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This version 11/9/2001. Includes WORD tables Lecture: Valuing Companies and Investment Projects Copyright K. Cuthbertson and D. Nitzsche 1 TOPICS Basic Ideas Compounding/Terminal Value Discounted Present Value DPV \ Discounted Cash Flow DCF Investment ( Project) Appraisal, Internal Rate Of Return, Valuation Of The Firm: Enterprise Vale and Equity ~ choice of discount rate ~ valuation in practice: EBITD, Depreciation, FCF etc. Complementary Valuation Techniques: EP, EVA,APV Self Study: Other Investment Appraisal Methods Copyright K. Cuthbertson and D. Nitzsche 2 READING Investments:Spot and Derivative Markets, K.Cuthbertson and D.Nitzsche Chapter 3 Discounted Present Value DPV \ Discounted Cash Flow DCF Internal Rate Of Return, IRR Investment ( Project) Appraisal Valuation Of The Firm And The Firm’s Equity (Incl. Continuing Value). Valuation In Practice: EBITD, Depreciaiton, FCF etc Other Investment Appraisal Methods Chapter 11 Economic Profit, Economic Value Added, Adjusted Present Value P. 342-346. Copyright K. Cuthbertson and D. Nitzsche 3 BASIC IDEAS Compounding/Terminal Value Discounted Present Value DPV Discounted Cash Flow DCF Internal Rate of Return Investment/ Project Appraisal Copyright K. Cuthbertson and D. Nitzsche 4 Compounding/ Terminal Value Assume zero inflation+cash flows known with certainty Vo = value today ($1000), r = interest rate (0.10) Value in 1,2 years time V1 = (1.1) 1000 = $1100 V2 = (1.1) 1100 = (1.1) 2 1000 = $1210 Terminal Value after n-years: Vn = Ao (1 + r)n We could ‘move all payments forward’ to time n=10 years and then add them - but we do not do this Copyright K. Cuthbertson and D. Nitzsche 5 Discounting ‘Bring all payments back’ to t=0 and then add. Value today of V2 = $1210 payable in 2 yrs ? DPV = V2 1210 = (1 + r ) 2 (11 . )2 Hence “ DPV of $1210 is $1000” Which means that $1000 today is equivalent to $ 1210 payable in 2-years “Discount Factor” d2 = 1 (1+ r )2 Copyright K. Cuthbertson and D. Nitzsche 6 Discounted Present Value (DPV) What is value today of stream of payments - usually called ‘Cash Flows’, assuming a constant discount factor? : DPV = V1 V2 + +... 2 (1 + r ) (1 + r ) = d1 V1 + d2 V2 + .. r = ‘discount rate’ d = “discount factor” < 1 Discounting, puts all future cash flows on to a ‘common time’ at t=0 - so they can then be “added up”. Copyright K. Cuthbertson and D. Nitzsche 7 Investment (Project) Appraisal:Decision Criteria Operating Cash Flows, (ie. revenues less operating costs, less taxes) V1 = $1100, and V2 = $1210 Then DPV(of ‘cash flows’ at r =10%) = $2000 Suppose Capital Cost (Investment Expenditure), KC = $2000 Net Present Value (NPV): NPV = DPV - KC RULE: If DPV > KC then invest in project OR If NPV > 0 then invest in project Our project is just ‘on the margin’ since NPV = 0 when r=10% Copyright K. Cuthbertson and D. Nitzsche 8 NPV (for given CFs) and the cost of borrowing, r NPV If r 10% you would NOT invest in the project NPV=0 r=5 r=10 Copyright K. Cuthbertson and D. Nitzsche r= loan rate or discount rate 9 Internal Rate Of Return (IRR) Businessmen think in terms the rate of return on the project What is the rate of return (on capital investment of $2000) ? 1100 + 1210 − 2000 = 0 (1 + IRR) (1 + IRR) 2 It is the rate of return which gives NPV = 0 Hence the IRR is the ‘break-even’ discount rate and IRR = 0.10 (10%) IRR INVESTMENT DECISION RULE Copyright K. Cuthbertson and D. Nitzsche 10 Intuitively what do NPV and IRR rules mean ? If NPV = 0 OR, IRR = cost of borrowing then this implies -the CF from the project will just pay of all the annual interest payments on the loan + the principal amount borrowed from the bank Note: Internal funds are not ‘free’ Copyright K. Cuthbertson and D. Nitzsche 11 Intuitively what do NPV and IRR rules mean ? Payoff all interest and principal if NPV=0 or IRR = 10% ? KC=2000 (borrowed at r=10%), CF are 1 Year 2 V1=1100 , Year V2=1210 Loan 2200 = Outstanding 2000(1.1) Net Receipts 1100 Amount Owed 1100 1210 = 1100 ( 1.1 ) Copyright K. Cuthbertson and D. Nitzsche 1210 0 12 Valuation of the Firm: Enterprise Value and Equity Value Copyright K. Cuthbertson and D. Nitzsche 13 Two Useful Math Results General Case V0 = FCF1 / (1+r) + FCF2 / ((1+r)2 + …… FCF= Free Cash Flows 1) Sum to infinity and FCF is constant: V0 = FCF / r 2) Sum to infinity and FCF grows at rate of g % p.a. (g=0.05 ) V0 = FCF1 / ( r - g) Copyright K. Cuthbertson and D. Nitzsche 14 ‘Enterprise Value’ and ‘Equity Value’ Enterprise DCF In practice investment costs occur every year so: V(whole firm) = DPV ( Free Cash Flows, FCF) FCF = (Operating ‘cash flows’ - Gross investment) each year Value of Equity V(Equity) = V(whole firm) - V(Debt outstanding) ‘Fair value for one share’ = V(Equity) / N N = no. of shares outstanding (+ ‘minority interests’) Copyright K. Cuthbertson and D. Nitzsche 15 ‘Enterprise Value’ and Equity Value In an efficient market the price of the share(s) should equal ‘fair value’ We will learn how to value corporate debt, in later lectures Copyright K. Cuthbertson and D. Nitzsche 16 ‘Valuing the ‘Firm’ :Continuing Value The DPV of ALL the firm’s future cash flows is often ‘split’ into two (or more) planning horizons: ‘ENTERPRISE DCF’ = DPV of FCF in years 1-5 + DPV of ‘Continuing Value’ after year-5 Copyright K. Cuthbertson and D. Nitzsche 17 ‘Valuing the ‘Firm’ :Continuing Value Special Case A: i) the discount rate is constant in each year ii) Cash flows, FCF are constant in each year and persist ‘for ever’ (ie. perpetuity) then CV = FCF/ r This is often used to calculate ‘continuing value’, CV. Copyright K. Cuthbertson and D. Nitzsche 18 ‘Valuing the ‘Firm’ :Continuing Value eg. Project has V5 =100 in year-5,6,7 etc., and r=0.10 then Continuing value CV (at t=5) = 100 / 0.10 = 1,000 and DPV (at t=0) of the CV = 1000/ (1+r)5 Copyright K. Cuthbertson and D. Nitzsche = 621 19 ‘Valuing the ‘Firm’ :Continuing Value Special Case B: If i) the discount rate is constant in each year and ii)FCF’s grow at a constant rate each year, say after year-5 then CV (at t=5) = FCF5 (1+g) / ( r - g) Copyright K. Cuthbertson and D. Nitzsche for r>g 20 ‘Valuing the ‘Firm’ :Continuing Value Project has FCF=100 in year-5 FCF grows at rate g=0.03 (3%) and r = 0.10 Then: Continuing value CV (at t=5) = DPV( at t=0) of the CV 100 (1.03) / (0.10 - 0.03)= 1471 = 1471/ (1+r)5 = 913 Notes: CV is very sensitive to the choices made for FCF5, R and g. CV can be a large & dominates DPV of the cash flows over years 1-5. Copyright K. Cuthbertson and D. Nitzsche 21 Company Valuation: M&A Suppose Value of firm using DPV of FCF’s is Enterprise DCF = DPV (FCF 1-5yrs) + DPV (of CV) = 679 + 621 = 1,300 Suppose: All equity financed firm N = 1000 shares and P= $1 Market Value (Capitalisation) = $1000 Hence the shares are undervalued by 30% Possible purchase or takeover target (by ‘arbs’) Copyright K. Cuthbertson and D. Nitzsche 22 Shareholder Value (All equity financed firm) If NPV of the project > 0 (discounted using R S) Implies the managers are ‘adding value’ for shareholders (which exceeds the return they could earn from investing their money in other hamburger firms). This is value based management or ‘creating shareholder value’. Copyright K. Cuthbertson and D. Nitzsche 23 Choice of Discount Rate Copyright K. Cuthbertson and D. Nitzsche 24 Discount Rate: All equity financed firm Note: ‘All equity’ financed = ‘unlevered firm’ - ie. no debt Discount rate should reflect ‘business risk’ of the project. Assume project is ‘scale enhancing’ (eg. more hamburger outlets for McDonalds) Hence, has same ‘business risk’ as the firm as a whole. Simple method Use the average (historic) return on equity, RS (e.g. 15%) for this (hamburger) firm as the discount rate This assumes the observed return on equity correctly reflects the payment for risk, that shareholders require from this hamburger company. Copyright K. Cuthbertson and D. Nitzsche 25 Discount Rate: All equity financed firm If the project being considered by MacDonalds is to build hotels, then we would use the average stock market return in “hotel sector” (20%pa. say) - as this reflects the “required return on equity capital” for the shareholders in that sector. - see CAPM / SML / APT later, where we provide more sophisticated methods for choosing the appropriate equity discount rate. Copyright K. Cuthbertson and D. Nitzsche 26 Discount Rate: levered firm Levered firm = financed by mix of debt and equity Assume debt-equity ratio will remain broadly unchanged after the new project is completed. Then discount FCF using: (‘After tax’)Weighted Average Cost of Capital WACC, WACC = (1-z) RS + z RB (1-t) z = B / V = propn of debt(bonds) , (1-z) = S / V V=market value of firm = S+B ‘weights’, z, sum to 1. Copyright K. Cuthbertson and D. Nitzsche 27 Discount Rate: levered firm S = market value of outstanding equity ( = N x stock price) B = market value of outstanding debt (ie. bonds issued and bank loans) RS = average return on equity in hamburger industry RB = interest rate (yield to maturity) on say 10-year corp. AArated bonds(If hamburger company is rated AA by S&Poor’s) t = corporate tax rate Note: Market value (‘cap’) of the firm V = S +B Copyright K. Cuthbertson and D. Nitzsche 28 Can Managers Increase the Value of the Firm? Assume firm is part-equity financed and part-debt financed Then the ‘intrinsic value’ of the firm is the DPV of its future cash flows from all of its current and future investment projects, discounted using WACC Managers can only increase the value of the firm by 1) investing in projects with ‘high’ FCFs 2) reducing the WACC ‘(2)’ is the so-called capital structure question - can managers change the mix of debt and equity financing to lower the overall WACC? - assuming FCF is unchanged - see Modigliani-Miller later Copyright K. Cuthbertson and D. Nitzsche 29 What about (business) risk in DCF ? 1) Key practical method is to use “sensitivity” or “scenario” analysis. Sensitivity - ‘one at a time’ 1) What is NPV if revenues are much higher/lower ? 2) What is the NPV if the discount rate is 1% higher? Scenario: 3) What is the NPV if both (1) and (2) apply. - scenario analysis (Monte Carlo simulation is a sophisticated way of doing this) Can “include” probabilities in (1) and hence calculate EXPECTED NPV and its standard deviation. Copyright K. Cuthbertson and D. Nitzsche 30 What about (business) risk in DCF ? 2) Can use decision trees - particularly useful where there are strategic options in the investment decision -eg. Suppose you can abandon the project and sell the ‘plant’ for $10m if demand turns out to be ‘low’ in year-2. On the other hand if demand is ‘high’ then you will continue production in year-2. This affects the NPV of the project compared with the ‘normal case’ where you assume you do not abandon In fact the ‘correct’ way to evaluate these strategic options is (not surprisingly) to use ‘real options theory’, but this cannot be done here ! Copyright K. Cuthbertson and D. Nitzsche 31 VALUATION IN PRACTICE: EBITD, DEPRECIAITON, FCF Copyright K. Cuthbertson and D. Nitzsche 32 Valuing a Company: ‘Cash is King’ Calculating ‘Free Cash Flow’ in Practice ACCOUNTING NIGHTMARES Earnings before interest, tax and depreciation,EBITD EBITD = R - C = Sales Revenues - Operating Costs (Labour+Materials) Free Cash Flow FCF = (R - C - T) - Inv(gross) - Increase in WC + (Net Non-Op. Inc) Copyright K. Cuthbertson and D. Nitzsche 33 Valuing a Company: ‘Cash is King’ Now the Accountants ‘Mess it About’ Published ‘Earnings’ or ‘profit’ are usually presented after a deduction for depreciation: These would be ‘earnings before interest and tax’ EBIT So, EBIT = EBITD - D = (R-C) - D Hence, to get FCF ‘add back’ depreciation and deduct taxes: FCF =(EBIT - T) + D - Inv(gross) - Increase in WC +(N.N.Op.Inc) Also, you often ‘see’ (in the UK): Net Op. Profit (Less Taxes) NOPLAT = EBIT - T = R-C-D-T Copyright K. Cuthbertson and D. Nitzsche 34 Valuing a Company CASH IS KING Table 3.7 : CAPITAL ACCOUNT 1. 2. 3. 4. 5. 6. Capital Cost, KC (1.) Depreciation (= KC – SV)/n Accumulated Depreciation (=”sum of depreciation”) Year End Book Value (= 4 – 3) Working Capital, WC Total Book Value (= 4 + 5) Year0 1,000 Year1 Year2 Year3 Year4 Year5 200 200 200 200 200 200 400 600 800 1,000 1,000 800 600 400 200 0 0 1,000 400 1,200 500 1,100 600 1,000 500 700 200 200 7. Change in Working 400 100 100 (100) (300) Capital,. ∆WC (= WCt – WCt-1) Notes: 1. Total capital cost is KC = $1,000. Scrap value SV = 0 at n=5 years. Hence D = (KC – SV)/5 = 200 per year (straight line depreciation). 2. ( . ) indicates a negative number Copyright K. Cuthbertson and D. Nitzsche 35 Valuing a Company Table 3.8 : DEPRECIATION AND TAX 1. 2. 3. 4. 5. 6. ote : Sales revenue, R Labour + Materials Cost, C (1.) EBITD (= 1 – 2) Depreciation, D Earnings after Depreciation, = R – C – D (= 3 – 4) (2.) Tax = 0.30(R – C – D) Year1 1,000 600 Year2 1,500 900 Year3 2,000 1,200 Year4 2,500 1,500 Year5 3,000 1,800 400 600 800 1,000 1,200 200 200 200 400 200 600 200 800 200 1,000 60 120 180 240 300 1. EBITD = earnings before interest, tax and depreciation. Accounting profits (before tax) reported in the ‘income-expenditure’ (or ‘profit-loss’) account would be (EBITD – D). 2. Corporate tax rate is assumed to be t = 0.30 (30%). Copyright K. Cuthbertson and D. Nitzsche 36 Table 3.9 : CALCULATING FREE CASH FLOW 1. 2. 3. 4. 5. 6. 7. 8. (1.) Sales revenue , R (1.) Labour + Material Cost Earnings before Interest, Tax and Depreciation, EBITD (= 1 – 2) (1.) Tax , T After Tax Operating Cash Flow (= 3 – 4) Increase in Working (2.) Capital , ∆WC Capital Cost, KC (Gross (3.) Investment Expenditure) Operating Cash Flow (after tax) Year1 1,000 600 400 Year2 1,500 900 600 Year3 2,000 1,200 800 Year4 2,500 1,500 1,000 Year5 3,000 1,800 1,200 60 340 120 480 180 620 240 760 300 900 400 100 100 (100) (300) 600 400 0 0 0 (660) (20) 520 860 1,200 50 0 0 100 0 10 15 20 15 10 0 (10) 20 15 (10) (600) (15) 560 990 1,200 (= 5 – 6 – 7) 9. 10 . 11 . 12 . Cash flow from Non(6) operating assets After tax Interest Income from Assets Decrease (Increase) in Marketable Securities (4.) Free Cash Flow , FCF (= 8 + 9 + 10 + 11) Note : 1. 2. 3. 4 5 6 Figures are from table 3.8. An increase in working capital is a cash outflow. Figures are from table 3.7 (row 7). These are the actual cash expenditures on investment in each year and they sum to the total capital cost KC (in table 3.7). Cash flow available to investors (ie. debt holders and equity holders). Note that some forecasts of FCF might exclude items 9 and 10. ( . ) indicates a negative number e.g. sale of a subsidiary, Copyright K. Cuthbertson and D. Nitzsche 37 Valuing a Company Table 3.10 : USE OF FREE CASH FLOW OF THE FIRM 1. Free Cash Flow (table 3.9, row 12) Year1 -600 Year2 -15 Year3 560 Year4 990 Year5 1,200 FINANCING (USE OF FREE CASH FLOWS) 2. 3. 4. 5. Interest Paid to Debtholders Dividends Paid Change in Share Capital + = repurchases (..) = new issues Change in Net Debt Outstanding + = decrease, (.. ) = increase Total Financing (= 2 + 3 + 4 +5) 30 100 100 30 105 100 30 110 100 30 115 100 30 120 100 (830) (250) 320 745 950 -600 -15 560 990 1,200 Copyright K. Cuthbertson and D. Nitzsche 38 Complementary Valuation Techniques: Economic Profit, EP Economic Value Added, EVA Adjusted Present Value, APV Copyright K. Cuthbertson and D. Nitzsche 39 Economic Profit EP and EVA are equivalent to ‘Enterprise DCF’ if the calculations are done consistently -ie. before the accountants get at the figures ECONOMIC PROFIT (McKinsey and Co) EP = ( ROC - WACC) x Capital Stock, K where Return on Capital, ROC = ‘Profit’ / K If ROC > WACC then the managers chosen investment projects are earning a rate of return in excess of WACC and therefore, the investment projects are ‘Adding value’. Copyright K. Cuthbertson and D. Nitzsche 40 Economic Profit ECONOMIC PROFIT (Example) Profit = 150, K = 1000 hence ROC = 15% p.a. Let WACC = 10% p.a. EP = (15% - 10%) 1000 = $50 p.a. Your current stock of capital is being used in such a way as to generate $50 p.a. even after allowing for an annual ‘dollar capital charge’ of $100 p.a. Copyright K. Cuthbertson and D. Nitzsche 41 Economic Value Added, EVA EVA= ‘Profit’ - ‘Capital Charge’ = 150 - (10%)1000 = $50 p.a. where ‘Capital charge’ = WACC x ‘Adjusted Capital’, K EVA is equivalent to EP if we measure ‘profit’ and ‘capital’ in the same way, for both techniques. eg. do we ‘add back’ to ‘capital’ past R&D expenditures on the grounds that this outlay increased ‘knowledge’ which is an ‘asset’ Copyright K. Cuthbertson and D. Nitzsche 42 EP and EVA You can compare different firms’ performance on EP and EVA in any one year (or over several years). The ‘plus’, compared to using say just ‘profits’ or ROC is that EP and EVA assess ‘profit’ in relation to ‘the cost of capital’. Value of the firm (at t=0 ) using EP or EVA = (Net) Capital Stock at t=0, K0 + DPV ( of EP or EVA p.a., ~ WACC as discount rate) Copyright K. Cuthbertson and D. Nitzsche 43 SELF STUDY Complementary Valuation Techniques: Simple proof that ‘Enterprise DCF’ and EP or EVA are equivalent: Assume K0 = 1000 (no depreciation), ROC = 15%, ‘Profit’ = 150 (perpetuity) 1) ‘Enterprise DCF = ‘Profit’ / WACC = 150/0.10 = $1500 2) EP or EVA: EP = (15% - 10%) 1000 = $50 p.a. 3) V(firm) = K0 + EP / WACC = 1000 + 50 / 0.10 = $1500 Copyright K. Cuthbertson and D. Nitzsche 44 Complementary Valuation Techniques: ROC, EVA and EP EVA Capital,K ROC WACC General Electric 251551,017 17.7 12.7 General Motors -3527 94,268 5.9 9.7 Johnson & Johnson 1327 15,603 21.8 13.3 A positive return on capital of 5.9% for GM is ‘not enough’ if you have a WACC of 9.7% - it results in a negative EVA (or EP) Source: Fortune Mag 10th Nov 97. Copyright K. Cuthbertson and D. Nitzsche 45 Adjusted Present Value, APV(Not Examinable) When using ‘Enterprise DCF’ we discounted the FCF using ‘after tax’ WACC Our measure of FCF did not contain any ’tax offsets/shields’ on (debt) interest payments (the only tax offsets we considered were on depreciation). This was because these ‘tax offsets’ are taken care of in the denominator, the WACC, which is reduces the cost of debt to R b(1-t). APV and Enterprise DCF give the same value for the firm if consistent measures of the cost of equity and debt are used. This is a difficult area which we cannot pursue here but note that APV = FCF discounted as if firm is all-equity + DPV of ‘tax offsets’ See Copeland, T. Koller, T and Murrin, J. Valuation (J. Wiley) for the best practical account of this and other valuation issues. Copyright K. Cuthbertson and D. Nitzsche 46 END OF LECTURE SELF STUDY SLIDES FOLLOW Copyright K. Cuthbertson and D. Nitzsche 47 SELF STUDY 1) SOME PATHOLOGICAL CASES ~ COMPLICATIONS WITH IRR ! 2) OTHER METHODS USED IN INVESTMENT APPRAISAL (These are of minor importance but you should be aware of these issues) Copyright K. Cuthbertson and D. Nitzsche 48 Complications: Mainly with IRR ! Table 2: ‘DIFFERENT CASH FLOW PROFILES Project A (-100, 130) Project B (100, - 130) Project C (-100, 230, - 132) ------------------------------------------------------------Project A ~ ‘normal’ Project B ~ ‘Rolling Stone’s Concert’ Project C ~ ‘Open cast mining’ ------------------------------------------------------------IRR gives wrong decision for B and C NPV gives correct decision for A,B,C ANSWER: Use NPV ! Copyright K. Cuthbertson and D. Nitzsche 49 Complications: Mainly with IRR ! Mutually exclusive projects (eg. garage or hamburger joint on one site, BUT NOT BOTH) - use NPV not IRR criterion (afficionados could use the incremental-IRR criterion ! ) Capital Constraint (ie. not enough funds for all projects with NPV>0) - rank projects by the ‘profitability index’, PI where: PI = ( NPV / Capital Cost) = “bang per buck” Choose those projects with largest PI values until you exhaust your funds. Copyright K. Cuthbertson and D. Nitzsche 50 Investment Appraisal: Alternative Methods Year-0 Year-1 Year-2 Year-3 Year-4 FV d -1000 1.0 500 0.8696 PV -1000 435 500 0.7561 378 700 0.4972 0 - 348 - Note: NPV = 161 1) Payback Period = 2 years 2) Discounted Payback = 2-3 years Copyright K. Cuthbertson and D. Nitzsche 51 Deficiencies: Alternative Methods Either Ignores cash flows after payback period (eg. never invest in ‘Dolly the sheep’) OR Ignores time value of money Copyright K. Cuthbertson and D. Nitzsche 52 END OF SLIDES Copyright K. Cuthbertson and D. Nitzsche 53 [...]... and (2) apply - scenario analysis (Monte Carlo simulation is a sophisticated way of doing this) Can “include” probabilities in (1) and hence calculate EXPECTED NPV and its standard deviation Copyright K Cuthbertson and D Nitzsche 30 What about (business) risk in DCF ? 2) Can use decision trees - particularly useful where there are strategic options in the investment decision -eg Suppose you can abandon... Copyright K Cuthbertson and D Nitzsche 14 ‘Enterprise Value’ and ‘Equity Value’ Enterprise DCF In practice investment costs occur every year so: V(whole firm) = DPV ( Free Cash Flows, FCF) FCF = (Operating ‘cash flows’ - Gross investment) each year Value of Equity V(Equity) = V(whole firm) - V(Debt outstanding) ‘Fair value for one share’ = V(Equity) / N N = no of shares outstanding (+ ‘minority interests’)... Cuthbertson and D Nitzsche 17 Valuing the ‘Firm’ :Continuing Value Special Case A: i) the discount rate is constant in each year ii) Cash flows, FCF are constant in each year and persist ‘for ever’ (ie perpetuity) then CV = FCF/ r This is often used to calculate ‘continuing value’, CV Copyright K Cuthbertson and D Nitzsche 18 Valuing the ‘Firm’ :Continuing Value eg Project has V5 =100 in year-5,6,7 etc., and. .. t=5) = 100 / 0.10 = 1,000 and DPV (at t=0) of the CV = 1000/ (1+r)5 Copyright K Cuthbertson and D Nitzsche = 621 19 Valuing the ‘Firm’ :Continuing Value Special Case B: If i) the discount rate is constant in each year and ii)FCF’s grow at a constant rate each year, say after year-5 then CV (at t=5) = FCF5 (1+g) / ( r - g) Copyright K Cuthbertson and D Nitzsche for r>g 20 Valuing the ‘Firm’ :Continuing... S +B Copyright K Cuthbertson and D Nitzsche 28 Can Managers Increase the Value of the Firm? Assume firm is part-equity financed and part-debt financed Then the ‘intrinsic value’ of the firm is the DPV of its future cash flows from all of its current and future investment projects, discounted using WACC Managers can only increase the value of the firm by 1) investing in projects with ‘high’ FCFs 2)... Outstanding 2000(1.1) Net Receipts 1100 Amount Owed 1100 1210 = 1100 ( 1.1 ) Copyright K Cuthbertson and D Nitzsche 1210 0 12 Valuation of the Firm: Enterprise Value and Equity Value Copyright K Cuthbertson and D Nitzsche 13 Two Useful Math Results General Case V0 = FCF1 / (1+r) + FCF2 / ((1+r)2 + …… FCF= Free Cash Flows 1) Sum to infinity and FCF is constant: V0 = FCF / r 2) Sum to infinity and FCF... options in the investment decision -eg Suppose you can abandon the project and sell the ‘plant’ for $10m if demand turns out to be ‘low’ in year-2 On the other hand if demand is ‘high’ then you will continue production in year-2 This affects the NPV of the project compared with the ‘normal case’ where you assume you do not abandon In fact the ‘correct’ way to evaluate these strategic options is (not...Intuitively what do NPV and IRR rules mean ? If NPV = 0 OR, IRR = cost of borrowing then this implies -the CF from the project will just pay of all the annual interest payments on the loan + the principal amount borrowed from the bank Note: Internal funds are not ‘free’ Copyright K Cuthbertson and D Nitzsche 11 Intuitively what do NPV and IRR rules mean ? Payoff all interest and principal if NPV=0 or... V(Equity) / N N = no of shares outstanding (+ ‘minority interests’) Copyright K Cuthbertson and D Nitzsche 15 ‘Enterprise Value’ and Equity Value In an efficient market the price of the share(s) should equal ‘fair value’ We will learn how to value corporate debt, in later lectures Copyright K Cuthbertson and D Nitzsche 16 Valuing the ‘Firm’ :Continuing Value The DPV of ALL the firm’s future cash flows is... B / V = propn of debt(bonds) , (1-z) = S / V V=market value of firm = S+B ‘weights’, z, sum to 1 Copyright K Cuthbertson and D Nitzsche 27 Discount Rate: levered firm S = market value of outstanding equity ( = N x stock price) B = market value of outstanding debt (ie bonds issued and bank loans) RS = average return on equity in hamburger industry RB = interest rate (yield to maturity) on say 10-year ... EP, EVA,APV Self Study: Other Investment Appraisal Methods Copyright K Cuthbertson and D Nitzsche READING Investments:Spot and Derivative Markets, K.Cuthbertson and D.Nitzsche Chapter Discounted... the IRR is the ‘break-even’ discount rate and IRR = 0.10 (10%) IRR INVESTMENT DECISION RULE Copyright K Cuthbertson and D Nitzsche 10 Intuitively what NPV and IRR rules mean ? If NPV = OR, IRR =... K Cuthbertson and D Nitzsche 18 Valuing the ‘Firm’ :Continuing Value eg Project has V5 =100 in year-5,6,7 etc., and r=0.10 then Continuing value CV (at t=5) = 100 / 0.10 = 1,000 and DPV (at t=0)