Investment appraisal and company valuation methods


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Investment appraisal and company valuation methods for beginners.
Concepts such as time value of money, simple interest, compound interest, CARG, cash-flows, WACC, inflation, discounting and capitalizing cash-flows are covered; in order to analyse and determine the economic feasibility of a project and what is the intrinsic or fair value of a company.

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Investment appraisal and company valuation methods

  2. 2. 4. Company valuation methods 3. Investment appraisal for economic feasibilityPRESENTS 2. Compound interest & CAGR 1. Time value of money definition
  3. 3. Why ($100, today) are not equivalent to ($100, when I was younger)?
  5. 5. *!$%?
  10. 10. OR…
  11. 11. Opportunity cost “Money can be invested today in different options with a different return ovetime”
  12. 12. OPTION 1 ($398 in t21=2011) OPTION 2 ($100 in t21=2011) ($100 in t0=1990) OPTION 3 ($0 in t21=2011)CAGR= Compound Annual Growing RateApple share price: 01/08/1990: $9.96 – 01/08/2011: $396.75 – CAGR: 19.17%Money at home below my pillow: 01/08/1990: $100 – 01/08/2011: $100 – CAGR: 0%Money placed at a default subprime product: 01/08/1990: $100 – 01/08/2011: $0 – CAGR: -100%
  13. 13. TIME VALUE OF MONEY MEANS OPPORTUNITY COST MEANING THAT IN FINANCE WE TALK ABOUT THE PAIR: ($,time) That is why different cash-flows at different moments in cannot be operated unless moved to the same point in time
  14. 14. How can be cash-flows moved in time?
  15. 15. Compound interest formula VF=V0 x (1+i)^t Two cash-flows are equal in time at a given interest rate VF: Future value of the cash-flow V0: Present or actual value of the cash-flow i: Compound annual interest or growing t: Time between both cash-flows
  16. 16. CAGR = ((V /V )^(1/t))-1 F O R” “CAG n as know Also CAGR=Compound Annual Growing t in years so CAGR on a yearly basis
  17. 17. …and moving cash-flows to the future is called: N T IO SA LI TA PI C A VF=V0 x (1+i)^
  18. 18. …and moving cash-flows from the future is called: Ic% VO Vf DISCOUNTING Vo=VF / (1+i)^
  19. 19. And what about simple interest?
  20. 20. Simple interest - Is VF=V0 x (1+i*t) “Interests earnt are not re-invested” Compound interest - Ic TIME VALUE OF MONEY VF=V0 x (1+i)^t “Interests earnt are re-invested”
  21. 21. Yield =12% [annual] I12=1% I6=2% I4=3% I2=6% MONTHLY BI-MONTHLY QUARTERLY SEMI-ANNUALLY NO REINVESTMENT REINVESTMENT Is IcBy convention yields are provided in a yearly basis IF NOT SPECIFIED
  22. 22. EXAMPLE 1 Banking deposit 3-years time 10% annual interest rate (*) Initial investment: €1.000(*) The 10% interest rate is an annual yield. It depends if there are reinvestment of interests, using compound interest.In the case there are not re-investment of interests we use simple interest formula
  23. 23. +€1000+€100+€100+€100 Is (+€100) (+€100) (+€100) 1 2 3 VF = 1000*(1+10%*3) = €1300 -€1000 +€1000+€100+€110+€121 Ic (+€100) (+€110) (+€121) 1 2 3 VF = 1000*(1+10%)^3 = €1331 -€1000 www.antonioalcocer.comCalculations made for a 3-years bank deposit with a 10% annual interest rate and €1000 initial investmentAs you can see due to “time value of money”, and if interests are reinvested or not reinvested; €1000 at t0 are equal to €1331 at a10% compound interest rate or €1300 at a 10% simple interestSimple interest is used if the interests earnt are not reinvested. Compound interest is used if interests are reinvestedAs general rule, investments lasting less than 1 year use simple interest and investments lasting>=1 year use compound interest but which one to use if determined by the existance or not of the re-investment of the interests
  24. 24. EXAMPLE 2 Banking deposit 2-years time 10% annual interest rate Bi-monthly re-investment of interests 4 semesters Initial investment: €1.000
  25. 25. Ic 12% ANNUAL YIELD = 12% / 2 = 6% BI-MONTHLY YIELDCAGR = ((V /V )^(1/t))-1=((1263/1000)^(1/2))-1 F O +€1000+€60+€63.6+€67.4+€71.412.38% (+€60) (+€63.6) (+€67.4) (+€71.4) 1s 2s 3s 4s VF = 1000*(1+6%)^4 = €1263 -€1000Annual yield is used to obtain the bi-monthly yield, and then apply compound interest formula for calculations in order to obtain €1263But this investment has not a compound annual growing rate (CAGR)=12% due to the bi-monthly reinvestment.
  26. 26. but as a general rule in finance we assume…
  27. 27. …reinvestment of interests & use compound interest!
  28. 28.
  29. 29. Compound interest’s power it’s one of the strongest powers on Earth Albert Einstein
  30. 30. Example 1: Investment in the S&P500 – CAGR: 7.16% Vf $337.494 Vo $30.000 t0=30 t35=65S&P500 CAGR = 7.16% in the period 01/02/1950-01/02/2010VF=30.000*(1+7.16%)^35=Vf*(1+i)^t
  31. 31. You better wouldhave invested inBerkshire Hathway- Oracle of Omaha’s word
  32. 32. Example 2: Investment in Berkshire Hat. – CAGR: 20.3% Vf $19.338.296 Vo $30.000 t0=30 t35=65Warren Buffet’s Berkshire Hathway Investment Fund CAGR = 20.3% in the period 1965-2009 year endingVF=30.000*(1+20.3%)^35=Vf*(1+i)^t
  33. 33. I rather go for - Get back soon Steve! -
  34. 34. Example 3: Investment in Apple shares – CAGR: 23.06% Vf $42.812.697 Vo $30.000 t0=30 t35=65Apple shares’ CAGR = 23.06% in the period 27 August 1985 – 27 August 2011VF=30.000*(1+23.06%)^35=Vf*(1+i)^t
  35. 35. $42.812.697? *!$%? REDBUBBLE.COM
  36. 36. Yes, $42.8 million But in 35-years time & we know about time value of money & the pair ($,t) & moving cash-flows in time & discounting Using Vo=Vf / (1+i)^t
  37. 37. So you are telling me that today I would not be worthy $42.8 million?
  38. 38. Yes, because of INFLATION! CPI CAGR=2.7%CAGR Consumer Price Index (inflation) in the period 1920-2005 = 2.7%
  39. 39. $42.8 millions in t=35 years would be $16.85 millions today at a 2,7% Vo=Vf/(1+i)^35=42.8/(1+2.7%)^35=$16.85 millions
  40. 40. So you better assumeyour purchasingpower todaywould be$16.85 millionrather than$42.8 million
  41. 41. Yes, if you would have invested in Apples HAVE YOU?
  42. 42. Now We are ready to understand Investment appraisal methods Used in Finance to study The economic feasibility Of a
  44. 44. GOLDEN RULE “We always work with cash-flows in investment appraisal”
  45. 45. “Cash-flow is a fact, net income just an opinion” -Pablo Fernández IESE-The net income amount is affected by accounting methods & assumptions made(i.e. depreciation & amortization that are not “real” cash inflows or outflows) www.antonioalcocer.comCash-flows are real money “entering” or “exiting” the company or project
  46. 46. P&L (*) Net sales -Cost of goods sold GROSS PROFIT HOW GOOD IS YOUR BUSINESS -Selling, General & Administration GENERATING “$” DUE THE OWN -Other operating expenses NATURE OF THE BUSINESS EBITDA -Depreciation & Amortization -Impairment EBIT -Interests FINANCING STRUCTURE INCOME BEFORE TAXES -Taxes CORPORATE TAXES FRAMEWORK NET INCOME(*) P&L=Profit & Loss account simplifiedP&L and Net Income are affected due to the accounting methods usedNet income is an opinion due to it depends on the calculationof the cost of goods sold, amortization method used & impairmentNet income is not real cash-flow outlays of money www.antonioalcocer.comDepreciation, amortization & impairment are not real cash-flow outlays
  47. 47. “So now I understand in investment appraisal we use CASH-FLOWS”
  48. 48. But how many cash-flows exist?
  49. 49. Free CASH-FLOW of the project (FCFF)= Available “$” for the funds providers: _BANKS
  50. 50. Free CASH-FLOW of the project (FCFF)= +EBIT (1-t) X +D&A +/-WORKING CAPITAL CHANGE -CAPEXFCFF= Real money generated by the project after accounting adjustments (no real cashflows outlays)D&A=Depreciation & Amortization (added because no real cash-outlay happened)CAPEX=Capital Expenditures (Investment in fixed assets)Working Capital Change= Investment in current assetst=Corporate taxes in %(*) Simplified formula of the cashflow, there are other terms: non-cash transactions adjustments, other current assets changes, proceeds from long term assets sales, changes in long term assets; to be considered
  51. 51. Equity Free CASH-FLOW (FCFE)= Available “$” for the equity providers:
  52. 52. Equity Free CASH-FLOW (FCFE)= +FCFF +PROCEEDS NEW BANKING DEBT - AMORTIZATION CURRENT DEBT - INTERESTS OF DEBT * (1-t) - DIVIDENDS PAID & T.S. REPUR.FCFE=Equity free cash-flow.Cash-flow available for shareholders after paying the banking funs providers.FCFE would be the money available for shareholdersT.S. REPUR= Treasury stock repurchase
  53. 53. …and many
  55. 55. Investment appraisal of a project with these free-cashflows + +$300m +$175m +$200m t0=0 t1=1 t2=2 t3=3 -$150m -$300m -Diagram of the project free-cashflows (FCFF)Data in millions of US$ www.antonioalcocer.comYearly data
  56. 56. Houston, we have a problem:Funding needed:$300 mill. in 1st year$150 mill. in 2nd year
  57. 57. Don’t worry Funds providers: _banks _shareholders will gently dispose
  58. 58. “OK, have your funds, but [BANK] at a 6.6% annual interest rate rat & maximum amount 65% Kd=
  59. 59. Ke= 20% [SHAREHOLDERS] “OK, have your funds, but at a 20% annual interest rate & 35% maximum amount”
  60. 60. So, which amount/ratio should I ask for Don E. Botín [banks] & Don C. Slim [shareholders]?
  61. 61. It seems clear that The cost of financing this project Would be the Weighted average Cost of capital
  62. 62. OPTIMAL FINANCING STRUCTURE [BANK] 50% 60% 65% [SHAREHOLDERS] 50% 40% 35% WACC Cheapest 12.31% 10.77% 10%WACC= % equity * expected return on equity + % banking_debt*(1-corporate tax)*cost of banking debtWACC= 35%*20%+65%*(1-30%)*6.6%=10%
  63. 63. So the $300 mill. + $150 mill. will be financed by a 65% banking debt by a 35% shareholders’ equity with a
  64. 64. Profitability of the project = 50% in 3-years? +$300m +$175m +$200m t0=0 t1=1 t2=2 t3=3 -$150m -$300m +300 + 175 + 200 - 300 - 150 %return= = 50% 450Diagram of the project free-cashflows (FCFF)Data in millions of US$Yearly data
  65. 65. Noooooo!!!!!!!!! TIME VALUE OF
  67. 67. 1. NET PRESENT VALUE = NPV www.antonioalcocer.com1) All FCFF are discounted to today & summed2) Using compound interest formula3) At a WACC rate
  68. 68. 1. NET PRESENT VALUE=$0 [Undertake project]Cash-flows generated exactly pay the cash-flows expectations requested bythe banking & shareholders (funds providers)
  69. 69. 1. NET PRESENT VALUE>$0[Undertake project]Cash-flows generated pay all the cash-flows requested by fund providers inorder to meet their profit expectations (NPV=0) & additional cash-flow=NPVgoes as excess profit for shareholders
  70. 70. www.antonioalcocer.com1. NET PRESENT VALUE<$0 [Do not undertake project]Cash-flows generated are not enoughto pay the cash-flows demmands byfunds providers according to theirprofit expectations (=WACC)
  71. 71. 1. Net present value = NPV – WACC=10% +$300m +$175m +$200m t0=0 t1=1 t2=2 t3=3 -$150m -$300m Undertake project NPV>0 +300 -150 +175 +200 NPV = $131.2 = -300 + + + (1+10%)^1 (1+10%)^2 (1+10%)^3Diagram of the project free-cashflows (FCFF)Data in millions of US$Yearly data+$131.2 million of excess cash-flow that shareholders get above their profit (20%) & cash-flow expectations
  72. 72. 2. INTERNAL RATE OF RETURN (IRR) = Project’s CAGR = _solve NPV=0 _get
  73. 73. 2. Internal Rate of Return (IRR) = 32.24% > WACC =10% Undertake project +$300m +$175m +$200m t0=0 t1=1 t2=2 t3=3 -$150m -$300m Solve non-linear equation +300 -150 +175 +200 NPV = $0 = -300 + + + (1+IRR)^1 (1+IRR)^2 (1+IRR)^3Diagram of the project free-cashflows (FCFF)Data in millions of US$Yearly data www.antonioalcocer.comIRR is obtained solving the equation
  74. 74. 1&2. Net present value summary IRR>WACC NPV>0 Fund providers more than happy NPV excess for shareholders IRR=WACC NPV=0 Fund providers exactly happy Fund providers unhappy IRR<WACC NPV<
  75. 75. 3. PAYBACK PERIOD Years to recover investment… …you better payExpected number of years in ordercumulative (+) cash-flows>= www.antonioalcocer.comcumulative (-) cash-flows
  76. 76. 3. Payback period= 1.85 years +$300m +$175m +$200m t0=0 t1=1 t2=2 t3=3 -$150m -$300m Cumulative -300 -300+300-150 -300+300-150+175 -300+300-150+175+200 -300 -150 +25 +225Payback period does not take into account time value of money, so it should not be used in a stand alone basis but as complementary info to NPV and IRRDiagram of the project free-cashflows (FCFF)Data in millions of US$Yearly dataPayback period: Positive cumulative cashflows are > negative cumulative cashflows in year 1-2175/12=14.58-150/14.58=10.29 months = 10.29/12= 0.85 years
  77. 77. www.antonioalcocer.comRE Time value of money Compound interest Moving cash-flows in timeWe have learnt: Investment appraisal methods Project free cashflows WACC NPV+IRR+Payback
  78. 78. [now we can strike back the Empire!] [and go for company valuations…]
  80. 80. THIS ONE MUST BE
  81. 81. THIS ONE…
  82. 82. ∞ = Infinite ^∞ ∞
  83. 83. = Enteprise value [EV] HEY!!!! WHAT IS THE VALUE OF A COMPANY?
  84. 84. “But in company’s valuation we need to calculate the “intrinsic” or “fair value” of the company’s equity “updated” based on its future cashflows”
  85. 85. But before we start remember the 2nd GOLDEN RULE: PRICE IS WHAT YOU PAY [demmand falls in love with supply]
  87. 87. [VALUATION METHODS USED] 1. fast 2. right MULTIPLES DISCOUNTING CASH-FLOWS PER Free-cashflows (FCFF) Sales Equity cashflows (FCFE) EBITDA Dividends Others Other cash-flows gross fine tune past future(*) I will not cover other valuation methods based: book value, adjusted book value, etc.PER = Price Earning Ratio = Share Price in stock market / earnings per share
  88. 88. MULTIPLES VALUATION DISCOUNTING CASH-FLOWS1. It is wrong2. Does not consider time value of money3. Based in “static” data: P&L4. Based in past performance5. Does not consider future cash-flows6. Assumes future = present7. But it is fast8. And it is widely used by investors9. Get a “rough” company value estimate 1. It is the right one method 2. Does consider time value of money 3. It is based in “dinamic” data: 4. Does consider future cash-flows 5. But it is a lot of work 6. Used to fine-tune the multiples valuation 5 minutes time 2 weeks time
  89. 89. I was captured by the dark side, and although I know it is WRONG… …explain me the MULTIPLES VALUATION method
  90. 90. [MULTIPLES VALUATION] www.antonioalcocer.comEV=ENTERPRISE VALUE [$5-9 millions] Industry comparable multiple x Company’s metric 1. Choose a metric: EBITDA 2. Company’s EBITDA = $1 million 3. Company in the food & beverage industry (F&B)4. Comparable purchasing transactions in F&B industry: 5-9 times
  92. 92. HOW much would you pay for a cow? Depends on the future milk that it can provide [& not the milk that provided in the past]
  93. 93. What is the value of a company? www.antonioalcocer.comDepends on the future cash-flows it can generate[you decide using either FCFF or FCFE_it’s up to you]
  94. 94. & the annual growing rate “g”(%) of these future cash-flows[Should not be greater than a economy’s GDP in the long run <3%][In the short term cash-flows growth can exceed long term trend]
  95. 95. Assuming the company will last forever [=infinite]
  96. 96. & the company’s financing structure: WACC %E equity [41%] Ke(%) profit expectations: 9.7% %L banking debt [59%] Kd(%) cost of debt
  97. 97. How do I calculate Ke=shareholders’ profit expectations? 4.54% 6.18% Ke=RF+B*(RM-RF) 9.7% 0.83RF: Money invested at no risk (RF=10-years german bonds yield considered a risk free investment)B*(RM-RF): Upside return/premium for investing in a company with specific risk www.antonioalcocer.comRM=Return of the stock market benchmarked = CAGR Ibex 35 in the 1995-2008 period = 10.72%B=Company beta = sistematic risk of the company versus the market = Let’s assume 0,83. Beta calculation is biased and depends on the time period analysed
  98. 98. WACC & g calculations 59% 28.2% 6.3% 41% 9.7% WACC= %L*(1-t)*Kd + %E*Ke WACC= 6,62% g=2,5% (*)(*) GDP for the European Union in the 1996-2008 period according to Central European Bank (2,2%). We will asume a g=2.5%T=Effective corporate tax rate paid by the company. It is less than 30% due to fiscal benefits awarded from previous years%L=proportion of banking debt %E=Proportion of equity
  99. 99. [DISCOUNTED CASH-FLOW METHOD SUMMARY] FCFF 1. [Determine which cash-flows you want to use] FCFE 2. [Determine company’s 5-years future cash-flows (*)] 3. [From year “n+5”, future cash-flows grows at “g” rate (**)] <3% @WACC if FCFF 4. [Calculate the NPV today of the infinite cash-flows] @Ke if FCFE [Enteprise value= NPV of all infinite future cashflows @ WACC](*) The number of years range from 5 to 10, in terms of estimating the future P&L, balance sheet and company cash-flows. www.antonioalcocer.comMore adecuate calculation should range 10 years.(**) Future cash-flows from year n+5 growth as an infinite geometric progression with a “g” growing rate. This geometric progression with infinite terms is called RESIDUAL VALUE
  100. 100. EXAMPLE: Company free cash-flows [FCFF] 5-YEARS CASH-FLOWS ESTIMATION CASH-FLOWS GEOMETRIC PROGRESSION X (1+g)^(n-3) X (1+g) X (1+g) X (1+g) 195 190 185 181 g=2,5% 149 123 102 87 2011 2012E 2013E 2014E 2015E 2016E 2017E 2018E 2019E ………. INFINITE TODAY RESIDUAL VALUEData in millions of $ www.antonioalcocer.comPlease note that we assume the company will last forever, so from year 2017 onwards we have infinite cash-flowsThe 5-years cashflows estimation must be done according to the mid-range business plan & investment/capex plan; and using the P&L & balance sheet & cashflow statementsAfter the 5th year, in 2017, we calculate cash-flows as a geometric progression increasing in a “g%”=2,5% every year the latest cash-flow. CFn=CFn-1*(1+g)It can be demonstrated that the geometric progression with infinite cash-flows starting at 2017, equal a single cash-flow located in 2016 year and value=Cf2017/(WACC-g)The infinite cash-flows from 2017 onwards are called RESIDUAL VALUE
  101. 101. EXAMPLE: Free cash-flows [FCFF] are discounted @ WACC RESIDUAL VALUE X (1+g)^(n-3) X (1+g) X (1+g) X (1+g) 195 190 185 181 G=2,5% 149 123 102 87 2011 2012E 2013E 2014E 2015E 2016E 2017E 2018E 2019E ………. INFINITE TODAY 5-YEARS CASH-FLOWS ESTIMATION CASH-FLOWS GEOMETRIC PROGRESSION 181*(1+2.5%) 87 102 123 149 181 6.6%-2.5% NPV=EV=$3780= + + + + + (1+6.6%)^1 (1+6.6%)^2 (1+6.6%)^3 (1+6.6%)^4 (1+6.6%)^5 (1+6.6%)^5 RESIDUAL
  102. 102. Have I done this? COMPANY’S EV $3780
  103. 103. COMPANY’S ENTERPRISE VALUE= What is the meaning?
  104. 104. “DYNAMIC” BALANCE SHEET “UPDATED” DUE TO IMPACT OF “STATIC” FUTURE CASH-FLOWS BALANCE SHEET TODAY - 2011 EO E 41% EV $3780 mill. ?? L 59%E: Equity www.antonioalcocer.comL: Liability (net financial debt) = short term debt + long term debt – cash($)EO = Company’s Estimated “fair value” of equity
  105. 105. [EO= fair value of company’s equities = 3780-400+150-50-200=$3280 mill.] BALANCE SHEET “UPDATED” EO EV $3780 - Net Financial Debt -$400 mill. mill. ?? +Shareholders’ right in other companies +$150 mill. - Minority interests -$50 mill. - Long-term pension liability -$200 mill.EO=Intrinsic value or fair value of the company’s equity www.antonioalcocer.comShareholders’ rights in other companies are real cash inflows into the company due to ownership of other companies as minority stakeNet financial debt is the net financial liability position with banks. It is a cash-outflow assuming all the debt is paid.Minority interests: It is a portion of the value of a company that it is own by “external” minority shareholders and it does not belongs to the company. Cash out-flowLong term pension liability & other liabilities correspond to future cash-outflows to be paid by the company.
  106. 106. BUY? Fair value>market value SELL? Fair value<market
  107. 107. PRICE IS WHAT YOU PAY MARKET CAP = $6000 mill. # shares = 10 mill. [demmand falls in love with supply] Market share price paid = $600
  108. 108. EO=$3280 mill.# shares = 10 mill.Equity fair/intrinsic value = $ VALUE IS WHAT YOU GET
  109. 109. [CONCLUSION 1] I shouldn’t have bought new shares!!! or I better sell the ones I already own@$150 $328 $600Fair value<market value
  110. 110. [CONCLUSION 2]The fair value EO does not change unless new inputs/info impact the company’s future cashflows overall picture & therefore EV
  111. 111. [CONCLUSION 3] [95% of time_estimating 5-10 years cash-flows] [5% estimating WACC & “g” rate (=residual value)] …but [Discounting cash-flows model is highly sensible to:] WACC & “g”
  112. 112. SENSIBILITY ANALYSIS Fair value per share in $ [WACC] 5% 6,62% 8% 2% 486,7 291,9 209,2 [g] 2,5% 586 328,7 229,4 3% 735 375,7 253,
  113. 113. [CONCLUSION 4] In company valuation, the most important issues to understand are: 1. Assumptions_How future cash-flows are calculated 2. Understand the risks associated to them in order they do not occur 3. Assume than in valuation we always obtain a price range 4. Company valuations can be highly manipulated by small changes in WACC & g 5. Use multiples valuation for a “rough” number & 5 minutes valuation 6. Use discounted cashflow for a “fine tuned” number & right calculation
  114. 114. Thank you very much for you time!Any comment, suggestion is more than welcome: