Project financial evaluation on the context of Bosch Suppliers Club initiative

Universidade do Minho Escola de Economia e Gestão Pedro Martins Francisco Project financial evaluation on the context of Bosch Suppliers Club initiative October 2020 Project financial evaluation on the context of Bosch Suppliers Club initiative Pedro Martins Francisco UMinho | 2020 Pedro Martins Francisco Project financial evaluation on the context of Bosch Suppliers Club initiative Master’s Project Master in Finance Work supervised by Professor Benilde Maria do Nascimento Oliveira, PhD October 2020 i Direitos de autor e condições de utilização do trabalho por terceiros Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho. https://creativecommons.org/licenses/by/4.0/ ii Acknowledgements First, I would like to thank all the professors with whom I learned during these last years, specially to Professor Benilde Oliveira, for guiding me throughout this thesis. Also, to Bosch, for proposing this project and for allowing me to put into practice the knowledge I acquired over the past years. To my colleagues, for being a part of my daily life and for, they to, teaching me. And finally, to my family, for all the support, in everything, since always. iii Statement of Integrity I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. Universidade do Minho, 31st of October, 2020 Pedro Martins Francisco Signature: iv Título Avaliação Financeira de um projeto no contexto da iniciativa da Bosch “Clube de Fornecedores” Resumo O presente trabalho tem como objetivo responder a um problema identificado pela Bosch Car Multimedia. As empresas parceiras na iniciativa “Clube de Fornecedores”, apesar de revelarem boas capacidades técnicas e científicas, revelam poucos conhecimentos sobre análise financeira de projetos de investimento. Desse modo, fez-se uma análise financeira de um projeto entre a Bosch e uma empresa fornecedora hipotética, com o objetivo de criar um quadro de referência que qualquer empresa possa aplicar, de forma a avaliar os próprios projetos. Para isso, foi realizada uma análise à literatura sobre métodos de avaliação de projetos, tendo-se chegado à conclusão de que o método mais apropriado, tendo em conta a tipologia do projeto em avaliação, seria o Expected Net Present Value (ENPV). Prosseguiu-se fazendo uma análise à metodologia para estimar os inputs necessários ao ENPV. De seguida, fez-se a avaliação financeira do projeto, tendo o ENPV sido estimado em 349 177,10€, pelo que o projeto deve ser aceite. Para finalizar e a título complementar, realizou-se uma análise de risco, tendo os resultados apontado para a viabilidade financeira do projeto. Palavras chave Análise de risco, avaliação de projeto de investimento, Clube de Fornecedores, ENPV v Title Project financial evaluation on the context of Bosch Suppliers Club initiative Abstract The present work aims to answer a problem identified by Bosch Car Multimedia. The partner companies in the “Clube de Fornecedores” initiative, despite showing good technical and scientific skills, reveal little knowledge about financial analysis of investment projects. Thus, a financial analysis of a project was carried out between Bosch and a hypothetical supplier company, with the objective of creating a framework that any company can apply, to evaluate its own projects. For this, an analysis of the literature on project evaluation methods was carried out, and the conclusion reached was that the most appropriate method, considering the type of project being evaluated, would be the Expected Net Present Value (ENPV). We proceeded with an analysis of the methodology to estimate the necessary inputs of the ENPV. Then, the financial evaluation of the project was made, which returned an ENPV of 349 177,10€, which means that the project should be accepted. Finally and complementary, a risk analysis was carried out, with the results suggesting the financial viability of the project. Keywords Clube de Fornecedores, ENPV, investment project valuation, risk analysis vi Index Direitos de autor e condições de utilização do trabalho por terceiros ......................................................... i Acknowledgements ................................................................................................................................. ii Statement of Integrity ............................................................................................................................. iii Resumo ................................................................................................................................................. iv Abstract .................................................................................................................................................. v 1. Introduction ........................................................................................................................................ 1 1.1 Problem Presentation ................................................................................................................... 1 1.1.1 Objective ................................................................................................................................... 1 1.1.2 Bosch ........................................................................................................................................ 1 1.1.3 Suppliers Club ........................................................................................................................... 2 1.1.4 The supplier .............................................................................................................................. 3 1.1.5 The project ................................................................................................................................ 3 2. Thesis Structure .................................................................................................................................. 3 3. Framework for project evaluation......................................................................................................... 4 3.1 Discounted Cash Flow Model ........................................................................................................ 9 3.1.1 Cash flow Estimation ...........................................................................................................10 3.1.2 Discount Rate ......................................................................................................................11 4. Methodology .....................................................................................................................................15 4.1 The DCF Model...........................................................................................................................15 4.1.1 Cost of capital .........................................................................................................................15 4.1.1.1 Cost of debt .....................................................................................................................16 4.1.1.2 Cost of equity ...................................................................................................................16 4.1.1.2.1 The risk-free rate ...........................................................................................................17 4.1.1.2.2 Beta ..............................................................................................................................17 4.1.1.2.3 Risk Premium ...............................................................................................................20 4.1.2 Risk Analysis .......................................................................................................................22 5. Project Valuation ...............................................................................................................................25 5.1 Cost of capital ............................................................................................................................25 5.1.1 Cost of debt .............................................................................................................................25 5.1.2 Cost of equity ..........................................................................................................................25 5.1.2.1 Risk-free rate ....................................................................................................................26 5.1.2.2 Beta .................................................................................................................................27 5.1.2.3 Risk premium ...................................................................................................................30 5.2 Estimating the Cost of Capital .....................................................................................................33 5.3 Estimating cash flows .................................................................................................................34 5.4 Risk Analysis ..............................................................................................................................40 6 The book (or accounting) rate of return is calculated by dividing the estimated book income by the book value of the asset. The downside of using book values is that they are dependent on how the accountant treats these values. The fact that they can be arbitrarily classified means that they are prone to manipulation. A project’s payback period is calculated by counting the number of years it takes for the cumulative cash flow to equal the initial investment. When a company uses the payback rule the projects are accepted if the payback period is less than the specified cut-off period. If, for a certain project, the initial investment would take 4 years to recover, but the firm’s cut-off period is 3 years, the project would be rejected. The problems with the payback method are that it ignores all cash flows after the arbitrarily set cut-off date, and it dismisses the time value of money. There is an alternative to the payback period, called the discounted payback period. Under this approach, the cash flows are first discounted and only then the payback period is calculated. Even though this might seem a better method than the payback period, the truth is that it has the same problems as the previous method – the cut-off date is set arbitrarily and the cash flows are ignored after that date. In addition to that, both methods have a more fundamental problem. As we discussed earlier, the role of the financial manager is to maximize the current value of the firm’s stock. We then said that there are tools and methods that can be used to answer the question of whether a project will increase the value of the company. However, neither the payback nor the discounted payback period offers an answer to that question. Instead, they only provide information on the amount of time it will take to recover the initial investment. The internal rate of return (IRR) rule is to accept an investment project if the opportunity cost of capital is less than the internal rate of return. Because the IRR is the rate for which the project has a zero NPV, an opportunity cost of capital lower/higher than the IRR means that the project has a positive/negative NPV and, therefore, should be accepted/rejected. Even though this method sounds straight-forward, there are a few considerations to make. We will start by distinguishing between independent and mutually exclusive projects. An independent project is one whose acceptance or rejection does not depend on accepting or rejecting other projects. When two projects are mutually exclusive only one of them can be accepted, or both rejected. There are three problems that are common to both types of project. First, it is necessary to assess if the project is borrowing or lending in nature. If the first cash flow is negative (such as 7 the investment projects) it is a lending project. If the cash flow is positive it is a borrowing project. The implication is that for lending projects a high rate of return is desirable, while for a borrowing project the lower the rate the better. Second, the project might have multiple rates of return. In fact, there can be as many internal rates of return as there are changes in the sign of the cash flows. The sign changes when, besides the initial investment, it is expected that the company will have to make additional investments during the length of the project. Moreover, there are also cases in which no IRR exists – in such projects, every rate of return will yield a positive/negative NPV. Lastly, the IRR is hard to use when there are several different opportunity costs. If a project has multiples stages and there are different levels of risk associated with each stage, it is reasonable to discount the riskier cash flows at a higher rate. However, an immediate question comes up. To which of these rates should the IRR be compared with? The fact that there is no simple answer to this question illustrates the shortcomings of this rule. In addition to these three problems, there is one – a scale problem - that is specific to mutually exclusive projects. As an illustration, let us assume that there are two mutually exclusive projects, project A and B. We will say that project A has an IRR of 50% and an NPV of 5000€, while project B has an IRR of 100% but an NPV of 2500€. According to the IRR rule, project B should be selected. However, project A would be the one to maximize the company’s value, because of its higher NPV and should, therefore, be accepted. These four methods (NPV, book rate of return, payback and IRR) are used to help the decision-maker on deciding on whether a project should be undertaken. The answer they give is a binomial yes/no. If, however, the decision-maker needs quantitative data, only the NPV meets that demand. Damodaran (2012) proposes three possible approaches to asset valuation – the previously discussed NPV, relative valuation and contingent claim analysis. Note that when these methods are applied the result is an absolute quantitative value. When the Relative valuation is used, the value of an asset is estimated by comparing that asset to a similar one, relative to a common variable such as earnings, cash flow, book value or revenues. One example of this approach is the use of an industry-average price-earnings ratio to value a firm, following the assumptions that the other firms are comparable to the firm being valued and that the market, on average, prices these firms correctly. Unlike discounted cash flows 8 valuation methods, such as the NPV, which search for the intrinsic value, relative valuation depends on the market being right. Despite its appeal, there are a few considerations to make about relative valuation. This method works better when a large number of comparable firms are traded on financial markets, and the market is, on average, pricing these firms correctly. However, it is more difficult to use when firms have no obvious comparables, little or no revenues, and negative earnings. One other shortcoming of this method is that it builds on the assumption that the market is valuing the comparable firms correctly, but that is not always the case. In contrast, discounted cash flow valuation is based on firm-specific growth rates and cash flows, so it is independent of market errors in valuation. Contingent claim analysis use option pricing models to compute the value of options that share characteristics with the asset being valued. A patent, for instance, can be analysed as a call option on a product, with the investment being the strike price and the patent life becoming the time to expiration of the option. The main premise behind the use of option pricing models is that discounted cash flow models underestimate the value of assets that are dependent on future events, because they do not value the rights of expanding, abandoning or delaying an investment. There are, however, limitations in using option pricing models to value long-term options on nontraded assets. When the underlying asset is not traded, the inputs for the value of the underlying asset and the variance in that value cannot be extracted from financial markets and must be estimated. Also, some assumptions hold for the short-term, such as constant variance and dividend yields, but do not hold for the long-term. For both reasons, the values obtained from option pricing models have a great estimation error associated. While real options are not going to be used, it is true that one of the most consensual methods to value R&D projects is the Black-Scholes formula (Black & Scholes, 1973). Nonetheless, some authors argue that this technique is too complex for most of the managers to implement. Not only the formula is opaque to most, but also some of the assumptions, such as the lognormality of the volatility of stock prices, may not always be appropriate for describing R&D activities (Faulkner, 1996). An alternative method - the Expected Net Present Value (ENPV) - is used by several authors (Borissiouk & Peli, 2001); (Faulkner, 1996); (Kellogg & John, 2000). The ENPV is a discounted cash flow model, which means that for each period, it is necessary to estimate a cash 9 flow, that will be discounted by an appropriate rate. What differentiates the ENPV from the NPV is that, with this technique, the problem is modelled as a decision tree, where in each node the possible outcomes and their probabilities are defined. This approach has two advantages over Black-Scholes. First, the analysis is more visible and understandable, and therefore easier and more prone to implementation. Second, this methodology eliminates the need to use the log-normal distribution to describe uncertainty. In fact, uncertainty can be modelled most appropriately, depending on the case being analysed (Faulkner, 1996). Also, Faulkner (1996) demonstrated that decision tree valuation can yield the same valuation and results as the Black-Scholes formula. There are, however, a few aspects to take into consideration about the ENPV. The first is that it uses a constant discount rate. The risk associated with R&D projects is typically higher than the remaining activities carried out by the company. The riskiness of an R&D project is projectspecific, which means that a discount rate cannot be replicated using market proxies. In addition to that, different stages of the research project have different levels of risk. Using a unique rate for the entirety of the project not only ignores the fact that the project is different from the rest of the company but also different between its several stages (Borissiouk & Peli, 2001). Second, the ENPV assumes that if a stage is successful the company will automatically invest in the subsequent phase of the project. However, the reality is that such a decision is not automatic because there are factors that might make the company ponder, such as unfavourable economic evolutions. The firm can choose to delay, to contract or even to abandon the project (Borissiouk & Peli, 2001). Lastly, the decision trees can become too big if the project has many options and uncertainties, which defeats the purpose of clarity (Faulkner, 1996). To value Company A’s investment project, the ENPV is going to be used. The reason is that it combines the positive aspects of the NPV with the ability to model the problem considering uncertainty. 3.1 Discounted Cash Flow Model As we said earlier, the ENPV is a discounted cash flow model. In this section, we will explore the two key aspects of discounted cash flow models: the cash flows and the discount rate. 10 3.1.1 Cash flow Estimation When the accounting measure of income in a project is used, the returns are measured using accounting principles and standards, while the cash flow generated by a project is measured as the difference between the cash inflows and the cash outflows. According to Damodaran (2014), cash flows are superior to accounting earning to measure true return on investment. Three arguments lead to this conclusion. The first factor is how accounting distinguishes between operating expenses and capital expenses. The difference between the two is that operating expenses, such as labour and materials costs, yield benefits only in the immediate period, while capital expenditure, such as land and buildings, have their benefits spread over multiple periods. Under accounting rules, operating expenses are subtracted from revenues when computing the accounting income, whereas capital expenses are spread over multiple periods and deducted, in each period, as an expense, called depreciation or amortization. This distinction leads to the second argument in favour of cash flows. Depreciations and amortizations are not a cash expense but, despite that, reduce the accounting income. In fact, due to their impact on the income, they have a positive impact on cash flows. This is because depreciations and amortizations reduce the taxable income, and, consequently, the taxes paid by the company, which are a cash outflow. The third and final factor is how and when revenue and expenses are recognized. The accrual system of accounting means that revenues and expenses are recognized when the sale/payment is made, rather than when the cash is received/paid. Consequently, accrual revenues/expenses can be very different from cash inflows/outflows. These differences between accrual earnings and cash earnings can be captured by changes in the non-cash working capital. A decrease in non-cash working capital will increase cash flows, whereas an increase will decrease cash flows. These three factors can lead to significant deviations between accounting earnings and cash flows. We can, however, calculate the cash flows using the after-tax operating earnings. To do this, all noncash charges, such as depreciations, are added back to the operating earnings. Then, all cash outflows that represent capital expenditure are subtracted out. Last, we must net out the effect of changes in non-cash working capital, that is changes in accounts receivable, inventory, and accounts payable. Therefore, we have that: 11 𝐶𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑡𝑜 𝑓𝑖𝑟𝑚 (𝐹𝐶𝐹𝐹)= =𝐸𝐵𝐼𝑇× (1 − 𝑡) + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑎𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 − 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑛𝑜𝑛𝑐𝑎𝑠ℎ 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑐𝑎𝑝𝑖𝑡𝑎𝑙− 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 (1) The bottom-line argument for the use of cash flows is very straightforward. A project with positive earnings and negative cash flows will drain the business out of cash. Conversely, a project with negative earning but positive cash flows will generate cash for the business. According to Ross, Westerfield, Jaffe, & Jordan (2015), there are a few important considerations to bear in mind. When analysing a project, the most important question is if that project will make the entire firm more valuable. In that sense, only the incremental cash flows, that is, the cash flows that occur as a direct consequence of accepting the project, matter. Therefore, the cash flows generated by the firm, whether the investment is accepted or rejected, should be ignored. There are, however, a few pitfalls that must be avoided, when estimating incremental cash flows. A sunk cost is a cost that occurred before accepting or rejecting the project and, for that reason, cannot be changed by that decision. Also, there may exist opportunity costs, that is, it is possible that the company, by accepting the project, will be forgoing opportunities of using assets that would generate revenues. Because the lost revenues are a direct consequence of accepting the project, they can be viewed as a cost. In addition to these costs, there are side effects to consider. They can be divided into two groups – synergy or erosion. Synergy occurs when a new project increases the cash flows of existing projects, while erosion has the opposite effect. Therefore, when building the model, sunk costs should be ignored, but opportunity costs, synergies and erosion must be considered. 3.1.2 Discount Rate According to Ross, Westerfield, Jaffe, & Jordan (2015), when the firm has extra cash it has two alternatives. It can pay out the cash directly to its investors or the firm can invest in a project, paying out the future cash flows that the project will generate. From the investors' point of view, which of the alternatives is preferable? If the investor can reinvest the cash in a financial asset with the same risk as that of the project, the most desirable alternative is the one with the higher 12 expected return. For the firm, this means that the project should only be undertaken if its expected return is greater than that of a financial asset of comparable risk. In other words, the discount rate of a project should be the expected return on a financial asset of comparable risk. Note that this is only true when the firm is financed exclusively with equity. However, the discount rate for a firm with a capital structure that includes both equity and debt can be easily computed if we can calculate the cost of the firm’s equity. As we said earlier, the cost of equity is equal to the highest expected return for an asset with a risk similar to the project. However, a problem arises – what is the required rate of return for a certain level of risk? Fortunately, the Capital Asset Pricing Model (CAPM) can be used to estimate that rate. According to DeMarzo & Berk (2017), under the CAPM, investments have a similar risk if they have the same sensitivity to market risk, as measured by their beta with the market portfolio. The market portfolio is a well-diversified, efficient portfolio representing the nondiversifiable risk in the economy. Therefore, the cost of equity of any investment opportunity equals the expected return of available investments with the same beta. This can be translated to the following formula: 𝑅𝐸=𝑅𝑓+𝛽×(𝑅𝑚−𝑅𝑓) (2) Where 𝑅𝐸 is the cost of equity, 𝑅𝑓 is the risk-free rate, 𝛽 is the beta of the project and (𝑅𝑚−𝑅𝑓) is the market risk premium. We will now discuss the case of when the companies are financed with both debt and equity. When that is the case, the total cost of capital is given by the Weighted Average Cost of Capital (WACC): 𝑊𝐴𝐶𝐶=𝑟𝐷×𝐷 𝑉+𝑟𝐸×𝐸 𝑉 (3) Where 𝑟𝐷 is the cost of debt, D is the amount of debt in the firm’s balance sheet, E is the value of equity, V is the sum of debt and equity and 𝑟𝐸 is the cost of equity. What the formula means is that the firm’s total cost of capital is given by a weighted average between the cost of 13 debt and the cost of equity. The weights are given by the percentage that both debt and equity represent in the total capital structure of the company. Note that if the firm has no debt then the cost of capital will be equal to the cost of equity. The same is true for the cost of equity – if the company has so much debt that the equity becomes worthless, the cost of capital will be equal to the cost of debt (Ross, Westerfield, Jaffe, & Jordan, 2015). This should make us ponder about what is the optimal capital structure, that is, how much debt should a company have. According to the trade-off theory, as presented by DeMarzo & Berk (2017), the total value of a levered firm (𝑉𝐿) equals the value of the firm without leverage (𝑉𝑈) plus the present value of the tax saving form debt, less the present value of financial distress costs: 𝑉𝐿=𝑉𝑈+𝑃𝑉(𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑)−𝑃𝑉(𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝐷𝑖𝑠𝑡𝑟𝑒𝑠𝑠 𝐶𝑜𝑠𝑡) (4) It is said that debt has a tax shield effect because corporations must pay taxes on the income they earn. Because they pay taxes on their profits after interest payments are deducted, interest expenses reduce the amount of corporate tax firms must pay. Even though with high debt its earnings will be lower, the value of the company will be higher because its value is equal to the total amount it can raise from all investors, not just equity holders. On the other hand, the debt level will influence the financial distress costs. Three factors determine the present value of financial distress costs: the probability of financial distress, the magnitude of the costs if the firm is in distress and the appropriate discount rate for the distress costs. The probability of financial distress depends on the amount of a firm’s liabilities relative to its assets – the higher this ratio the higher the likelihood that the firm will not be able to meet its debt commitments and therefore default. Note, however, that different companies can afford to maintain different levels of debt. For example, a firm with steady cash flows can have higher debt levels when compared to firms with very volatile cash flows. The magnitude of the costs if the firm is in distress will, again, change depending on the firm and on what industry that firm operates in. For instance, firms whose value comes largely from human capital are likely to incur high costs when they risk financial distress, due to the need to retain key personnel and the lack of tangible assets that can easily be sold. 14 Finally, the discount rate for the distress costs will depend on the firm’s market risk. Because distress costs are high when the firm does poorly, the beta of distress costs will have an opposite sign to that of the firm. Also, the higher the firm’s beta, the more likely it will be in distress in an economic downturn, and thus the more negative the beta of its distress costs will be. Because a more negative beta leads to a lower cost of capital (below the risk-free rate), ceteris paribus the present value of distress costs will be higher for high beta firms. We can now reach a conclusion about the optimal capital structure of a company. According to the trade-off theory, debt has two opposite effects on the company’s value – in one hand it creates a tax shield, but in the other, it also creates financial distress costs. Therefore, according to the trade-off theory, the firm should increase their leverage until it reaches a level where the tax savings are just offset by the increased probability of incurring the costs of financial distress (DeMarzo & Berk, 2017). 15 4. Methodology In this section, we will take the theoretical framework one step further, by discussing how we will estimate all the necessary inputs. 4.1 The DCF Model The ENPV is, in its essence, a DCF model. The discounted cash flow models calculate the value of any asset by estimating the present value of its cash flows (Brealey, Myers, & Allen, 2011). That is: 𝑉𝑎𝑙𝑢𝑒=∑ 𝐶𝐹𝑡 (1+𝑟)𝑡 𝑡=𝑛 𝑡=0 + 𝑃𝑉𝐻 (1+𝑟)𝑛 (5) Where n is the lifetime of the asset, 𝐶𝐹𝑡 is the cash flow in period t, 𝑃𝑉𝐻 is the terminal value, r represents the discount rate and 𝑛 is the time horizon of the project. Therefore, to calculate the value of the project, it is going to be necessary to estimate a proper discount rate and the cash flows that the project will generate. 4.1.1 Cost of capital As we discussed earlier, the discount rate is the firm’s cost of capital. We also said that the cost of capital is a blend of the cost of equity and the cost of debt, which can be calculated using the weighted average cost of capital (WACC). Because the values of debt and equity add up to overall firm value, the after-tax WACC is 𝑊𝐴𝐶𝐶=𝑟𝐷×𝐷 𝑉×(1−𝑡𝑐)+𝑟𝐸×𝐸 𝑉 (6) 22 relative standard deviation methodology. The other two require the use of a country sovereign bond, however, as we will see in chapter 5, the market index we chose covers several European countries and there is no bond issued by this set of countries. For that reason, there are no bonds that suit the needs of these two methodologies. The relative standard deviation rationale is that the equity risk premiums of markets should reflect the differences in equity risk, as measured by the volatility of the stock prices. If the standard deviation of two different markets is compared, we get a measure of relative risk (Damodaran, 2014). 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑋 =𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑋 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑌 (14) The relative standard deviation multiplied by the premium of a base country (country Y) should yield a measure of equity risk premium (ERP) for any market. 𝐸𝑅𝑃𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑋 =𝑅𝑖𝑠𝑘 𝑃𝑟𝑒𝑚𝑖𝑢𝑚𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑌 × 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑋 (15) Even though this approach has an intuitive appeal, it should be used with caution when the markets are widely different. For instants, there are very risky emerging markets that have low standard deviations for their equity markets because the markets are illiquid. Thus, this approach would understate the equity risk premiums in those markets (Damodaran, 2014). 4.1.2 Risk Analysis Up until this point, we have made an argument in favour of discounted cash flow models. We said that their superiority came from the fact that they use cash flows instead of profits and they discount these cash flows properly. One could think, therefore, that a high positive expected net present value is a sufficient condition to accept the project. In reality, it would be reckless to assume that that is true. Because these models are dependent on projections, when the project starts, it may become evident that many of those forecasts were wrong. Depending on how far apart from reality they are, the expected net present value may be significantly different from the projections. For this reason, it is fundamental to perform a risk analysis. By using different risk 23 analysis methodologies, one can get a more realistic perspective on the possible outcomes of the project. We will, therefore, proceed by going through several of these methodologies, as described by Ross, Westerfield, Jaffe, & Jordan (2015). The first method we will explore is sensitivity analysis. Sensitivity analysis breaks the NPV calculation into several variables and shows how the NPV varies as the underlying assumptions change. This analysis reveals the critical variables, that is, which of the assumptions have a major impact on the NPV. By identifying the critical variables, we can invest further resources to refine the projections of these variables, which will reduce the estimation risk. To calculate the NPV, the company must make estimations about variables such as quantities to be sold, price levels and both variable and fixed costs. To perform the sensitivity analysis, the firm’s analysts would make a forecast, for each of these variables, based on a pessimistic, an expected/most likely, and an optimist scenario. Then, the NPV would be calculated for all three possibilities of a single variable, along with the expected forecast for all other variables. This means that the company would calculate an NPV using the pessimist scenario for the sales quantities while maintaining the expected scenario for all other variables. After that, the NPV would be calculated using the pessimist scenario for the price and the expected scenario for all other variables. This process should be repeated until there is an NPV for each of the variables for every scenario. This analysis allows the managers to understand the behaviour of the NPV when each of the variables change. For instance, if, after conducting the analysis, the NPV values on the pessimistic scenario were highly negative and all the values in the optimist scenario were highly positive, it could be concluded that the project is very sensitive to changes on the forecasted variables. If, however, the sensitivity analysis shows that only a few variables are critical, it gives useful information to the managers. For instance, if the sensitivity analysis shows that the NPV is highly sensitive to selling price changes, but not so much to costs changes, more information about the factors that determine price changes might be needed. The reason is that the effect of an incorrect estimate for the selling price will be much greater than the effect of incorrect estimates on costs. This information is useful because it allows the managers to focus on the critical variables and to consequently reduce the estimation errors. There are, however, a few drawbacks to keep in mind. For example, sensitivity analysis may increase the false sense of security among managers. If the NPV values in the pessimist 24 scenario are positive one could be led to think that the project is a sure money-maker. Of course, the truth is that the scenarios are also forecasts, so, in that case, the forecasters were probably not pessimist enough. An additional drawback is how the analysis treats each variable in isolation when, in reality, the different variables are related. For example, if the market is not as receptive to a product as expected both the quantities and the price will be affected simultaneously. The second method we will be using is Monte Carlo simulations. When we reviewed the sensitivity analysis method, we considered the effect of changing one variable at a time. That means that we could only analyse a limited number of possible outcomes. Monte Carlo simulations, however, allow studying the impact of changing multiple variables at a time, while considering the relations between these variables (Brealey, Myers, & Allen, 2011). This is achieved by assigning distribution probabilities to each of the variables that underlie the cash flows. Then, the simulations are run thousands of times. In each simulation, an outcome from each distribution is drawn and the present value is estimated based on those draws. The result is a distribution of the expected value of the project (Damodaran, 2012). What this means is that, while sensitivity analysis answered the question “What if?”, the Monte Carlo simulation, calculates, instead, the probability of a specific scenario to happen. As Damodaran (2012) states, even though Monte Carlo simulations are very informative there are a few key issues that should be considered when performing simulations. The first one is that the distributions chosen for the inputs should be based on analysis and data. The outputs of the simulation will only be as good as the inputs. A second problem is that real-world data does not always fit a probability distribution. In those cases, using a probability distribution that has little resemblance to the true distribution of an input variable will yield misleading results. Lastly, even when the data fits a statistical distribution there is no guarantee that a future shift in the market will also shift the statistical distributions. Ideally, the probability distributions should be forwardlooking, but, due to the difficulty in estimating them, that is rarely done. Diagram 2 represents a summary of the framework we have been discussing and that we will be using to calculate the ENPV. 25 5. Project Valuation In this section, we will apply the previously reviewed methods to Company A’s project. First, the cost of capital will be calculated, which will be proceeded by the cash flows estimation. We will then calculate the value of the ENPV. The section will be concluded with a risk analysis. 5.1 Cost of capital As we previously mentioned, to calculate the cost of capital we need to estimate the cost of debt and the cost of equity. The mixture of the two, weighted by the capital structure of the firm will return the opportunity cost of capital. 5.1.1 Cost of debt Ideally, the cost of debt is obtained directly from the company, by looking at the most recent borrowing history. Because that was not possible, because we are not using a real company, we will use the cost of debt Damodaran (2020b) estimated for auto & parts European companies: 3.96%. 5.1.2 Cost of equity Diagram 2 – Framework Structure ENPV Discount Rate Cost of Capital Cost of Debt Cost of equity Risk-free Rate Beta Risk Premium Free Cash Flows EBIT * (1-t) Changes in Working Capital Depreciations Capex 26 As we stated before, to estimate the cost of equity three variables are needed – the riskfree rate, the beta and the risk premium. 5.1.2.1 Risk-free rate Under periods of high and unstable inflation, government-issued bonds might be risk-free in nominal terms, but not in real terms. A standard approach to estimate the real risk-free rate is to subtract the inflation rate from the nominal riskless rate (Damodaran, 2014). Nevertheless, in the period under analysis, we expect the inflation rate to be low and stable. In addition to that, all values used will be in nominal terms, so the nominal risk-free rate is going to be used. The risk-free rate that is going to be used is the Euro-area Aaa rated bonds, issued in the 1st of November 2019 (the day the model is being built), with twelve-years to maturity. The rate is, therefore, -0,2444% (European Central Bank, 2020). The scenario of having long term negative risk-free rates is still a novelty and there is no consensus on its meaning and long-term impacts. Damodaran (2020c) discussed the use of negative rates in the context of valuation and corporate finance. According to the author, there are three ways of dealing with negative rates: we can switch currencies, we can normalize the rate, by calculating average rates across long periods of time or we can leave the rates negative. Switching currencies has the downside that, at some point in time, the alternative currency will possibly also have negative rates. By normalizing rate, three issues arise. The first is the period to choose to calculate the average and the second is that it is fundamental to be rigorous with how the normalized rate is estimated, as it influences the investment decisions. The third is that using a high normalized risk-free rate with high equity risk premiums, that are prevalent today, will lead to too high a hurdle rate. According to Damodaran, the more reasonable solution is to leave the risk-free rate negative. The fact that this rate is rarely used alone, but only in conjunction with a risk premium means that if we can update the risk premium it may offset the impact of using a negative risk-free rate. Note that small negative rates (-0,25% to -0,50%) also have small mathematical consequences. 27 5.1.2.2 Beta The conventional approach for estimating betas is using historical market data. In this method, the correlation between the market excess returns and the company’s excess returns is calculated. The slope of the regression is the beta of the company, which measures the riskiness of the stock. For private companies such as Company A, however, this approach is not possible, because the company is not publicly traded, which means that there is no stock price information. Thus, the bottom-up betas approach, as suggested by Damodaran (2014), will be used. The first step is to identify a group of publicly traded comparable firms. To do this, first, we had to identify the business area where Company A operates. According to Amadeus, the industry codes where the firm operates are “Primary code: 22292 - Manufacture of other plastic products, n. e. c.” and the “Secondary code(s): 29320 - Manufacture of other parts and accessories for motor vehicles.” Using Amadeus, we identified a group of ten companies that operate in the same industry as Company A, are publicly traded and operate on the Euro-28 area. To increase the number of comparable firms, a different database was also used. Using Thompson Reuters DataStream, and filtering by companies in the auto & parts industry, the final number of comparable firms was increased to forty-four. The next step is to estimate the levered betas for each of the identified companies. To do so, using Thomson Reuters DataStream, we downloaded the price information (total return index) and calculated the returns. The selected period was the earliest available in the database, which was the 29th, December 2000 and the frequency was daily. Afterwards, we followed the same procedure with the market index. The index chosen was the STOXX Europe 600. The index covers the 600 largest companies in Europe and is weighted according to free-float market capitalization (STOXX Index Methodology Guide (Portfolio Based Indices), 2019). After that, we downloaded the historical yield to maturities of three-month German bonds, which will be used as the risk-free asset. The period was the same used for the risky assets - between the 1st of January 2001 and the 1st of November 2019. Because the yields are in annual terms, but the data is daily, we must transform the annual rates in daily rates. To do that we used the following formula: 𝐷𝑎𝑖𝑙𝑦 𝑟𝑎𝑡𝑒=(1+𝑟𝑖)(1∕365)−1 (16) 28 Where 𝑟𝑖 is the annual rate, in period 𝑖. We proceeded by estimating the excess returns for each period. To do that, for each period, we subtract the risk-free to the daily return rates of both the risky assets, which gives us the excess returns of the market and the excess returns of the firms. With the excess returns of both the index and the companies calculated it was possible to compute the levered betas for each of the companies, by performing a regression between the market index excess returns and the firms’ excess returns. The results were that the average beta is 0.7923 and the median beta is 0.7789. This regression produced an average 𝑅2 of 16.28% and a median 𝑅2 of 12.74 %, which means that market risk, on average, explains only 12.74% of the variance in auto & parts companies’ returns. Even though we now know the levered betas, what we need is the unlevered betas. The difference is that the first measures both the market risk and the firm-specific risk, while the second only measures the market risk. We will follow the methodology proposed by Damodaran (2014). To calculate the unlevered beta for the sector, we started with the median levered beta and we corrected it for the median debt-to-equity industry ratio and for the median cash balance. To be able to do that, the total debt, common equity, cash and enterprise values for each of the companies was downloaded from DataStream and Amadeus. Due to the tax shield effect of debt, the tax rates for each of the origin countries of each of the companies are also needed. This data was retrieved from Damodaran website (Damodaran, 2020a). The unlevered beta, corrected for the debt-equity ratio is given by: 𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝑏𝑒𝑡𝑎 (𝐷 𝐸 ⁄ 𝑟𝑎𝑡𝑖𝑜)= =𝑚𝑒𝑑𝑖𝑎𝑛 𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝑏𝑒𝑡𝑎 (1+(1 − 𝑚𝑒𝑑𝑖𝑎𝑛 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒)(𝑚𝑒𝑑𝑖𝑎𝑛 𝐷 𝐸 ⁄ 𝑟𝑎𝑡𝑖𝑜)) (17) 𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝑏𝑒𝑡𝑎 (𝐷 𝐸 ⁄ 𝑟𝑎𝑡𝑖𝑜)=0,7789 (1+(1−30%)(0,8734))=0,4834 (18) The unlevered beta, corrected for cash is given by: 29 𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝑏𝑒𝑡𝑎 (𝑐𝑎𝑠ℎ)=𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝑏𝑒𝑡𝑎 (𝐷 𝐸 ⁄ 𝑟𝑎𝑡𝑖𝑜) (1 − 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑎𝑠ℎ 𝑏𝑎𝑙𝑎𝑛𝑐𝑒) (19) 𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝑏𝑒𝑡𝑎 (𝑐𝑎𝑠ℎ)=0,4834 (1−13,41%)= 0,5582 (20) Finally, Company A’s levered beta is calculated by levering the unlevered beta corrected for cash. This is achieved by using Company A’s debt/equity ratio and tax rate. For the cash balance, it was assumed that it was equal to the market’s. Company A’s levered beta is, therefore: 𝐶𝑜𝑚𝑝𝑎𝑛𝑦 𝐴′𝑠 𝐿𝑒𝑣𝑒𝑟𝑒𝑑 𝑏𝑒𝑡𝑎=0,5582[1+(1−0,21)(2,4529)]=1,63986 (21) There is, however, a final consideration. Under CAPM, it is assumed that risk in an investment is risk as perceived by a well-diversified investor. Also, risk has to be measured from the perspective of a marginal investor. Thus, under CAPM, only the risk that an investment adds on to a well-diversified portfolio should be compensated. Risk can, therefore, be broken down into two components: a market component, that is common to all companies that operate on that market and a firm-specific component that only affects that investment. Because only the market component is non-diversifiable, only that component should be rewarded (Damodaran, 2014). For the owner of a private firm, however, this assumption is not very reasonable, because generally, the company represent a major part of his/her wealth. Therefore, the analysis must be done not with the perspective of an average investor, but from the perspective of the company owner. Consequently, what we must calculate is a beta for the total risk of the business rather than just the market risk. According to Damodaran (2014), the total risk beta is calculated by dividing the market beta by the square root of the average 𝑅2, because the 𝑅2 of the regression measures the proportion of the variance that is market risk. That is: 𝑇𝑜𝑡𝑎𝑙 𝐵𝑒𝑡𝑎=𝑀𝑎𝑟𝑘𝑒𝑡𝐵𝑒𝑡𝑎 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 ⁄𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 (22) This means that the total beta of Company A is 4.02821. 30 𝑇𝑜𝑡𝑎𝑙 𝐵𝑒𝑡𝑎=𝑀𝑎𝑟𝑘𝑒𝑡 𝐵𝑒𝑡𝑎∕ √𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅2 (23) 𝑇𝑜𝑡𝑎𝑙 𝐵𝑒𝑡𝑎=1.63986 √16.28% ⁄=4.06409 (24) 5.1.2.3 Risk premium To calculate the risk premium, three different approaches are going to be used – geometric average returns, arithmetic average returns, and relative standard deviation. The first step to estimate the risk premium was to download the yearly prices and dividend yields for both the S&P 500 index and the STOXX 600 index. The earliest dates available on DataStream were used. Regarding the prices, for the S&P 500, there are fifty-five years available, from 1963 to 2018, while for the STOXX 600 there are thirty-two years available, from 1986 to 2018. However, the dividend yield information is scarcer. For the S&P 500, the dividend yields were obtained from Damodaran website (2020d) for the period between 1963 and 2018. For the STOXX 600, however, DataStream only has information on the dividend yields for the period between 2000 and 2018. Therefore, the returns will only be calculated for that period. To calculate them we used the following formula: 𝑅𝑒𝑡𝑢𝑟𝑛𝑠𝑁=𝑉𝑎𝑙𝑢𝑒𝑁+ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑁−𝑉𝑎𝑙𝑢𝑒𝑁−1 𝑉𝑎𝑙𝑢𝑒𝑁−1 (25) Where 𝑉𝑎𝑙𝑢𝑒𝑁 and 𝑉𝑎𝑙𝑢𝑒𝑁−1 corresponds to the stock value in period N and N - 1, respectively and 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑁 is the dividend value, paid in period N. The dividend value for each period was calculated by multiplying the price by the dividend yield. Afterwards, the average arithmetic yearly returns for the STOXX 600 index were calculated using the formula: 𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑅𝑒𝑡𝑢𝑟𝑛=1 𝑛∑𝑎𝑖 𝑛 𝑖=1 =𝑎1+𝑎2+⋯+𝑎𝑛 𝑛 (26) 31 Where 𝑎𝑖 are the returns in period 𝑖 and 𝑛 is the number of periods. The same procedure was followed to compute the geometric average returns, but the formula used was: 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑒𝑡𝑢𝑟𝑛=[∏(1+xi) n i=1 ]1 n (27) Where n corresponds to the number of periods and xi is the return in period i. With the returns of the risky asset calculated, we proceeded by calculating the returns of the risk-free asset. To do so, we started by downloading the yields to redemption of 10-year to maturity German and US government bonds, with a yearly frequency. To calculate the returns, we applied the formula: 𝑅𝑁=(𝑌𝑁×(1−(1+𝑌𝑁+1)−𝑀 𝑌𝑁+1 )+ 1 (1+𝑌𝑁+1)𝑀−1)+𝑌𝑁 (28) Where 𝑌𝑁 is the yield to redemption on period N, 𝑌𝑁+1 is the yield to redemption on period N+1, and M is the maturity of the bond. According to Damodaran (2020d), the return on a constant maturity bond is computed by adding two components - the promised coupon at the start of the year and the price change due to interest rate changes. After computing the returns for each period, the arithmetic and geometric average returns are calculated the same way as we did for the market indexes. The results are presented in tables 1 and 2. Geometric Average Returns S&P 500 Index 9,76% US 10-year bond 6,36% STOXX 600 Index 2,12% German 10-year bond 5,78% Table 1 – Geometric Average Returns, for the American and European markets . Arithmetic Average Returns S&P 500 Index 11,07% US 10-year bond 6,75% STOXX 600 Index 4,19% German 10-year bond 5,98% Table 2 - Arithmetic Average Returns, for the American and European markets. With the average arithmetic and geometric returns for both the market index and the riskfree assets determined, it was possible to estimate the risk premium for the American and 38 Free Cash Flow (Values in €) Period 2020 2021 2022 2023 2024 2025 2026 202 2028 2029 2030 2031 2032 Sales 0 0 0 0 0 500 000 750 000 1 125 000 1 687 500 2 531 250 3 796 875 5 695 313 5 695 313 Growth Rate 50,00% 50,00% 50,00% 50,00% 50,00% 50,00% 0,00% COGS 0 0 0 0 0 250 000 375 000 562 500 843 750 1 265 625 1 898 438 2 847 656 2 847 656 SG&A 104 850 105 659 106 475 107 300 108 133 397 883 401 623 405 399 409 211 413 064 416 956 420 884 424 853 Inv./Desinv. In Working Capital 5 172 1 173 23 24 24 -92 513 14 378 -43 173 -64 812 -97 272 -145 962 -218 999 114 Depreciations & Amortizations 2 500 2 500 2 500 2 500 2 500 96 250 96 250 96 250 93 750 93 750 93 750 93 750 93 750 EBIT * (1 – Tax Rate) -84 807 -85 445 -86 090 -86 742 -87 400 -192 865 -97 070 48 072 269 223 599 461 1 096 308 1 843 087 1 839 952 Capex -20 000 0 0 0 0 -750 000 0 0 0 0 0 0 0 Free cash flow -97 135 -81 772 -83 567 -84 218 -84 876 -939 128 13 558 101 149 298 161 595 939 1 044 096 1 717 839 1 933 816 Table 11 - To calculate the free cash flow we had to first estimate the sales for the first year and a growth rate for the following years. We also estimated the operational margin and the SG&A costs. After that, based on estimated investment in working capital, depreciations and invested capital we were able to compute the free cash flow. 39 Expected Net Present Value (Values in €) Discount Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 8,60% 2020 2021 2022 2023 2024 2025 2026 202 2028 2029 2030 2031 2032 Possible Outcomes -97 135 -81 772 -83 567 -84 218 -84 876 -939 128 13 558 101 149 298 161 595 939 1 044 096 1 717 839 1 933 816 0 0 0 0 0 0 0 0 0 Probability of Bad Outcome 0% 0% 0% 0% 50% 0% 0% 0% 0% 0% 10% 10% 10% Cumulative Cash flow 349 177 484 716 615 232 758 929 1 831 395 2 081 161 3 280 176 3 547 701 3 743 118 3 741 386 3 795 671 3 320 379 1 933 816 ENPV 349 177 Table 12 – Calculation of the Expected Net Present Value (ENPV). The ENPV is computed by considering different possible outcomes, and their probabilities. Decision Tree Representation (€) 0 1 2 3 4 5 6 7 8 9 10 11 12 Table 13 – Visual representation of the possible outcomes and their value. 349 177 484 716 615 232 758 929 1 831 395 2 081 161 3 280 176 3 547 701 3 743 118 3 741 386 3 795 671 3 320 379 1 933 816 0 0 0 0 40 5.4 Risk Analysis In the previous section, we estimated the cash flow associated with the investment project under analysis. Because they are only, in the best of cases, reasonable estimations, there is great uncertainty that the values used represent the project accurately. Even if this was not the case, the future is always uncertain and, therefore, any estimation invariably carries that uncertainty. Although we cannot make that fact disappear, there are tools that allow measuring how sensible our project is to that uncertainty. A simple tool we can use is the sensitivity analysis. The objective of doing this analysis is to measure how sensitive the NPV is to changes in underlying assumptions. The usefulness of this analysis is that it allows to better manage the operations and the risks of an investment, after the acceptance phase (Damodaran, 2014). To perform a sensitivity analysis of our project, we started by defining the key variables of the project – Sales, Sales Growth Rate, Variable Costs (Gross Margin), SG&A costs and likelihood of success. After that, we established three scenarios – an expected, an optimistic and a pessimistic. The optimist and the pessimist scenarios were 50% better and worse, respectively, than the base scenario. Then, for each of the scenarios, we changed one variable at a time, while maintaining everything else constant. Note that the fixed costs are set relative to the expected scenario, that is, they are 100% in the base scenario and 50 p.p. higher/lower in the optimist/pessimist scenario. The result of this analysis is presented in tables 14 and 15, and graph 1 offers a visual representation. Scenarios Variable Pessimist Expected Optimist Sales 250 000 € 500 000 € 750 000 € Sales Growth Rate 25% 50% 75% Variable Costs 75% 50% 25% SG&A Costs 150% 100% 50% Likelihood of success 25% 50% 75% ENPV Variable Pessimist Expected Optimist Sales - 479 589 € 349 177€ 1 187 887 € Sales Growth Rate - 523 789 € 349 177€ 2 095 001€ Variable Costs - 479 589 € 349 177€ 1 005 240 € SG&A Costs - 119 492 € 349 177€ 638 569 € Likelihood of success 22 509,88 € 349 177€ 619 725 € Table 14 – Scenarios and variables used in the sensitivity analysis Table 15 – The results of the sensitivity analysis. 41 Graph 1 – Visual representation of the sensitivity analysis Graph 2 - Visual representation of how critical the variables are As we can see, because the ENPV is sensitive to the sales, sales growth rate, variable costs, and SG&A costs these are the critical variables. They are critical because if the pessimist scenario €(1 000 000,00) €(500 000,00) €-€500 000,00 €1 000 000,00 €1 500 000,00 €2 000 000,00 €2 500 000,00 Sales Sales Growth Rate Variable Costs SG&A Costs Likelihood of success Discount Rate Sensitivity Analysis Pessimist Optimist €(750 000) €(250 000) €250 000 €750 000 €1 250 000 €1 750 000 €2 250 000 -50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% Sensitivity Analysis Sales Sales Growth Rate Variable Costs SG&A Costs Likelihood of success 42 occurs in any of these variables the ENPV is negative, while the opposite is also true, that is, if the optimist scenario happens the ENPV will be significantly higher than expected. We can also observe that for the likelihood of success variables, independently of the scenario that occurs, the ENPV will be positive. Also, we can see in graph 2 how critical the variables are – the higher the slope the higher the impact of a change on that variable. We can observe that the variable that has the highest impact on the ENPV is sales growth rate, followed by sales and variable costs. SG&A costs are a border case, because in the pessimist scenario it will barely lead to a negative ENPV. We can also observe that in graph 2 – SG&A costs have a rather low slope, which indicates that ENPV is not very reactive to its changes. What we can conclude from this analysis is that the management team should focus on the critical variables, trying to gather more information on their drivers, to reduce the estimation risk - which means that the projections will have a decreased probability of being significantly different from reality. This analysis also reinforces the results we got from the ENPV. If the results of the sensitivity analysis were large negative values in the pessimist scenario and large positive number in the optimist scenario, it would mean that a change in a single forecasted variable could greatly alter the ENPV estimate, which would make us doubtful of the ENPV results. In this case, however, we did not observe that. Even though sensitivity analysis is frequently used in the real world it has one big limitation, that is the fact that it only allows for one variable to change at a time. Monte Carlo simulation, however, is a further attempt to model real-world uncertainty, as it allows to measure the outcome as many variable changes at the same time. This means that, while sensitivity analysis attempted to answer the question “What if this scenario happens?”, the Monte Carlo simulation tries to calculate how likely a certain scenario is to happen (Ross, Westerfield, Jaffe, & Jordan, 2015). According to Ross, Westerfield, Jaffe, & Jordan (2015), the first step to build a Monte Carlo simulation is to specify the basic model, which, in our case, will be the model we used earlier to calculate the ENPV. The variables that make up the model are: Sales, Sales Growth Rate, Gross Margin, SG&A costs, Probability of the R&D stage to be successful, and the discount factor. The next step is to specify a probability distribution for each variable. This choice should be based on historical data or cross-sectional data, but, in reality, it is always a mixture of real data and reasonable assumptions. The final step is to run the simulation. In each cycle, the computer will, based on the 43 assigned probabilities, draw one value for each of the variables, which will result in an ENPV value. After this process is repeated thousands of times, the result will be a distribution of all possible ENPV values. Given this, we can say that simulations provide the most complete assessment of risk since they are based on a probability distribution for each input, rather than a single expected value. This results in the output taking the form of an expected value across a probability distribution. This distribution reinforces the point that valuation models yield estimates of the value of risky asset that are imprecise and can explain why there might be different valuations for the same asset (Damodaran, 2014). To perform a Monte Carlo simulation of the project under analysis, we started, as mentioned earlier, by defining that the variables that make the model are Sales, Sales Growth Rate, Gross Margin, SG&A costs, probability of the R&D stage to be successful, and the discount factor. For the sales, we defined that their variation was described by a triangular distribution, with a minimum value of 150 000€, a likely value of 500 000€ and a maximum value of 750 000€. The triangular distribution should be used when the minimum, maximum and the likeliest values are known. We are assuming that Company A knows that they will not sell less than 150 000€ in the first year and that selling more than 750 000€ in the same period is very unlikely. Only the sales value for 2025 was simulated since the subsequent values are calculated using the first year. 44 Figure 1 – Probability distribution of the expected sales. Next, we assigned a normal distribution to the sales growth rate, with a 50% mean and 10% standard deviation. We are assuming that the probability of the rate being larger than expected is the same as being smaller. Figure 2 – Probability distribution of the expected sales growth rate. The gross margin was assigned a BetaPERT, with a 50% likeliest value, a 20% minimum and 80% maximum. The reason was that we think that there is a high probability of the gross margin to not be significantly different from the likeliest value and we also expect that it will never be less than 20% or more than 80%. 45 Figure 3 – Probability distribution of the gross margin. We expect that the SG&A expenses will follow a student’s t distribution, with a 100% midpoint, a 15% scale and 30 degrees of freedom. The reason is that we expect the value to be close to 100%, but we know that the actual SG&A expenses value can be significantly different from the midpoint. Figure 4 – Probability distribution of the SG&A expenses. 46 For the probability of success, we assigned a normal distribution, with a 50% mean and 10% standard deviation. The reason is that we know that 50% is the most likely value, we expect that the actual probability could as likely be above or below the mean and also that that probability is more likely to be close to the mean than far away. Figure 5 – Probability distribution of the probability of success. The last variable we simulated was the discount factor. We assigned it a lognormal distribution, with a location of 2%, a mean of 8,60% and a standard deviation of 2%. The reason is that we expect the values to be positively skewed, that is, most of the values will be close to the minimum. 47 Figure 6 – Probability distribution of the discount factor. Next, we defined that the SG&A expenses would have a coefficient of correlation of 1 with the sales. This guarantees that when the sales revenues are at their maximum so are the costs. The final step was to run the simulation. Even though there are rigorous methods to estimate each of these variables, there is no way of guaranteeing that our estimations will fit future contexts. That is the reason why simulating a big number of scenarios is important. For that reason, we used 20 000 trails. The results were that, with a 95% confidence level, the probability of a positive ENPV value is 66.50% (figure 7). Also, ENPV can range from -909 632€ to 6 469 507€, the mean value is 383 300€ and the median value is 228 869€, which are close to the base value of 387 756,68 € (table 16). These results show that it is not expected to observe a large deviation from the base scenario. Also, it is important to notice that even though there is a 33,5% probability of the project having a negative ENPV, there is a 25% chance that the ENPV will be between – 333 352€ and 0€. That is, in case of a negative outcome, the ENPV will be a small negative number (Figure 8). The results of the Monte Carlo simulation are aligned with the ENPV results and point at the viability of the project. For that reason, the final verdict is that the project should be accepted.