Traditional Investment Metrics PDF

Traditional Investment Metrics Why revisiting them? Lecturer: Gonçalo Faria School of Economics and Finance  Some traditional valuation metrics Three metrics under revision: Net Present Value (NPV) Payback Period Internal Rate of Return (IRR) A brief revision...

Traditional Investment Metrics Why revisiting them? Lecturer: Gonçalo Faria School of Economics and Finance  Some traditional valuation metrics Three metrics under revision: Net Present Value (NPV) Payback Period Internal Rate of Return (IRR) A brief revision of traditional valuation metrics is due. Why? o In the real world, they always appear in a meeting and eventually in a deal proposal o It is very important to understand if and how they can be used in the context of a valuation exercise  Some traditional valuation metrics Source: Hillier et al, 2016. Updated figures regarding NPV, IRR and payback in Hillier et al, 2024: qualitative insights unchanged and no more indicators. Net Present Value Lecturer: Gonçalo Faria School of Economics and Finance  Net Present Value (NPV) Rational: estimate future cash flows (CF) and discount those CF to present time using a discount rate (k) where 𝐼0 represents the initial investment Three immediate topics: 1. estimate CF. How? Which CF? 2. which discount rate k to be used? 3. if n→∞, work the terminal value  Net Present Value (NPV) Example: Company A considers an investment of €100 in a project that delivers a single CF of €107 within one year. k = 6%. NPV? Should the company invest or not?  Net Present Value (NPV) NPV investment rule: NPV > 0 : accept project NPV < 0 : reject project Very important: A project contribution for the value of a company is its NPV. Additive rule Three main attributes of NPV: Uses cash-flows and not accounting measures (as, for example, net earnings). Remember: (i) cash is king!; (ii) financial vs. accounting value Uses all cash-flows from the project (vs. other methods that ignore CF after some date) Considers the value of time: discounts CF Payback Period Lecturer: Gonçalo Faria School of Economics and Finance  Payback Period Definition: time period to recover initial investment Example: Initial Investment: €50000 Estimated CF for the first three years: €30000, €20000, €10000 Alternative Notation: (-€50000; €30000; €20000; €10000) Payback period?  Payback Period Payback Investment rule: Set a “cut-off” date ○ How? If Payback > “cut-off”: reject project If Payback < “cut-off”: accept project  Payback Period Problems with Payback: Consider the following three projects A, B and C: What is the payback period of each project? From a valuation perspective, are they equally attractive?  Payback Period Problems with Payback: Problem 1: Timing of CF during the payback period ○ Project A vs. B during the first three years: project B has higher CF in short term => NPVB > NPVA ○ However, projects A and B have the same payback… ○ Payback, on the contrary of NPV, does not discount CF Problem 2: CF after payback period ○ Projects B and C have the same CF during the payback period. However, Project C is preferable vs. B because CF4 = 60000vs 60 ○ Payback does not consider all CFs ○ Short term perspective Problem 3: how is the “cut-off” date defined?  Payback Period Discounted Payback: Aim: overturn the problem of CF discount in the payback method Two steps: ○ Discount all CFs ○ Time period such that discounted CF equal initial investment Notes ○ If CF > 0 and k > 0: discounted payback is always higher that the “standard” payback ○ Keeps problems 2 and 3 above mentioned with respect to the “standard” payback Internal Rate of Return Lecturer: Gonçalo Faria School of Economics and Finance  Internal Rate of Return Internal Rate of Return (IRR) It is an intrinsic number of the project (that is why it is referred as internal rate): ○ only depends on the project CF ○ summarizes the project worth. Probably the greatest advantage of IRR It is a very close concept to NPV, but has limitations that make it technically less interesting and robust IRR: discount rate such that NPV = 0 Example: (-€100, €110)  Internal Rate of Return Investment rule: IRR > discount rate k: accept project; NPV > 0 IRR < discount rate k : reject project; NPV < 0 Source: Hillier et al, 2016  Internal Rate of Return Consider three projects: A: (- €100, €130) B: (€100, - €130) C: (- €100, €230, - €132)  Internal Rate of Return Note 1: Investment or Financing? If project => kick-off investment and, afterwards, CF>0: ○ Project is an Investment and the IRR decision rule is the one disclosed before ○ Example: Project A If project => initial cash inflow and, afterwards, CF < 0: ○ Project is Financing and the IRR decision rule is: o IRR > discount rate k : reject project; NPV < 0 o IRR < discount rate k : accept project; NPV > 0 ○ Example: Project B  Internal Rate of Return Note 2: Multiple IRR Project C: change in CF sign as CF0 < 0, CF1 > 0, CF2 < 0. We call this “flip-flop” projects In this case there are two IRR: 10% and 20% ○ Why? Because in the stream of CF there is more than one sign change ○ Which IRR to use? No criteria... => With “flip-flop” projects, using IRR does not make sense NPV rule allows always to make a decision: in this example, accept project if 10% < k < 20% Internal Rate of Return Internal Rate of Return Problems Lecturer: Gonçalo Faria School of Economics and Finance  Internal Rate of Return - Problems Using the IRR in the context of mutually exclusive projects – i.e. if the company can only accept one of them – may have relevant problems Problem 1: Scale Example: Choose one of the following business opportunities: Opportunity 1 - Invest €1 now and receive €1.50 at the end of the week Opportunity 2 - Invest €10 now and receive €11 at the end of the week Which opportunity to choose?  Internal Rate of Return - Problems Answer: opportunity 2! Why? Because it has higher NPV (assuming k=0) Why does IRR leads to the wrong conclusion? IRR ignores project's scale. Scale is one of the most crucial aspects when valuing an investment project (optimal dimension?)  Internal Rate of Return - Problems It is possible to overturn this scale problem with IRR: Consider two projects A and B Ignore IRR and compare NPVA with NPVB (previous example) Calculate incremental NPV (NPVinc ) of project B vs A. If NPVinc > 0: choose project B Compare incremental IRR (project B vs. A) and k. If IRRinc > k: choose project B What is incremental NPV and incremental IRR?  Internal Rate of Return - Problems Example: Incremental NPV: NPV of the CF difference of B vs. A: Incremental IRR: discount rate such that NPVinc = 0: Decision: NPVinc = €5 > 0 and IRRinc > k = 25% => choose project B  Internal Rate of Return - Problems Problem 2: CF timing profile Example IRRA > IRRB , but… NPVB > NPVA for low k. Opposite for high k. This because B has higher CF in the long term. IRR ignores “timing” of the cash flows  Internal Rate of Return - Problems If k < (>) 10.55% then choose project B (A) As with the “scale” problem, three methods to overturn this IRR limitation: (i) compare NPVA vs NPVB, (ii) compare IRRinc vs k, (iii) calculate NPVinc Free Cash Flow Model Analysing Financial Statements – Why is it relevant for valuation? Lecturer: Gonçalo Faria School of Economics and Finance  Analysing Financial Statements From a valuation perspective, what is the relevance of a proper Financial Statements analysis? It is critical for: the diagnostic of a business model (past and present) and for monitoring activity evolution (vs. expectations) => Financial Statements are key inputs for the valuation exercise  Analysing Financial Statements Financial Statements are: o The main instrument for the financial communication of a company towards its stakeholders (current and potential) o Should be reliable, audited documents Overall, Financial Statements are a critical input for the financial decision process  Analysing Financial Statements Very important to distinguish: o economic/financial perspective (ours!) from o accounting perspective, under which Financial Statements are elaborated Our aim: o Discuss an approach towards accounting information to properly inform the valuation exercise o focus: Balance Sheet (BS), Income Statement (IS) and Cash Flow Statement (CFS)  Analysing Financial Statements Example: Wirecard, a German payments group, collapsed into insolvency in June 2020 after revealing that €1.9bn in cash in its accounts probably did “not exist”. For years it was seen as a “star”. Follow-up for students: proposed discussion Free Cash Flow Model Analysing Financial Statements – Balance Sheet Lecturer: Gonçalo Faria School of Economics and Finance  Analysing Financial Statements – Balance Sheet Portrait of the company's book (accounting) value at a certain date: o Portrait + date: static vision at a certain date o Accounting or book value: perspective is not of the intrinsic/fundamental value Informs about what the company has (assets) and how it was financed (equity and liabilities): 𝐴𝑠𝑠𝑒𝑡𝑠 = 𝐸𝑞𝑢𝑖𝑡𝑦 + 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠  Analysing Financial Statements – Balance Sheet Assets – what the company has, reflecting capital budgeting decisions: o Classified by easiness of transforming it into cash (non-current vs current assets): Example: cash vs tangible assets o Reflects the nature of the business and how it is implemented. Examples: Non-current assets reflect capital expenditure (capex) policy in tangible and intangible assets, as well as in long-term financial (non-core) assets Trade receivables reflects commercial policy Inventories reflects inventory management policy and business cycle Cash and Equivalents: reflects cash management and cash generation  Analysing Financial Statements – Balance Sheet Example: BMW – Assets @ December 31st 2019 (vs 2018). Source: BMW report  Analysing Financial Statements – Balance Sheet Equity and Liabilities – how assets have been funded, reflecting financing decisions: o Classified by redemption time-horizon o Reflects decisions about capital structure (own sources versus third parties) o Reflects decisions about external funding (bank debt, bonds, trade suppliers, etc...). Again, the nature of the business and how it is implemented plays a crucial role  Analysing Financial Statements – Balance Sheet Example: BMW – Equity and Liabilities @ December 31st 2019 (vs 2018). Source: BMW Report  Analysing Financial Statements – Balance Sheet Balance Sheet analysis, from a valuation perspective, should consider at least the following vectors: 1. Liquidity: speed with which assets can be converted into cash, without significant loss of value 2. Capital structure and different levels of stakeholders seniority: Liabilities (Banking Debt, Bond Loan,....): are senior claims versus Equity in case of financial distress Equity: shareholders receive remuneration after the company fulfils all its obligations with remaining stakeholders  Analysing Financial Statements – Balance Sheet 3. Accounting Value vs. Financial Value Accounting Value: static nature, normally valued at historical cost although, when possible or required, there are “mark-to-market” and revaluations exercises Financial Value: forward looking nature, reflecting the value at which the asset would be traded in the market => Only by coincidence, Accounting Value = Financial Value!  Analysing Financial Statements – Balance Sheet Working capital (W.C.) 𝑊. 𝐶.𝑡 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠𝑡 − 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑡 o Do not underestimate the relevance of Changes in W.C. (∆𝑊. 𝐶.𝑡 = 𝑊. 𝐶.𝑡 − 𝑊. 𝐶.𝑡−1 ) o Working Capital investment is a very important element in financial management, with strong impact on value: Too much resources allocated to inventories? Average payment period to suppliers versus average collection period from clients? Liquidity cycle and potential liquidity constrains? Free Cash Flow Model Analysing Financial Statements – Income Statement Lecturer: Gonçalo Faria School of Economics and Finance  Analysing Financial Statements – Income Statement Flows (profits - costs) during a certain period (year, semester, quarter...). Contrasts with BS rational: Flow vs. Static Divided in: o Operational. Flows from company's operational activity. EBIT and EBITDA o Financial Results. Flows with strictly financial nature, including net interest paid, foreign exchange impact, derivatives mark-to-market, … o Non-recurrent Results. Example: capital gains from real estate sale (if that isn't the main activity of the company) o Corporate Income Taxes o Net Income  Analysing Financial Statements – Income Statement Example: BMW – Consolidated Income Statement year 2019 (vs 2018). Source: BMW report  Analysing Financial Statements – Income Statement Note on “Non-cash costs (revenues)”: accounting costs (revenues) that do not imply cash outflow (inflow). Impact on net income but not on cash flow Our concern is CASH! Examples: Depreciations: accounting recognition of the periodic wear of an asset. But there is no cash outflow Provisions: accounting “protection” against some event, but without any immediate cash outflow  Analysing Financial Statements – Financial Ratios Financial ratios are useful: o to compare companies of different dimensions and from different sectors o to complement analysis of information contained in Financial Statements (BS, IS, CFS) Financial ratios are usually grouped in four classes: o Liquidity o Financial Leverage o Asset Management (turnover) o Profitability We are going to skip this topic due to focus reasons (covered in modules focused on Financial Statement Analysis). Please see chapter 3 in Hillier et al (2021) for further insights. Free Cash Flow Model Analysing Financial Statements – Cash Flow Statement Lecturer: Gonçalo Faria School of Economics and Finance  Analysing Financial Statements – Cash Flow Statement Purpose: understand the change in cash position o Always remind that “Cash is King”! o Cash Flow Statement summarizes the company activity through changes in cash - the main angle of analysis when valuing companies and projects Three blocks: o Operating Cash Flow o Investment Cash Flow o Financing Cash Flow  Analysing Financial Statements – Cash Flow Statement Operating Cash Flow: change in cash position due to the operational activity of the company. Can be presented in two ways: o Top-down: = 𝐸𝐵𝐼𝑇 + "non cash costs" − "non cash revenues" − ∆𝑊. 𝐶 − 𝑡𝑎𝑥𝑒𝑠 o Bottom-up: = 𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑅𝑒𝑐𝑜𝑛𝑐𝑖𝑙𝑖𝑎𝑡𝑖𝑜𝑛 𝑢𝑛𝑡𝑖𝑙 𝐸𝐵𝐼𝑇 + "non cash costs" − "non cash revenues" − ∆𝑊. 𝐶 − 𝑡𝑎𝑥𝑒𝑠  Analysing Financial Statements – Cash Flow Statement Operating Cash Flow - Note 1: Although the “top-down” and the “bottom-up” approaches must give the same outcome, the “top-down” approach is simpler and with lower possibility of errors Taxes. Two potential avenues: 1. EBT* corporate tax rate 2. EBIT*corporate tax rate => in this 2nd alternative, the disentanglement of the Free Cash Flow (FCF) computation from financing decisions is guaranteed. This is why this is the appropriate way for estimating taxes in the context of FCF estimation.  Analysing Financial Statements – Cash Flow Statement Operating Cash Flow - Note 2: Reconciliation from Net income until EBIT in the “bottom-up approach”: o Rational has always to be cash in/ cash out and with respect to the operating activity. Example: interest paid need to be added to the net income o Each company has its own idiosyncrasy. Example: BMW has a Financial division, implying that interest received/paid under this division is considered operational income/cost  Analysing Financial Statements – Cash Flow Statement Example: BMW – Operating Cash Flow year 2019 (vs 2018). Source: BMW report  Analysing Financial Statements – Cash Flow Statement Investment Cash Flow: Change in cash position resulting from the company's investment activity in tangible assets, intangible assets and financial (non-core) assets 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 = ෍ 𝐷𝑖𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠 − ෍ 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠  Analysing Financial Statements – Cash Flow Statement Example: BMW – Investment Cash Flow year 2019 (vs 2018). Source: BMW report  Analysing Financial Statements – Cash Flow Statement Financing Cash Flow: Change in cash position due to the company's financing activity (shareholders, bank debt, bond issuance, etc...). This funding supports the operating and investment activity of the company. 𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 = 𝑁𝑒𝑡 𝑖𝑠𝑠𝑢𝑒𝑑 𝑑𝑒𝑏𝑡 − 𝑁𝑒𝑡 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑝𝑎𝑖𝑑 + 𝑁𝑒𝑡 𝑖𝑠𝑠𝑢𝑒𝑑 𝑒𝑞𝑢𝑖𝑡𝑦 − 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑝𝑎𝑖𝑑 𝑐𝑟𝑒𝑑𝑖𝑡𝑜𝑟𝑠 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠 o Net issued debt: new interest bearing debt (bank, bonds,...) - debt redemption o Net interest paid: interest paid – interest received o Net issued equity: capital increase – capital redemption  Analysing Financial Statements – Cash Flow Statement Example: BMW – Financing Cash Flow year 2019 (vs 2018). Source: BMW report  Analysing Financial Statements – Cash Flow Statement Final Note 1: Operating CF + Investment CF + Financing CF = Change in cash position during the period o Example BMW (year 2019): € mn Operating CF 3.662 Investment CF -7.284 Financing CF 4.790 Adjustments (fx and consolidation) -111 Total 1.057 o Cash and Equivalents BMW @ 31st December 2019 and 2018: €12.036𝑚𝑛 − €10.979𝑚𝑛 = €1.057𝑚𝑛  Analysing Financial Statements – Cash Flow Statement Final Note 2: 𝐹𝑟𝑒𝑒 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 𝑡𝑜 𝑡ℎ𝑒 𝐹𝑖𝑟𝑚 = 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐶𝐹 + 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝐶𝐹 (𝑒𝑥𝑐𝑙𝑢𝑑𝑖𝑛𝑔 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠) The FCF is the relevant cash flow for the valuation exercise of a company or project: o Cash generated from operational activity o Net of investment effort o Net of taxes o Independent of financing decisions => Cash available for all stakeholders Free Cash Flow Model BMW FCF Model construction: Model set-up, historical data Lecturer: Gonçalo Faria School of Economics and Finance  BMW FCF Model – Purpose and Model set-up Purpose of this multi-stage activity: develop step-by-step, over the next weeks, a Free Cash Flow (FCF) model for BMW Objective: Develop a “buy-side” model for BMW o A simple model designed to give a quick valuation assessment of a company. o Useful to illustrate concepts as we go through them in our module. o Ultimate objective is that students “play” with the model so that they develop practical skills and sensitivity towards the valuation topic and modelling skills. o Two worksheets: revenues and free cash flow statement o A more detailed “sell-side” model should contain, at least, the full estimation of balance- sheet, income statement and cash flow statement o Valuation exercise at year-end 2025  BMW FCF Model – Historical Data This week activity: o Present the model set-up o Fill in the model with recent historical data (full year 2023) o Going through BMW Investor Presentation (2024) and BMW Investment Case (2011) o Put in context the model design versus identified value drivers Suggestions for students after this activity: “play” with the model by o Changing its design in accordance with their view on what are the key value drivers of the company (Discussion) o Eventually increase the level of detail, by estimating the full balance-sheet, income statement and cash flow statement.  References o BMW FY2023 Report (available at qm+) o BMW Investor Presentation, September 2024 (available at qm+) o BMW Investment Case, 2011. Douro Equity Fund (available at qm+) o Excel file: BMW-FCFModel-Step1.xls (available at qm+) Free Cash Flow Model DCF Models: Characterization Lecturer: Gonçalo Faria School of Economics and Finance  DCF Models: Characterization Discounted Cash Flow (DCF) models are defined by the following expression: 𝑛 𝐶𝐹𝑡 𝑉𝑎𝑙𝑢𝑒 = ෍ 𝑡 1+𝑟 𝑡=1 where: o 𝑉𝑎𝑙𝑢𝑒: “fair” value of the asset (at moment zero) o 𝐶𝐹𝑡 : expected cash flow of period 𝑡 o 𝑟: required rate of return for the invested capital (opportunity cost) o 𝑛: expected life-time of the asset. Most of the cases: 𝑛 → ∞  DCF Models: Characterization As the life period of the asset can be very high, usually what is done is: 1. Detailed estimation of cash flows during a limit period 𝑛 o normally, 𝑛 = 5 or 6 years o Highly relevant to consider idiosyncrasy of the company or project being valued (start- up? cyclical? maturity stage?...): impacts the relevant number of years for CF estimation o Also institutional circumstances are relevant for the estimation period. For example, in Private Equity funds, CF's are projected for the period during which the Fund is expected to be invested in the company and/or the duration of the Fund's vehicle through which the investment in the company is made  DCF Models: Characterization 2. Computation of a terminal value TV (perpetuity value) assuming the continuity principle w.r.t. to the existence of the asset and stability of its future cash flows Value, in such context, is therefore given by: 𝑛 𝐶𝐹𝑡 𝑇𝑉𝑛 𝑉𝑎𝑙𝑢𝑒 = ෍ 𝑡 + 𝑛 1+𝑟 1+𝑟 𝑡=1  DCF Models: Characterization Different DCF models differ due to different assumptions regarding: Valuation perspective: o Company perspective (enterprise value): valuation of assets / business o Equity perspective (equity value): valuation of equity Relation between investment and funding: o Strict separation, or not, between investment and funding o Relevance of levels / degrees of leverage  DCF Models: Characterization The 'family' of DCF models includes: o Free Cash Flow model (FCF) o Equity Free Cash Flow model (EFCF) o Capital Cash Flow model (CCF) o Adjusted Present Value model (APV) o Compressed Adjusted Present Value (CAPV) Free Cash Flow Model Characterization Lecturer: Gonçalo Faria School of Economics and Finance  Free Cash Flow Model: Perspective Free Cash Flow (FCF) model perspective: company => Enterprise value  Free Cash Flow Model: Perspective o FCF is the available cash flow to remunerate all sources of capital => Discount rate is consistent with this: weighted average cost of capital (𝑟𝑤𝑎𝑐𝑐 ) o FCF = Operating CF + Investment CF (excluding financial investments)  Free Cash Flow Model: Terminal value The “Perpetuity” or “Terminal Value” (𝑇𝑉𝑛 ) is given by: 𝐹𝐶𝐹𝑛 1 + 𝑔 𝑇𝑉𝑛 = 𝑟𝑤𝑎𝑐𝑐 − 𝑔 where: o 𝑔: nominal growth of FCF in the perpetuity. Huge impact on valuation! The reference is economy’s long-term nominal growth (proxy: for e.g., inflation), but must be estimated case-by-case depending on the company and industry o 𝐹𝐶𝐹𝑛 : last FCF estimated rigorously (BMW FCF model we are building - year 2028)  Free Cash Flow Model: Terminal value Due to the high relative weight that 𝑇𝑉 normally has, when estimating 𝐹𝐶𝐹𝑛 it is important to recall that: o as 𝐹𝐶𝐹𝑛 is a “steady state” 𝐹𝐶𝐹, it should not contain huge discontinuities in its inputs versus previous years o if it is a cyclical company, should be estimated as the expected average 𝐹𝐶𝐹 of the cycle o Depreciation = Capex (very important!)  Free Cash Flow Model The measure of Value using the FCF model is therefore given by: 𝑛 𝐹𝐶𝐹𝑡 𝑇𝑉𝑛 𝑉𝑎𝑙𝑢𝑒 = ෍ 𝑡 + 𝑛 1 + 𝑟𝑤𝑎𝑐𝑐 1 + 𝑟𝑤𝑎𝑐𝑐 𝑡=1 o The 𝐹𝐶𝐹 measure is independent of funding decisions o The (explicit) impact from the capital structure is exclusively through the discount factor o Validity condition: a constant level of debt, i.e., target capital structure Free Cash Flow Model Total Risk Analysis Lecturer: Gonçalo Faria School of Economics and Finance  Free Cash Flow Model: Total Risk Analysis o The valuation exercise is complex and requires complementary analysis beyond the use of a specific valuation model o Total Risk Analysis is something an analyst should try to do, in order to put into perspective the key outcomes from the valuation model Traditional investment metrics such as the NPV and standard DCF models include risk in the discount factor, i.e, the opportunity cost of invested capital This is fine, but the robustness of the valuation exercise should be tested  Free Cash Flow Model: Total Risk Analysis It is important that the analyst develops sensitivity about the value impact from unanticipated changes in the value drivers. Some tools help to develop this sensitivity: o Sensitivity analysis o Critical point analysis o Scenario analysis o Simulation analysis  Free Cash Flow Model: Sensitivity Analysis o Sensitivity analysis: value impact from changes in a certain variable, everything else constant o An example of a sensitivity analysis measure is the elasticity Example: Margin = 10%, NPV = 1.000 Margin = 11%, NPV = 1.200 => elasticity = 200% o The higher is the elasticity, the more attention should the analyst have with respect to that variable  Free Cash Flow Model: Critical Point Analysis Critical point analysis: evaluate the required change in a certain variable such that a certain valuation metric (example the NPV) reaches a certain level Example: Margin = 10%, NPV = 1.000 Which Margin in order to have NPV = 0? Margin = 6.75% Security margin = (10% - 6.75%)/10% = 32.5% (i.e, margin would have to fall 32.5% in order to have NPV=0)  Free Cash Flow Model: Scenario Analysis o Scenario analysis: similar to sensitivity analysis but considering the value impact from changes in a set of variables (versus one single variable), everything else constant o Potential scenarios: base case, optimistic (bullish), pessimistic (bearish), etc... And then the analyst may associate to each scenario a certain probability and compute the expected value o Examples of metrics used in scenario analysis: mean, standard deviation, percentiles, etc...  Free Cash Flow Model: Simulation Analysis Simulation analysis: evaluate the value impact from the change in a set of variables that follow a certain probability distribution Using appropriate software (e.g. Crystal Ball, @risk) can lead to hundreds of thousands of simulations Final output: probability distribution for the value of the company/project Examples: 𝑃(𝑁𝑃𝑉 < 0) = 2% 𝑃(€ 0𝑚𝑛 < 𝑁𝑃𝑉 < € 5𝑚𝑛) = 95% Free Cash Flow Model BMW FCF Model construction: FCF estimation, Scenario Analysis Lecturer: Gonçalo Faria School of Economics and Finance  BMW FCF Model This week activity: o Free Cash Flows (𝐹𝐶𝐹) estimation o Terminal Value (𝑇𝑉) estimation o Introduction of scenario analysis in the model Suggestions for students after this activity: “play” with the model by o Changing assumptions backing the estimation of different items of the FCF o Changing assumptions backing the estimation of the TV o Introduce additional variables to be made part of the scenario analysis. This should be consistent with alternative value drivers. Example: electric cars o Eventually adding simulation analysis to the model, applying insights from other Modules in the MSc Free Cash Flow Model Risk, Return and Cost of Capital: rational of the discount rate Lecturer: Gonçalo Faria School of Economics and Finance  Discount rate: rational The Free Cash Flow (FCF) model is defined by the following expression: ∞ 𝐹𝐶𝐹𝑡 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒 = ෍ 𝑡 1+𝑟 𝑡=1 where 𝑟 is the required rate of return for the invested capital (opportunity cost), including all sources of funding But what is the rational backing 𝑟 estimation?  Discount rate: rational What does “opportunity cost of capital” exactly means? An investor has cash available to invest in the company/project under valuation: => the expected return from that investment has to be equal or higher than the expected return from an investment in an asset with comparable risk profile  Discount rate: rational Some relevant outcomes: o the opportunity cost of capital is a market based rate The more liquid and informative is the market for comparable assets the easier it is to estimate the opportunity cost of capital o risk: non-diversifiable, idiosyncratic, both? o level of seniority of the investment: equity? debt? hybrid? o remuneration policy. Company has cash: either distributes it to shareholders as dividend or share redemption, or keeps it to invest in future projects. But the opportunity cost of capital retention is critical Free Cash Flow Model Risk, Return and Cost of Capital: CAPM and APT Lecturer: Gonçalo Faria School of Economics and Finance  Capital Asset Pricing Model (CAPM) Associated with tradable assets but used for valuing any project/company - relevance of the opportunity cost of capital concept Starting point - Expected Return of the Market (𝑟𝑚 ): 𝑟𝑚 = 𝑟𝑓 + 𝑟𝑝 o 𝑟𝑓 : risk-free rate o 𝑟𝑝 : market risk premium  Capital Asset Pricing Model (CAPM) Question: what is, in equilibrium, the expected return of an asset 𝑖 (𝑟𝑖 )? 𝑟𝑖 = 𝑟𝑓 + 𝛽𝑖 𝑟𝑚 − 𝑟𝑓 (1) where 𝛽𝑖 : beta of asset 𝑖 (1) is the central equation of CAPM  Capital Asset Pricing Model (CAPM) Equation (1) is graphically represented by the Security Market Line (𝑆𝑀𝐿)  Capital Asset Pricing Model (CAPM) Some notes regarding the 𝑆𝑀𝐿: o 𝑆𝑀𝐿 slope: 𝑟𝑚 − 𝑟𝑓 as long as 𝑟𝑚 > 𝑟𝑓 => 𝑆𝑀𝐿 slope is positive o positive linear relation between the expected excess return of asset 𝑖 (𝑟𝑖 − 𝑟𝑓 ) and 𝛽𝑖 : assets below the 𝑆𝑀𝐿 (example 𝑆 and 𝑇 in previous figure) are expensive: in order to be in equilibrium, those assets prices have to decrease until the asset is at the 𝑆𝑀𝐿 opposite for assets above the 𝑆𝑀𝐿  Capital Asset Pricing Model (CAPM) What does 𝛽𝑖 represents? 𝑐𝑜𝑣(𝑟𝑚 , 𝑟𝑖 ) 𝛽𝑖 = 𝜎𝑟2𝑚 𝑐𝑜𝑣(𝑟𝑚 , 𝑟𝑖 ): covariance between asset 𝑖 return (𝑟𝑖 ) and the market return (𝑟𝑚 ) 𝜎𝑟2𝑚 : variance of market return From a finance conceptual point of view, what is the information carried by 𝛽𝑖 ?  Capital Asset Pricing Model (CAPM) The CAPM measures the exposure of asset 𝑖 towards the market risk factor o Systematic risk vs diversifiable risk o Assumption that asset 𝑖 is priced in a context of a well diversified portfolio => from a risk perspective the relevant angle is asset 𝑖 contribution for that portfolio => relevant angle is that of systematic risk, which in the CAPM is represented by the market risk factor  Capital Asset Pricing Model (CAPM) So 𝛽𝑖 can be interpreted as the sensitivity of asset 𝑖 return towards changes in the market return: o 𝛽𝑖 < 1: relatively low sensitivity of asset 𝑖 return o 𝛽𝑖 = 1 : average sensitivity of asset 𝑖 return o 𝛽𝑖 > 1 : relatively high sensitivity of asset 𝑖 return Note that, from equation (1), market 𝛽 is equal to 1  Arbitrage Pricing Theory Model (APT) APT Model: o an alternative to the CAPM o the return of asset i is considered as a function of 𝑛 systematic factors (𝐹𝑗 , 𝑗 = 1, … 𝑛): 𝑟𝑖 = 𝑟𝑓 + 𝛽1,𝑖 𝐹1 + 𝛽2,𝑖 𝐹2 + ⋯ + 𝛽𝑛,𝑖 𝐹𝑛 + 𝜀𝑖 (2) Notes: o 𝛽𝑖,𝑗 : 𝛽 of asset 𝑖 with respect to the systematic factor 𝑗 o Examples of 𝐹: inflation, GDP, market volatility,... o 𝜀𝑖 - unsystematic risk of asset 𝑖. Should be totally diversifiable  APT versus CAPM o In the CAPM model the systematic risk of asset 𝑖 is fully represented by its market 𝛽 => Implications from CAPM and APT model with one factor are the same, if the systematic factor in the latter is the market risk o In APT model, the systematic risk of an asset 𝑖 is represented by several factors: potentially a more “granular” analysis of the expected return of asset 𝑖 but....... it is necessary to establish a subjective criteria to identify the relevant factors 𝐹 o Both in CAPM and APT model, the expected return of asset 𝒊 is a function of its systematic risk, measured by a single 𝛽 (CAPM) or by a set of 𝛽's (APT) Free Cash Flow Model Risk, Return and Cost of Capital - CAPM: 𝛽 Lecturer: Gonçalo Faria School of Economics and Finance  Capital Asset Pricing Model (CAPM): 𝛽 𝛽𝑖 estimation? Using historical data on asset 𝑖 and market returns: 𝑐𝑜𝑣(𝑟𝑚 ,𝑟𝑖 ) o 𝛽𝑖 = 𝜎𝑟2𝑚 o Estimate slope of CAPM fundamental equation: 𝑟𝑖 = 𝑟𝑓 + 𝛽𝑖 𝑟𝑚 − 𝑟𝑓  Capital Asset Pricing Model (CAPM): 𝛽 𝛽𝑖 estimation? Problems using historical data: o Appropriate sample dimension? Previous example (BMW vs DAX): 10/13/2014 – 10/12/2016 o Appropriate benchmark? Profile of market indexes changes in time: example S&P500 and Big Techs o 𝛽𝑖 changes in time. Depends on different factors with special highlight for: 𝐹𝐶𝐹 volatility, operational leverage, financial leverage  Capital Asset Pricing Model (CAPM): 𝛽 𝑭𝑪𝑭 volatility: companies with more volatile 𝐹𝐶𝐹, normally have higher 𝛽's o Cyclical companies (e.g media, advertisement, pulp&paper,…): their FCF's are strongly impacted by the economic cycle Operational leverage: amplifies the cyclical effect. Consequently, everything else constant, the higher the operational leverage, the higher should be 𝛽's o Operational leverage is measured by the relative weight of fixed costs in the cost structure of the company: the higher that relative weight, the higher the operational leverage  Capital Asset Pricing Model (CAPM): 𝛽 Financial Leverage: relevant to distinguish between 𝛽𝑎𝑠𝑠𝑒𝑡 (or unlevered 𝛽) and 𝛽𝑒𝑞𝑢𝑖𝑡𝑦 Until now we assumed ∄ debt → 𝛽𝑎𝑠𝑠𝑒𝑡 = 𝛽𝑒𝑞𝑢𝑖𝑡𝑦 𝐵 𝛽𝑒𝑞𝑢𝑖𝑡𝑦 = 𝛽𝑎𝑠𝑠𝑒𝑡 1+ 1−𝑇 𝑆 o 𝐵 and 𝑆: debt and equity, respectively o 𝑇: corporate tax rate 𝐵 → if there exists financial leverage (𝐵 > 0) then 𝛽𝑒𝑞𝑢𝑖𝑡𝑦 > 𝛽𝑎𝑠𝑠𝑒𝑡 as 1 − 𝑇 >0 𝑆 o formula above assumes two unrealistic assumptions: 𝛽𝑑𝑒𝑏𝑡 = 0 and tax effect as the sole effect from debt. But, at least partially, they have offsetting implications in real 𝛽𝑒𝑞𝑢𝑖𝑡𝑦  Capital Asset Pricing Model (CAPM): 𝛽 𝛽𝑖 estimation? In the context of valuation, 𝛽𝑖 needs to be a forward looking assumption Considering the limitations from using historical data, the analyst needs to be very careful when using backward-looking based 𝛽𝑖 estimation: o Intrinsic characteristics of company 𝑖 business and/or sector: expected to change? o Long-term capital structure of company 𝑖: expected to change? At the end of the day, 𝛽𝑖 estimation carries a lot of subjectivity and uncertainty (just like for all other inputs for a valuation exercise)  Capital Asset Pricing Model (CAPM): 𝛽 What if you are valuing a project, that has 𝛽 different of that of the company? o Rational is the same as before, but at the project level o Discount rate has to consider project’s 𝛽 How to estimate project’s 𝛽? o Follow an idiosyncratic assessment: project 𝐹𝐶𝐹 cyclical profile, operational leverage,... o One way is to consider the average 𝛽 of the industry to which the project belongs. However, be careful with heterogeneity within an industry (see next slide)...  Capital Asset Pricing Model (CAPM): 𝛽 𝛽 for UK oil and gas industry (5Y monthly 𝛽, @ 03/08/2020): Company Ticker (@finance.yahoo.com) Beta Premier Oil PMO.L 3.48 Royal Dutch Shell RDSB.L 0.85 Hunting HTG.L 0.82 JKX JKX.L 0.98 BP BP.L 0.56 Tullow Oil TLW.L 2.63 Petrofac PFC.L 0.88 Cairn Energy CNE.L 1.91 Median 0.93 max 3.48 min 0.56 Std. Deviation 1.05 Source: https://finance.yahoo.com Free Cash Flow Model Risk, Return and Cost of Capital: Weighted Average Cost of Capital Lecturer: Gonçalo Faria School of Economics and Finance  Weighted average cost of capital Given the exposure of asset 𝑖 towards the systematic risk factor(s), the CAPM (APT) gives the required rate of return of invested capital If company 𝒊 has no debt, the CAPM (APT) rate can be directly used as the discount rate in the valuation exercise of company 𝑖 If company 𝒊 has debt: which discount rate should be used? It requires o Consideration of the target capital structure o Estimation of the cost of equity o Estimation of the cost of debt  Weighted average cost of capital o consideration of the target capital structure long-term capital structure linked with the steady state view of company 𝑖 o estimation of the cost of equity (𝒓𝒆 ) equity remuneration for the exposure towards systematic risk (CAPM, APT, …) highest level of contingency long-term view o estimation of the cost of debt (𝒓𝒅 ) debt remuneration for the exposure towards credit risk lower level of contingency (versus equity) long-term view, as it should be linked with the target capital structure consideration of the tax shield associated with debt  Weighted average cost of capital The weighted average cost of capital (𝑟𝑤𝑎𝑐𝑐,𝑖 ) of company 𝑖 is computed with those inputs 𝑟𝑤𝑎𝑐𝑐,𝑖 = 𝑤𝑒,𝑖 𝑟𝑒,𝑖 + 𝑤𝑑,𝑖 𝑟𝑑,𝑖 where: o 𝑟𝑒,𝑖 : estimated cost of equity of company 𝑖 CAPM: 𝑟𝑒,𝑖 = 𝑟𝑓 + 𝛽𝑖 𝑟𝑚 − 𝑟𝑓 o 𝑟𝑑,𝑖 : estimated cost of debt of company 𝑖 𝑟𝑑,𝑖 = 𝑟𝑓 + 𝑠𝑝𝑟𝑒𝑎𝑑𝑖 1 − 𝑇 𝑠𝑝𝑟𝑒𝑎𝑑𝑖 respects to the credit risk associated with the target capital structure of company 𝑖 𝑇: corporate tax rate o 𝑤𝑒,𝑖 , 𝑤𝑑,𝑖 : equity and debt weights of company 𝑖’s estimated target capital structure  Weighted average cost of capital The 𝑟𝑤𝑎𝑐𝑐,𝑖 is constant through the estimation period Why? Because it represents the estimated cost of capital of the target capital structure. There is an underlying assumption of capital structure stability Alternatives: 1. Rolling WACC: adjust with the reference periodicity the 𝑟𝑤𝑎𝑐𝑐 , reflecting a dynamic capital structure and/or relevant changes in inputs 2. Adjusted Present Value (APV) model (which we are not going to study), that separates value of operations into two components: a) value of operations as if the company was all-equity financed b) value of tax shields that arise from debt financing Free Cash Flow Model BMW FCF Model construction: WACC estimation, Enterprise Value Lecturer: Gonçalo Faria School of Economics and Finance  BMW FCF Model This week activity: o Weighted average cost of capital (𝑟𝑤𝑎𝑐𝑐 ) estimation o Enterprise value estimation o Relative weight of the terminal value (𝑇𝑉) on the enterprise value Suggestions for students after this activity: “play” with the model by o Changing assumptions backing the estimation of different items of the 𝑟𝑤𝑎𝑐𝑐 o Changing assumptions backing the estimation of the TV and measure the sensitivity on the enterprise value Free Cash Flow Model Capital Structure and Value Lecturer: Gonçalo Faria School of Economics and Finance  Capital Structure and Value Two leading questions: 1. Do decisions regarding financing impact value? 2. If yes, what is the optimal decision regarding capital structure (from a value perspective)?  Capital Structure and Value Notation: 𝑉𝐿 : company value with leverage (debt) 𝑉𝑈 : company value without leverage 𝐵: interest bearing debt 𝑆: equity 𝑇: corporate tax rate 𝑟𝑒 : cost of equity 𝑟𝑑 : cost of debt 𝑟𝑤𝑎𝑐𝑐 : weighted average cost of capital. 𝑟𝑤𝑎𝑐𝑐 = 𝑤𝑒 𝑟𝑒 + 𝑤𝑑 𝑟𝑑  Capital Structure and Value Modigliani-Miller Propositions (1958) Assumptions: 1. ∄ taxes (T = 0) 2. ∄ transaction costs 3. individuals and companies borrow at the same rate Results: o Proposition I: 𝑉𝐿 = 𝑉𝑈 𝐵 o Proposition II: 𝑟𝑒 = 𝑟0 + 𝑟0 − 𝑟𝑑 𝑆 where 𝑟0 stands for cost of equity when there is no debt  Capital Structure and Value Proposition I: 𝑉𝐿 = 𝑉𝑈 Debt has no impact on the company/project value because: o there is no tax shield associated with debt service (interest) From assumption 1 o if 𝑉𝐿 > 𝑉𝑈 , the investor leverages at personal level, at the same rate at which the company leverages itself, to buy companies without debt. “Homemade” leverage offsets corporate leverage From assumptions 2 and 3  Capital Structure and Value Proposition II: 𝐵 𝑟𝑒 = 𝑟0 + 𝑟0 − 𝑟𝑑 𝑆 As long as 𝑟0 > 𝑟𝑑 , the cost of equity (𝑟𝑒 ) increases with debt because risk for equity increases with leverage However, note that in such context 𝑟𝑤𝑎𝑐𝑐 = 𝑟0 always!  Capital Structure and Value Cost of capital and capital structure (𝑇 = 0) 𝑅𝐵 = 𝑟𝑑 , 𝑅𝑆 = 𝑟𝑒 , 𝑅𝑊𝐴𝐶𝐶 = 𝑟𝑤𝑎𝑐𝑐  Capital Structure and Value Unrealistic assumptions supporting those propositions: o It is crucial to consider the existence of corporate taxes o It is necessary to consider costs associated with excessive leverage (e.g bankruptcy, reputational damage,...)  Capital Structure and Value Modigliani-Miller Propositions with Corporate Taxes: Assumptions: 1. 𝑇 ≠ 0 2. ∄ transaction costs 3. Individuals and companies borrow at the same rate Results: o Proposition I revised: 𝑉𝐿 = 𝑉𝑈 + 𝑇 × 𝐵 𝐵 o Proposition II revised: 𝑟𝑒 = 𝑟0 + 𝑟0 − 𝑟𝑑 1 − 𝑇 𝑆  Capital Structure and Value Proposition I revised: 𝑉𝐿 = 𝑉𝑈 + 𝑇 × 𝐵 Debt impacts the company value because: o there exists a tax shield related with the debt service (interest payment). Derives from assumption 1 𝑇 × 𝐵: tax shield associated with debt o in such context, the company value is maximized when all-debt financed!  Capital Structure and Value 𝐵 Proposition II revised: 𝑟𝑒 = 𝑟0 + 𝑟0 − 𝑟𝑑 1 − 𝑇 𝑆 As long as 𝑟0 > 𝑟𝑑 , cost of equity (𝑟𝑒 ) increases with debt because risk for equity increases with leverage However note that, in such context, as long as 𝑟0 > 𝑟𝑑 then 𝑟𝑤𝑎𝑐𝑐 < 𝑟0 → 𝑁𝑃𝑉 ↑(everything else constant)  Capital Structure and Value Cost of capital and capital structure (𝑇 ≠ 0) 𝑅𝐵 = 𝑟𝑑 , 𝑅𝑆 = 𝑟𝑒 , 𝑅𝑊𝐴𝐶𝐶 = 𝑟𝑤𝑎𝑐𝑐 Free Cash Flow Model Capital Structure and Value: optimal and target capital structure Lecturer: Gonçalo Faria School of Economics and Finance  Capital Structure and Value: Optimal Capital Structure In real-world, companies have more moderate levels of debt versus the theoretical result of 100% debt (MM II) In reality, there are costs associated with excessive financial leverage that impact the optimal level of leverage: o direct costs. Example: accounting and lawyer costs in case of bankruptcy o indirect costs. Example: Incentive towards underinvestment Incentive to accept projects with higher risk Impairs management activity (relation with clients, suppliers, etc...)  Capital Structure and Value: Optimal Capital Structure It therefore should exist an optimal level of debt 𝐵∗ such that: 1. The difference 𝑟0 − 𝑟𝑤𝑎𝑐𝑐 is maximized, i.e, 𝑟𝑤𝑎𝑐𝑐 is minimized  Capital Structure and Value: Optimal Capital Structure 2. The value of the company 𝑉 is maximized  Capital Structure and Value: Target Capital Structure For the strategic financing decision process, the target capital structure (TCS) concept is much more relevant than the optimal capital structure (OCS) o TCS: capital structure that is more adequate to support the business strategy o TCS is a long term target, defined by the company’s top management o TCS allows to separate financing decisions from capital budgeting decisions, eliminating the iteractive calculus  Capital Structure and Value: Target Capital Structure How to define TCS? No clear answer But there are some relevant factors to take into account Examples: o expected 𝐹𝐶𝐹 uncertainty: ↑ 𝐹𝐶𝐹 uncertainty => ↓ debt in the TCS o type of assets: ↑ % intangible assets => ↓ debt in the TCS links for e.g with loan-to-value (LTV) restrictions o Tax rate 𝑇: ↑ 𝑇 => ↑ debt in the TCS  Capital Structure and Value: Target Capital Structure How to implement TCS? Variable speed and variable ways For example through: o Recapitalization process (switch of funding sources) o Investment and divestment operations with specific funding solutions o Through the dividend policy  Capital Structure and Value: Target Capital Structure Regarding the fundamental valuation equation, the TCS is the relevant capital structure for the computation of 𝑟𝑤𝑎𝑐𝑐 , as it impacts: o 𝑟𝑒 , through 𝛽𝑒𝑞𝑢𝑖𝑡𝑦 o 𝑟𝑑 , through the credit risk spread o weights 𝑤𝑒 and 𝑤𝑑 Free Cash Flow Model Capital Structure and Value: empirical evidence Lecturer: Gonçalo Faria School of Economics and Finance  Capital Structure and Value: empirical evidence Evidence from real-world - three stylized facts 1. Most companies have low debt-asset ratios < 50% Estimated debt-equity ratios  Capital Structure and Value: empirical evidence Figure in previous slide shows that: o there exists a lot of variation in the average debt ratios among different European countries o companies do not seem to issue debt up to the point where tax shelters are fully used o this suggests that limits for debt issuance, namely financial distress costs, play a very important role More empirical evidence on this stylized fact: http://pages.stern.nyu.edu/~adamodar/  Capital Structure and Value: empirical evidence 2. Differences in the capital structures of different industries Average capital structure ratios  Capital Structure and Value: empirical evidence Table in previous slide shows that: o there are significant inter-industry differences in debt ratios (persistent over time) o debt/asset ratios tend to be low in high growth industries with large future investment opportunities, as healthcare and technology industries o industries with large investments in tangible assets, as real estate, tend to have higher leverage o there are differences in average industry capital structures across countries More empirical evidence on this stylized fact: http://pages.stern.nyu.edu/~adamodar/  Capital Structure and Value: empirical evidence 3. Most companies use target debt-equity ratios o a great percentage of companies across countries (except France) use target ratios o the strictness of those targets varies across companies and countries Free Cash Flow Model Enterprise and Equity Value Lecturer: Gonçalo Faria School of Economics and Finance  Enterprise and Equity Value Using the FCF model, the value of the company (assets) is given by: ∞ 𝐹𝐶𝐹𝑡 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒 = σ𝑡=1 1+𝑟𝑤𝑎𝑐𝑐 𝑡 How to obtain, from here, the equity value? Enterprise value - Net debt (= interest bearing debt – cash & equivalents) - Minority interests + Non-core assets (financial non-current items) = Equity Value  Enterprise and Equity Value Some notes: o All those balance sheet items (net debt, minority interests and non-core assets) should be estimates at the moment of valuation Example: if the valuation is at year-end 2022 then those items should be expected values at year-end 2022 o In case you are working with a simple model with no balance sheet estimation, the suggestion is to use the most recent reported values for those items (or mark-to-market if possible) o An alternative would be to use Equity Free Cash Flow model (out-of-scope of this module): cash flows are those available for equity holders and the discount rate is the cost of equity Free Cash Flow Model BMW FCF Model construction: Capital structure, Equity value Lecturer: Gonçalo Faria School of Economics and Finance  BMW FCF Model This week activity: o Impact of capital structure changes in the valuation outcome Tax shield associated with debt Credit risk perception: cost of debt Financial risk perception: cost of equity o Equity value estimation o Sensitivity of the valuation outcome towards changes in some critical variables Suggestions for students after this activity: o Revisit all steps of model construction and build-up your investment case from “A to Z” o (more ambitious) move towards a more detailed model, with balance-sheet and income statement estimation