  based  on  accounting  methods  and   assumptions  rather  than  performance   • Net  finance  expenses  removed  since  it  is  a  function  of  how  the  company  manages  capital   • Taxes  are  removed  because  it  is  based  on  jurisdiction  where  the  income  is  earned   • Leverage  and  the  return  on  equity  (Du  Pont)   𝑛𝑒𝑡  𝑖𝑛𝑐𝑜𝑚𝑒 𝑎𝑠𝑠𝑒𝑡𝑠 𝑠𝑎𝑙𝑒𝑠 𝑁𝑂𝑃𝐴𝑇 𝑛𝑒𝑡  𝑖𝑛𝑐𝑜𝑚𝑒 𝑅𝑂𝐸 = = × × ×   𝑒𝑞𝑢𝑖𝑡𝑦 𝑒𝑞𝑢𝑖𝑡𝑦 𝑎𝑠𝑠𝑒𝑡𝑠 𝑠𝑎𝑙𝑒𝑠 𝑁𝑂𝑃𝐴𝑇 𝑅𝑂𝐸 = 𝑙𝑒𝑣𝑒𝑟𝑎𝑔𝑒  𝑟𝑎𝑡𝑖𝑜×𝑎𝑠𝑠𝑒𝑡  𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟×𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔  𝑝𝑟𝑜𝑓𝑖𝑡  𝑚𝑎𝑟𝑔𝑖𝑛×𝑑𝑒𝑏𝑡  𝑏𝑢𝑟𝑑𝑒𝑛   o Leverage  increases  ROE  when  the  firm’s  return  on  assets  is  higher  than  the  interest  rate  on  debt   Measuring  Liquidity   • Book  values  of  liquid  assets  are  more  reliable     • Measure  of  liquidity  cab  become  quickly  outdated     • Sometimes  liquid  assets  can  become  illiquid  (ex.  Subprime  mortgage  crisis)     • High  levels  of  liquidity  can  indicate  sloppy  use  of  capital   o EVA  penalizes  manager  who  keep  more  liquid  asses  than  they  need   • Net  working  capital  to  total  assets  ratio:   net  working  capital  measures  company’s  potential  net  reservoir  of  cash.     𝑛𝑒𝑡  𝑤𝑜𝑟𝑘𝑖𝑛𝑔  𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑎𝑠𝑠𝑒𝑡𝑠 − 𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠   𝑛𝑒𝑡  𝑤𝑜𝑟𝑘𝑖𝑛𝑔  𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑛𝑒𝑡  𝑤𝑜𝑟𝑘𝑖𝑛𝑔  𝑐𝑎𝑝𝑖𝑡𝑎𝑙  𝑡𝑜  𝑡𝑜𝑡𝑎𝑙  𝑎𝑠𝑠𝑒𝑡𝑠  𝑟𝑎𝑡𝑖𝑜 =   𝑡𝑜𝑡𝑎𝑙  𝑎𝑠𝑠𝑒𝑡𝑠 • Current  ratio:  just  the  ratio  of  current  assets  to  current  liabilities   𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑟𝑎𝑡𝑖𝑜 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑎𝑠𝑠𝑒𝑡𝑠   𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 o It  is  possible  for  working  capital  to  be  unchanged  but  alter  the  current  ratio   o Good  to  net  short-­‐term  investments  against  short-­‐term  debt  when  calculating  current  ratio   • Quick  (Acid-­‐test)  ratio:  some  current  assets  are  closer  to   cash  than  other   𝑐𝑎𝑠ℎ  𝑎𝑛𝑑  𝑐𝑎𝑠ℎ  𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡𝑠 + 𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑜𝑡ℎ𝑒𝑟  𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠 + 𝑡𝑟𝑎𝑑𝑒  𝑟𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠 𝑄𝑢𝑖𝑐𝑘  𝑟𝑎𝑡𝑖𝑜 =   𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 • Cash  ratio:  most  liquid  assets  are  holding  of  cash  an d  cash  equivalents   𝑐𝑎𝑠ℎ  𝑎𝑛𝑑  𝑐𝑎𝑠ℎ  𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡𝑠 𝑐𝑎𝑠ℎ  𝑟𝑎𝑡𝑖𝑜 =   𝑐𝑢𝑟𝑟𝑒𝑛𝑡  𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 o A  low  cash  ratio  might  not  matter  if  the  firm  can  borrow  on  short  notice   Calculating  Sustainable  Growth   • Leverage  and  liquidity  ratios  are  checks  on  whether  its  financing  policies  are  safe  and  sound   • In  a  well-­‐functioning  financial  market,  a  company’s  growth  is  limited  not  by  financing  opportunities  but  by  limits  to   good  investment  opportunities  and  by  limits  to  other  resources   o Including  trained  management  and  staff   • Financial  manager  who  believes  that  investors  are  unduly  pessimistic  will  be  reluctant  to  issue  shares  at  what   he/she  sees  as  a  depressed  stock  price   • Interested  in  knowing  how  fast  the  firm  can  grow  if  it  relies  only  on  internal   financing   o Keeping  long-­‐term  debt  to  equity  ratio  constant    Calculates  sustainable  growth  rate   • Payout  ratio:  the  proportion  of  earnings  (net  income)  paid  out  as  dividends   𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠   𝑃𝑎𝑦𝑜𝑢𝑡  𝑟𝑎𝑡𝑖𝑜 = 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠   • Plowback  ratio:  the  proportion  of  earning  reinvested  into  the  business  and  added  to  equity  capital   Page  10  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 − 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑃𝑙𝑜𝑤𝑏𝑎𝑐𝑘  𝑟𝑎𝑡𝑖𝑜 = = 1 − 𝑝𝑎𝑦𝑜𝑢𝑡  𝑟𝑎𝑡𝑖𝑜   𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 • Sustainable  rate  of  growth:  the  firm’s  growth  rate  if  it  plows  back  a  constant  fraction  of  earnings,  maintains   constant  return  on  equity,  and  keeps  its  debt  ratio  constant     𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 − 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑆𝑢𝑠𝑡𝑎𝑖𝑛𝑎𝑏𝑙𝑒  𝑔𝑟𝑜𝑤𝑡ℎ  𝑟𝑎𝑡𝑒 = 𝑔𝑟𝑜𝑤𝑡ℎ  𝑖𝑛  𝑒𝑞𝑢𝑖𝑡𝑦  𝑓𝑟𝑜𝑚  𝑝𝑙𝑜𝑤𝑏𝑎𝑐𝑘     = 𝑒𝑞𝑢𝑖𝑡𝑦 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 − 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 = × = 𝑝𝑙𝑜𝑤𝑏𝑎𝑐𝑘×𝑅𝑂𝐸   𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑒𝑞𝑢𝑖𝑡𝑦 o As  ROE  and  plowback  decline,  growth  must  also  slow    Typically  in  a  more  mature  industry     Interpreting  Financial  Ratios   • Necessary  to  judge  whether  ratio s  are  high  or  low   • Some  cases  there  may  be  a  natural  benchmark   o If  negative  value  added  or  ROC  is  less  than  cost  of  capital,  it  is  not  creating  wealth  for  shareholders   • Often  levels  vary  from  industry  to  industry  (pg.  119,  table  4.7)   o Some  businesses  can  generate  high  level  of  sales  from  relatively  few  assets   o Makes  sense  to  limit  comparison  to  firm’s  major  competitors           Page  11  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan     Chapter  5   -­‐ Future  Values  and  Compound  Interest   • Future  value  is  the  amount  to  which  an  investment  will  grow  after  earning  interest   • Compounding  interest  is  when  you  earn  interest  on  interest   ▯ 𝐹𝑉  𝑜𝑓  $𝐼  𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 𝐼 ∗ (1 + 𝑟)   • The  future  value  interest  factor  is  (1+r)   • When  $  is  invested  at  compound  interest,  the  growth  rate  is  the  interest  rate   -­‐ Present  Values   • “A  dollar  today  is  worth  more  than  a  dollar  tomorrow”   • Value  today  of  some  future  cash  flow   ▯▯▯▯▯▯  ▯▯▯▯▯  ▯▯▯▯▯  ▯  ▯▯▯▯▯▯▯ • 𝑃𝑟𝑒𝑠𝑒𝑛𝑡  𝑣𝑎𝑙𝑢𝑒 = (▯▯▯) ▯   • Discount  rate  is  the  interest  rate  used  to  compute  PV  of  future  cash  flows  (PV  is  the  discounted  value  of  the  future   payment);  as  the  interest  rate   ↑,  PV  ↓   -­‐  Never  compare  cash  flows  @  different  times-­‐  first  discount  them  to  a  common  date   -­‐ Finding  Interest  rate   • Use  calculator   • Rule  of  72  –  time  it  will  take  for  investment  to  double  in  value:  72/r,  r  is  expressed  as  percentage   Works  better  with  relatively  low  interest  rates   -­‐ Finding  investment  period   •  You  have  10$,  and  you  want  to  know  how  long  (given  an  interest  rate  of  5%)  it  will  take  to  turn  into  15$   -­‐ Multiple  Cash  Flows   -­‐ FV  of  multiple  cash  flows   -­‐ To  find  value  at  some  future  date   –  calculate  what  each  will  be  worth  at  that  future  d ate  and  then   add  up  these  future  values   E.g.  $1200*(1.08) +$1000*(1.08) +$1400*1.08=  FV   -­‐ PV  of  multiple  cash  flows   E.g.  $8000+  $4000/1.08+$4000/1.08 2   • The  cost  of  a  payment  in  the  future  is  less  than  one  today  because  you  can’t  earn  interest  on  it  until  t hen   -­‐ Level  Cash  Flows:  Perpetuities  and  annuities   • Annuity  is  an  equally  spaced  and  level  stream  of  cash  flows   • Perpetuity  is  a  steam  of  level  cash  payments  that  never  ends   • How  to  value  perpetuities   𝑐 𝑐𝑎𝑠ℎ  𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑃𝑟𝑒𝑠𝑒𝑛𝑡  𝑣𝑎𝑙𝑢𝑒  𝑜𝑓  𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑖𝑡𝑦 = 𝑟 = 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡  𝑟𝑎𝑡𝑒   Two  warnings  about  the  formula:   1. Don’t  confuse  it  with  the  PV  of  a  single  cash  payment   2. The  formula  tells  us  the  value  of  a  regular  stream  of  payments  starting  one  period  from  now,  not  this  period   –  they’d  have  to  invest  more  in  order  to  be  able  to  receive  the  perpetuity  from  the  beginning       • To  calculate  the  value  of  a  perpetuity  that  doesn’t  make  payments  for  several  years,  multiply  tperpetuity  by   1/(1+r)    where  x=  the  number  of  periods  until  it  becomes  a  regular  perpetuity   Remember:  it  becomes  a  regular  perpetuity  1  period  before3  the  first  perpetuity  payment   –  so  if  the  first   payment  is  year  4,  the  PV  formula  is  multiplied  by  1/(1+r)   • How  to  value  annuities   • An  immediate  perpetuity  =   C*  1/r   • Delayed  annuity  =  C*  1/r  *1/(1+r) ,  or  C*1/r(1+r)   • PV  of  a  t-­‐year  annuity  =  C*  [ ▯ − ▯ ]   ▯ ▯(▯▯▯) ▯ • Between  [  &  ]  is  the  t-­‐year  annuity  factor     • PV  of  t-­‐year  annuity  =  payment  *  annuity  factor  =C*PVA  (r,t)   Page  12  of  24   FINE2000   Midterm  Notes        Jessica  Gahtan   • Some  annuities  (i.e.  mortgages)  can  be  called  an  amortizing  loan -­‐  part  of  the  monthly  payment  is  used  to  pay   interest  on  the  loan     • Amortization  of  the  loan  gets  faster  as  time  goes  on  b/c  the  payments  s tay  the  same  but  the  principal  keeps   decreasing,  so  less  $  from  each  payment  goes  to  interest  and  more  to  the  principal  as  time  goes  on   • Annuities  due   • Level  steam  of  cash  flows  starting  immediately   • PV  will  be  larger  than  that  of  an  ordinary  annuity     PV  annuity  due=PVAD r,t =  1+PV  ordinary  annuity  of  t-­‐1  payments   1 1 =1+ r  r 1+r­‐ t-­‐1     = 1+r x  PV  of  an  ordinary  annuity     • Future  value  of  an  annuity   • The  formula  for  the  future  value  of  an  annuity  is:   Future  value  of  annuity=present  value  of  annuity  of  $1  per  year   x   1+r  of  $1  per  year     t 1+r -­‐  1 FVA r,t = r   • For  an  annuity  due:   FV  of  an  annuity  due  =  (1+r)  x  FV  of  an  ord  y  annuity   • Cash  flows  growing  at  a  constant  rate —variations  on  perpetuities  and  annuities   • All  of  these  formulas  are  for  when  there  are  streams  of  equa l  cash  flow  –  not  always  the  case   • A  perpetual  stream  of  cash  flows  that  is  GROWING  at  a  constant  rate  is  called  a   growing  perpetuity   C 1 Present  value  of  a  perpetuity  growing  at  a  constant  rate,     r-­‐g Where  C 1  is  the  payment  to  occur  at  the  end  of  the  first  period,  r  is  the  discount  rate,  and  g  is  the  growth  rate  of  the  payments.    If  the   growth  rate  is  zero,  it  becomes  the  regular  f  la  C/r.   • Growing  annuities  area  finite  stream  of  cash  flows  growing  at  a  con stant  rate,  contrasting  with  the  perpetual  stream   above   C 1 1+g t Present  value  of  a  finite  stream  of  payments  growing  at  a  constant  rat  x  (1-­‐   r-­‐g 1+r Where  C 1  is  the  payment  to  occur  at  the  end  of  the  first  period,  r  is  the  discount  rate,  t  is  the  number  of  payments,  and  g  is  the  gro wth  rate   of  the  payments.    If  g  is  zero,  it  becomes  the  familiar  present  value  of  an  annuity  formula.   • Inflation  and  the  time  value  of  money   • Real  v.  nominal  cash  flows   • Inflation  =  rate  @  which  prices  as  a  whole  are  rising   • Real  value  of  $1  is  the  purchasing  power  adjusted  value  of  a  dollar     • E.g.  if  the  CPI  is  100  in  1950,  872  in  2006,  the  dollar  could  only  buy  100/872=11.47%  of  what  it  could  in  1950.   • The  real  value  of  $1  would  have  declined  by  100 -­‐11.47  =  88.53%  from  1950  to  2006   • Since  things  can  be  fixed  in  nominal  terms,  they  can  decline  in  real  value   –  i.e.  fixed-­‐payment  mortgage   payments  decline  in  real  value  over  time   • Inflation  and  interest  rates   • Nominal  interest  rate  is  the  rate  at  which  money  invested  grows  –  actual  #  of  dollars  you’ll  be  paid  with  no   offset  for  future  inflation     ▯▯▯▯▯▯▯▯▯  ▯▯▯▯▯▯▯▯  ▯▯▯▯ • Real  rate  of  interest  1 + 𝑟𝑒𝑎𝑙  𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡  𝑟𝑎𝑡𝑒 =  or  (For  an  approx.)  𝑟𝑒𝑎𝑙  𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡  𝑟𝑎𝑡   ≈ ▯▯▯▯▯▯▯▯▯▯▯  ▯▯▯▯ 𝑛𝑜𝑚𝑖𝑛𝑎𝑙  𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡  𝑟𝑎𝑡𝑒 − 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛  𝑟𝑎𝑡𝑒  (this  works  best  when  the  inflation  rate  and  the  real  rate  are  small.   If  they  aren’t  small  don’t  use  the  approx.)   • Valuing  real  cash  payments   • Discount  PV  of  $100  with  r=10%  by  doing  PV=100/1.1=$90.91   • You  would  get  the  exact  same  result  by  discounting  the   real  payment  by  the  real  interest  rate.   • Assume  inflation  will  be  7%  next  year,  so  the  real  value  of  $100  i s  100/1.07=$93.46