School of Architecture Urban Planning Construction Engineering
Master of Science in Management of Built Environment
APPLYING MONTE CARLO SIMULATION IN REAL
ESTATE CAPITAL BUDGETING FOR INVESTMENT
EVALUATION
Supervisor: Liala Baiardi
Author: Marco Isella
Matriculation number: 897863
Contents
Figures Index ... vi
Tables Index ... viii
Abstract ... x
Introduction ... xiii
PART 1 – ITALIAN REAL ESTATE MARKET OUTLOOK ... 2
PART 2.1 - BUILDING BLOCKS IN CAPITAL BUDGETING ... 8
2.1.1 - The Choice To Invest ... 8
2.1.1.1 - Time Value of Money ... 8
2.1.1.2 - Present Value and Future Value ... 9
2.1.1.3 - Opportunity Cost of Capital ... 10
2.1.1.4 - Discounted Cash Flow – DCF ... 10
2.1.2 - Cash flows Estimation ... 11
2.1.2.1 - Relevant Cash Flows ... 11
2.1.2.2 - Project Cash Flows ... 12
2.1.3 - Investment Criteria ... 14
2.1.3.1 - Net Present Value - NPV ... 14
2.1.3.2 - Internal Rate of Returns – IRR... 15
2.1.3.3 - Profitability Index – PI... 16
2.1.3.4 – Payback Time ... 17
2.1.3.5 - Modified Internal Rate of Return – MIRR ... 17
PART 2.2 – INVESTMENT RISK ... 19
2.2.1 - Some Definitions About Risk and Risk Management ... 19
2.2.2 - Returns of Real Estate Assets ... 21
2.2.2.1 - Nominal and Real Returns ... 25
2.2.2.2 - Is It Better to Use Nominal or Real Interest Rates? ... 26
2.2.3 - Risk and Returns Relationship ... 27
2.2.3.1 - Security Market Line ... 28
2.2.3.2 - Leverage and Risk ... 31
2.2.3.3 - Risk-free and Risk Premium ... 32
2.2.5 - Measuring Risk ... 35
2.2.5.1 - The Range ... 35
2.2.5.2 - Standard Deviation ... 36
2.2.5.3 - Semi-standard Deviation ... 37
2.2.5.4 - Value at Risk – VaR... 37
2.2.5.5 - Annualizing Volatility and Returns ... 38
2.2.6 - Risk-adjusted Performances Measures ... 39
2.2.6.1 - Coefficient of Variation ... 39 2.2.6.2 - Information Ratio ... 40 2.2.6.3 - Sharpe Ratio ... 40 2.2.6.4 - Treynor Ratio ... 40 2.2.6.5 - Sortino Ratio ... 40
2.2.7 - Covenants on Debt ... 41
2.2.7.1 - Interest Coverage Ratio – ICR ... 41
2.2.7.2 - Loan to value – LTV ... 42
2.2.7.3 - Debt Service Coverage Ratio – DSCR ... 42
2.2.8 - Cost of Capital ... 42
2.2.8.1 - Cost of Equity ... 42
2.2.8.2 - Cost of Debt and Mortgages ... 45
2.2.8.3 - Weighted Average Cost of Capital ... 51
2.2.9 - Sources of Risk Identification in the Real Estate Investment ... 52
2.2.9.1 - Market Risk ... 52
2.2.9.2 - Operative Risk ... 53
2.2.9.3 - Interest Rates Risk ... 53
2.2.9.4 - Legal Compliance Risk ... 53
2.2.9.5 - Asset Concentration Risk ... 54
2.2.9.6 - Strategic Risk ... 54
2.2.9.7 - Other Risk Classification ... 54
PART 2.3 ANALYSIS TOOLS AND TECNIQUES ... 55
2.3.1 - Project Analysis ... 55
2.3.1.1 - Scenario Analysis... 55
2.3.1.2 - Sensitivity Analysis ... 56
2.3.1.3 - Break-Even Analysis ... 57
2.3.1.4 - Monte Carlo Simulation ... 57
2.3.2 - Risk assessment ... 59
PART 3 – CASE STUDY ... 63
3.1 - Case Study Asset ... 63
3.2. - Cash Flows Estimation in Practice ... 64
3.2.2 - Estimated Rental Value – ERV ... 64 3.2.3 - Vacancy Length ... 71 3.2.4 - Vacancy Allowance ... 71 3.2.5 - Operative Expenses ... 73 3.2.6 - Capital Expenditure... 77 3.2.7 - Reversion Value ... 78 3.2.8 - Discount Rate ... 79
3.3 - Project Analysis ... 86
3.3.1 – Most Likely DCF ... 863.3.2 - Applied Scenario Analysis ... 87
3.3.3 - Applied Sensitivity Analysis ... 90
3.3.4 - Applied Break-even Analysis ... 93
3.4 - Run the Monte Carlo Simulation ... 94
Conclusions ... 98
Bibliography ... 102
Figures Index
Figure 1. Debt and GDP growth rate and rates differential – Italy 2000-2017 ... 2
Figure 2. Value added and measures of productivity, Italian whole economy - 1996-2017, percentage variations ... 3
Figure 3. Normalized transaction (NNT) percentage change of the Italian real estate market 2004-2017 ... 3
Figure 4. Investment volume in the Italian real estate market by origins of the capital ... 4
Figure 5. Real estate investments in Italy by location and sector ... 4
Figure 6. Stock of grade A offices - % of total stock ... 5
Figure 7. SGR and number of operative funds in Italy 2007-2017 ... 6
Figure 8. Selected indicators of Italian REIF’s performances during the period 2005-2010 ... 6
Figure 9. The circular flows diagram ... 9
Figure 10. Typical cash flows pattern of an investment... 15
Figure 11. Risk management process ... 21
Figure 12. Typical peaked profile of a maintenance plan costs over the asset’s life cycle ... 23
Figure 13. NCREIF index components of returns ... 24
Figure 14. Deflated Euribor 3 months interest rates – three different deflation assumption ... 26
Figure 15. Probability distribution of returns of three assets ... 28
Figure 16. Systematic and unsystematic risks ... 29
Figure 17. Security market line ... 30
Figure 18. Risk and return relationship in USA major asset class (1970-2003) ... 33
Figure 19. S&P 500 daily returns in 2018 ... 36
Figure 20. Returns distribution and 95% confidence interval ... 37
Figure 21. β estimation for Adobe and Amazon stocks calculated on monthly returns from January 2010 to July 2019 ... 44
Figure 22. Average Overall Effective Rate – AOER – for mortgage loans with fixed and variables rate compared with Eurirs 10 years and Euribor 1 month ... 46
Figure 23. Interest-only loan – total payment and interest expense (figures in €) ... 48
Figure 24. Constant-Amortization Mortgage – total payment and interest expense (figures in €) ... 49
Figure 25. Constant-Payment Mortgage – total payment and interest expense (figures in €) ... 49
Figure 26. Adjustable Rate Mortgage – total payment and interest expense (figures in €) ... 50
Figure 27. Balloon mortgage – total payment and interest expense (figures in €) ... 51
Figure 28. Example of sensitivity analysis ... 56
Figure 29. Inputs variables aggregation with Monte Carlo simulation - 5,000 iterations... 58
Figure 30. Derivation of probability distribution from empirical observations ... 60
Figure 31. Asset geolocalization ... 63
Figure 32. Vodafone Village main facade ... 63
Figure 33. Inflation trend (5 years moving average) in Italy 2000-2018 ... 65
Figure 34. Performance decay over time ... 67
Figure 35. Effect of maintenance on performances degradation and useful life length ... 68
Figure 36. Indexes of the nominal ERV components - trend and effects sum ... 69
Figure 37. ERV - trend and simulated ... 70
Figure 38. 5 ERV simulations with trend ... 70
Figure 39. ERV probability distribution in year 1 and 10 obtained with a Monte Carlo simulation – 5,000 iteration ... 70
Figure 40. Poisson distributions with λ equals to 1, 2, 3 ... 71
Figure 41. Maintenance expenses profile over building life cycle ... 76
Figure 42. Capex profile over building life cycle ... 76
Figure 43. Regression analysis for β estimation using monthly returns of COIMA and FTSE MIB (left) and FTSE EPRA NAREIT Index (right) – January 2017-July 2019 ... 82
Figure 44. NPV and IRR for the three scenarios ... 89
Figure 45. NPV tornado chart with +30% and -30 % variation ... 92
Figure 46. IRR tornado chart with +30% and -30 % variation ... 92
Figure 47. Sensitivity of risky variables ... 93
Figure 48. Monte Carlo simulation outcomes distributions – NPV (left) and IRR (right) – 20,000 thousand of iterations ... 96
Figure 49. Monte Carlo simulation NPV frequency distribution of "exercised" (left) and "not exercised break-option" (right) ... 96
Tables Index
Table 1. Italy's national account selected figures ... 2
Table 2. Survey of Italy's REIFs’ balance sheet main figures in 2003-2016 ... 5
Table 3. IRR e NPV of investments A and B with a discount rate of 10% ... 16
Table 4. IRR e NPV of investments A and B with a discount rate of 25% ... 16
Table 5. PI and NPV of investments A, B and C ... 17
Table 6. IRR reinvestments assumptions break-down... 18
Table 7. Capex sub-categories ... 24
Table 8. Portfolio expected returns and beta for different levels of asset allocation ... 30
Table 9. The effect of leverage on returns ... 32
Table 10. Historical records of USA major asset classes ... 33
Table 11. Elements the determine the current market price of a property ... 35
Table 12. Milan central apartment sub-market annualized returns and volatility (2015-2019) ... 38
Table 13. Comparison of two project with different scale ... 41
Table 14. Interest-only loan (figures in €) ... 48
Table 15. Constant-Amortization Mortgage (figures in €)... 48
Table 16. Constant-Payment Mortgage (figures in €) ... 49
Table 17. Adjustable Rate Mortgage (figures in €) ... 50
Table 18. Balloon mortgage (figures in €) ... 51
Table 19. Risks classification ... 54
Table 20. Project A scenario analysis ... 55
Table 21.Break-even point calculations on NPV ... 57
Table 22. Most likely values for the income statement of firm A for the next year ... 58
Table 23. Assumptions of distributions and parameters of firm A income statement variables ... 58
Table 24. Inflation Forecasts ... 64
Table 25. Historical Eurostat HICP inflation in Italy 2008-2018 ... 65
Table 26. Historical Istat CPI inflation in Italy 2000-2018... 65
Table 27. Milan office rent values and growth rates at Q2 2019... 66
Table 28. Assumed real growth rate of the market rent in the south-west Milan periphery sub-market ... 66
Table 29. ERV simulation applying effects sum and formula (47) ... 69
Table 30. Vodafone Village operative costs in 2017 and 2018 ... 73
Table 31. Example of building components technical card... 75
Table 32. Study case maintenance expenses - years 1-25 ... 76
Table 33. Annual Capex ratio for NCREIF office buildings, 1978-2014 ... 77
Table 34. Study case capex - years 1-25... 77
Table 35. U.S. cap rate survey - H1 2019. Suburban offices markets in Tier I cities ... 79
Table 36. Going-out cap rate spread estimation ... 79
Table 37. risk-free rate estimation using 10 years and 12 months Italian government bonds rates ... 80
Table 38. Risk premium estimation with the Empirical Historical Method... 81
Table 39. Average levered and unlevered β of a selected basket of firms in the real estate sector in western Europe ... 82
Table 40. Average excess of return of FTSE MIB vs 12 months BOT - 2002-2018 ... 83
Table 41. Different methods WACC estimation and average ... 85
Table 43. DCFA assumption and formulas ... 86
Table 44. Most Likely DCF excerpt ... 87
Table 45. Different scenarios ERV trend calculations ... 88
Table 46. Annualized standard deviation calculation for the sub-market "D25" OMI zone in Milan ... 89
Table 47. Sensitivity analysis summary ... 91
Table 48. Break-even analysis ... 94
Table 49. Assumptions on variables' distribution and parameters ... 95
Abstract
L’oggetto di questa tesi è la valutazione di un asset immobiliare considerato come opportunità d’investimento. Le ipotesi che stanno alla base del seguente elaborato sono due; la prima è che il metodo tradizionale di valutazione degli asset immobiliari dell’income approach applicato per mezzo di una
discounted cash flows analisi (in seguito DCFA o DCF) non è uno strumento capace di fornire indicazioni
affidabili ad un investitore immobiliare, in quanto non permette di quantificare la rischiosità dell’asset che sta valutando. Questa mancanza porta a valutazioni del prezzo incorrette, dal momento che uno dei principi cardine dell’economia finanziaria è che asset più rischiosi hanno prezzi bassi e rendimenti relativamente elevati rispetto ad asset meno rischiosi, che hanno prezzi alti e rendimenti relativamente bassi. La seconda ipotesi è che rappresentare le funzioni obiettivo della DCFA – sia che essi siano il prezzo, il valore attuale netto, il tasso interno di ritorno, o altre – come una variabile aleatoria (o stocastica) permette di quantificare la rischiosità di un asset e quindi fornire indicazioni più precise sia al fine della stima del prezzo (argomento che non verrà trattato) che per quanto riguarda la valutazione della convenienza dell’investimento in un asset immobiliare. Per riuscire in questo intento è stato utilizzato il tradizionale metodo del DCF in combinazione con la simulazione Monte Carlo, grazie alla quale è stato possibile aggregare i rischi derivanti dalle singole variabili contenute nel DCF ed ottenere una descrizione quantitativa del rischio globale dell’asset. Le variabili del DCF devono necessariamente essere rese stocastiche per poter applicare il metodo Monte Carlo, dunque devono essere scelti i parametri e il tipo di distribuzione che meglio le rappresenta. La peculiarità della parte applicativa della tesi è rappresentata dalla presenza di una break-option nel contratto di locazione, la quale viene incorporata nel DCF seguendo il modello sviluppato da C. Amédée‐Manesme et all (2013), per poterne verificare gli effetti sulla redditività e sulla rischiosità dell’asset. I risultati raggiunti applicando il metodo brevemente appena descritto sono che la presenza della break-option crea due scenari completamente disgiunti, i quali portano a far assumere una forma bimodale alla distribuzione di probabilità delle variabili aleatorie dell’NPV e dell’IRR, dovuta proprio alla compresenza nel suo dominio di valori derivanti da uno scenario in cui la break-option viene esercitata e uno in cui non lo è. Grazie all’uso del Monte Carlo è stato possibile stimare la probabilità di avvenimento dei due scenari e quantificarne sia i valori attesi di performances che i livelli di rischio. Le ipotesi sono state verificate tramite l’applicazione degli strumenti e della metodologia appena descritta per mezzo di un caso studio in cui viene analizzato un immobile di proprietà di COIMA RES conosciuto come Vodafone Village; un edificio per uffici con una superficie commerciale di circa 46 mila metri quadri localizzato nella periferia sud-ovest di Milano.
Abstract – English version
The object of this thesis is the evaluation of a real estate asset considered as an investment opportunity. The hypotheses underlying the following paper are two; the first is that the traditional method of valuing real estate assets of the income approach applied by means of a discounted cash flows analysis (hereinafter DCFA or DCF) is not a tool capable of providing reliable indications to a real estate investor since it does not allow to quantify the riskiness of the asset being evaluated. This lack leads to incorrect price evaluations, since one of the key principles of the financial economy is that riskier assets have low prices and relatively high returns compared to less risky assets, which have high prices and relatively low returns. The second hypothesis is that representing the objective functions of the DCFA - whether they are the price, the net present value, the internal rate of return, or others - as a random variable (or stochastic) allows to quantify the riskiness of an asset and therefore provide more precise indications both for the purpose of estimating the price (a topic that will not be dealt with) and as regards the evaluation of the convenience of investing in a real estate asset. To achieve this, the traditional DCF method was used in combination with the Monte Carlo simulation, thanks to which it was possible to aggregate the risks deriving from the individual variables contained in the DCF and obtain a quantitative description of the global risk of the asset. The DCF variables must necessarily be made stochastic in order to apply the Monte Carlo method, therefore the parameters and the type of distribution that best represents them must be chosen. The peculiarity of the applicative part of the thesis is represented by the presence of a break-option in the lease contract, which is incorporated into the DCF following the model developed by C. Amédée-Manesme et all (2013) and so be able to verify the effects on profitability and on the riskiness of the asset. The results achieved by applying the method just briefly described above are that the presence of the break-option creates two completely disjointed scenarios, which lead the NPV and IRR random variables to be represented by a bimodal probability distribution. This id due to the coexistence in the same domain of values deriving from a scenario in which the break-option is exercised and one in which it is not. Using the Monte Carlo method it was possible to firstly separate two scenario, then estimate their probability of occurrence and to quantify both the expected values of performances and the levels of risk. The hypotheses were verified through the application of the tools and methodology just described by means of a case study in which is analysed a property owned by COIMA RES known as Vodafone Village; that is an office building with a commercial area of approximately 46 thousand square meters located in the south-west suburbs of Milan.
Introduction
The following thesis has as its main object the development of a "stochastic" discounted cash flows analysis (hereinafter DCFA or DCF) as it presents in input, and returns in output, random variables. This approach was designed thinked starting from one of the fundamental concepts of the financial economy, namely that with the same expected return, riskier assets - or more volatile, characterized by a greater standard deviation of the probability distribution of returns - have less demand on the market, which lowers the price and increases potential returns; vice versa for less risky assets. Considering this assumption true, it is clear that the real estate valuation that does not contain any type of indication on the riskiness of the asset, is partial and incomplete and can lead to the overestimation of the asset value, since the riskiness is not known. The objective of the following paper is therefore to develop a tool called stochastic discounted cash flows, or stochastic DCF, through the application of the Monte Carlo method that allows to represent the objective functions of the DCF as random variables and therefore to be able to quantify the risk of an asset. To do this it is necessary to choose the type and parameters of the most suitable probability distributions to represent the single variables that make up the DCF. In the applicative part, a particular emphasis was given to the analysis of the effects that the presence of a break-option has on the profitability and riskiness of the asset using the model developed by C. Amédée-Manesme et all (2013). The structure of the thesis is divided into three major parts. The first is a brief outlook on the Italian real estate sector and its recent developments and evolutions; the second is the theoretical part and a last is dedicated to a case study. As far as the theoretical part is concerned, the starting point is the treat of the “building blocks” of the capital budgeting, because if the main instrument of evaluation is the DCF, this means that it was first of all necessary to identify the relevant cash flows for the analysis and then find a proper discount rate for actualized the future values. To this follow a brief explanation of the classic performance evaluation tools such as NPV and IRR (but not only) in order to be able to evaluate the result given by the DCF, focusing in particular on the assumption about the reinvestment of the net cash flow on which the NPV and the IRR are built. In the second part of the theoretical discussion, rist of all I tried to give some definition of what risk is, then I deepened the relationship between risk and return and the reason why they are inextricably linked and the conseguences that this link generates on the relationship between price and expected return. In the last part of the theoretical discussion I described the classic investment analysis tools such as the scenario and the sensitivity analysis, focusing in particular on the Monte Carlo simulation. From a methodological point of view, for reasons of greater clarity I presented easy examples for each tool I explained. The third part of the thesis is the practical one, in which I developed a case study analysing the Vodafone Village building owned by COIMA RES looking at it as an investment possibility and trying to understand if it is worth the trouble to invest in it. The first part of the case study is focused on the explanation of how cash flows are been estimated, on the models applied and the assumption made. The analysis tool are used to extrapolate information from the “deterministic” DCF and then I used the Monte Carlo to prepare the stochastic DCF and analyse the effect that the presence of a break-option in the leasing contract generates of the DCF’s objective functions.
PART 1
PART 1 – ITALIAN REAL ESTATE MARKET OUTLOOK
Looking at the main figures of Italian public finance, debt and GDP, it can be seen that after the 2008 “sub-prime” crisis, public debt grew at rates higher than GDP. After the difficult 2008-2013 period, marked by the global crisis of 2008-2009 and the subsequent “sovereign debt crisis” of 2011, Italy is back to a path of growth, albeit weak, of productivity - Figure 2 - and of GDP - Figure 1 and Table 1.
Table 1. Italy's national account selected figures
2000 2001 2002 2003 2004 2005 2006 2007 2008
Government debt A 1.303 1.360 1.372 1.397 1.450 1.519 1.588 1.606 1.671
Debt growth rate [%] B=At/At-1-1 1,37 4,42 0,84 1,87 3,73 4,76 4,57 1,14 4,06
GDP C 1.299 1.346 1.391 1.448 1.490 1.548 1.610 1.632 1.573 GDP growth rate [%] D= Ct/Ct-1-1 4,81 3,61 3,34 4,15 2,86 3,94 3,94 1,40 -3,63 Debt/GDP [%] E=A/C 100,29 101,08 98,64 96,49 97,31 98,08 98,67 98,41 106,27 rate differential [%] F=B-D -3,44 0,81 -2,49 -2,27 0,88 0,82 0,63 -0,26 7,69 2009 2010 2011 2012 2013 2014 2015 2016 2017 Government debt A 1.770 1.852 1.908 1.990 2.070 2.137 2.173 2.220 2.269
Debt growth rate [%] B=At/At-1-1 5,91 4,61 3,03 4,31 4,03 3,24 1,69 2,16 2,19
GDP C 1.605 1.637 1.613 1.605 1.622 1.652 1.690 1.727 1.757
GDP growth rate [%] D= Ct/Ct-1-1 2,01 2,05 -1,48 -0,54 1,07 1,87 2,28 2,22 1,71
Debt/GDP [%] E=A/C 110,33 113,09 118,27 124,03 127,65 129,37 128,62 128,54 129,14
rate differential [%] F=B-D 3,90 2,56 4,51 4,84 2,95 1,37 -0,60 -0,06 0,48
Notes: Debt stands for Government consolidated gross debt, figures are in billions of current euro. GDP stands for Gross domestic product at market prices, figures are in billions of current euro.
Source: author’s elaboration based on Eurostat database
Figure 1. Debt and GDP growth rate and rates differential – Italy 2000-2017
Note: Debt-GDP growth rate differential is calculated subtracting the GDP growth rate from the Debt growth rate. A positive value indicate that the debt has grown faster than the GDP.
Source: author’s elaboration based on Eurostat database
-6,00% -4,00% -2,00% 0,00% 2,00% 4,00% 6,00% 8,00% 10,00%
Figure 2. Value added and measures of productivity, Italian whole economy - 1996-2017, percentage variations
Note: The leasing activities of real estate, families and cohabitation, international organizations and bodies and all the economic activities that are part of the institutional sector of Public Administrations are excluded from the field of observation.
Source: [1] Istat, «Misure di produttività. Anni 1995-2017,» 2018
As can be seen from Figure 3, the real estate sector also comes back to increasing number of transactions only after 2013-2015, after the "pause" of the 2008-2013 period due to the sub-prime mortgage crisis and then to that of sovereign debts. In addition to transactions, investments were also start again in 2013 - Figure 4 - driven mainly by foreign investors, to which domestic investors have also joined since 2015-2016. As can be seen from Figure 5, Milan is by far the most attractive real estate market for investors, followed by Rome, which in any case collects investment volumes equal to about a third of those in the Lombard capital. The sectors considered the best by investors are the office and retail, which share the same two-thirds of the total pie.
Figure 3. Normalized transaction (NNT) percentage change of the Italian real estate market 2004-2017
Figure 4. Investment volume in the Italian real estate market by origins of the capital
Source: [3] CBRE, «Real Estate Market Outlook. Italia,» 2018
Figure 5. Real estate investments in Italy by location and sector
Source: [2] Pwc, «Real Estate Market Overview. Italy 2018,» 2018
Despite the relative dynamism of the Milanese real estate sector, a report edited by PwC says that in Milan: "Office demand is strong, [...] If you have a good product in Milan, there is a queue of tenants because there is a construction backlog of 10 years."1 All this is confirmed by the annual report of 2018 of COIMA RES, which shows the graph in Figure 6, which highlights the lack of quality assets in Milan compared to other European metropolises, moreover in a leading sector such as the offices. This means that despite the strong growth observed from 2013 onwards, other investments are also needed in the coming years to double the share of high-quality office stocks, in order to align Milan with other high-ranking cities in Europe.
Figure 6. Stock of grade A offices - % of total stock
Source: [4] COIMA RES, «Relazione finanziaria annuale,» 2018
Table 2. Survey of Italy's REIFs’ balance sheet main figures in 2003-2016 Real estate funds: market structure
Years # of funds Total assets Debts NAV Leverage
Mln of € Real estate Total 2003 19 5.141 3.718 573 4.414 1,16 2004 31 12.309 10.520 3.979 8.084 1,52 2005 61 18.326 15.215 6.019 11.859 1,55 2006 119 27.248 22.110 9.890 16.384 1,66 2007 174 36.058 30.434 13.453 21.531 1,67 2008 229 42.390 36.791 16.630 24.446 1,73 2009 267 47.517 40.936 19.517 26.306 1,81 2010 281 47.771 41.678 19.347 26.846 1,78 … … … … 2013 361 55.212 47.963 19.821 32.846 1,67 2014 395 58.367 50.239 18.511 37.529 1,55 2015 417 60.338 51.502 17.342 40.526 1,49 2016 439 64.526 54.890 18.232 43.777 1,47
Source: author’s elaboration based on [5] Banca d'Italia, «Focus sull’industria dei fondi immobiliari retail,» 2017 and [6] M. L. Bianchi e A. Chiabrera, «Italian real estate investment funds: market structure and risk measurement,» Questioni di Economia e Finanza, April 2012
Table 2 shows the main balance sheet statistics and the number of Real Estate Investment Funds - REIFs - operating in Italy from 2003 until 2016. The sector has grown steadily throughout the period considered, both as regards the total number of operational funds, and for the net asset value and also for the financial leverage used, at least until 2009. From Figure 7 it is possible to find confirmation of what reported in Table 2, and to observe a progressive reduction of the overall number of SGR that happens contextually to the strong growth in the number of funds. “Real estate funds in Italy represent about 3% of the Italian asset
management market. […] During 2017, the weight of the first 5 SGRs, which amounted to 32.8 bn, has slightly decreased from 47.9% to 46.3%. The main component of Italian real estate funds reserved funds accounting for 96% over the total amount. […] The increase of the total number of reserved funds also during 2017 is not related to the growth of the number of asset management companies but from the greater efficiency achieved by the companies in relation to a larger amount of asset under management.”2 The paper "Italian
real estate investment funds: market structure and risk measurement" contains some statistics, reported in Figure 8, on the performances of Italian REIFs in the period 2005-2010 and it is noted that despite the increase in leverage (and funds fees) ROE was overall decreasing, due to the adverse market conditions highlighted by the overview presented so far. “We also find that the ROE relative to retail products has been
in general less volatile, although it has suffered from the negative cycle in recent years. However, in the long-term it remains, in most cases, positive. As expected, the recent financial crisis has affected both the financial drivers and the market value of REIF assets.”3
Figure 7. SGR and number of operative funds in Italy 2007-2017
Source: [2] Pwc, «Real Estate Market Overview. Italy 2018,» 2018
Figure 8. Selected indicators of Italian REIF’s performances during the period 2005-2010
Note: The median values are in black, the mean values in blue, and the strips between the red lines contains 70 per cent of the analyzed funds. Non-development funds active for at least two years are considered. One-year moving average of the 6 month Euribor is reported in the chart of the cost of debt.
Source: Italian real estate investment funds: market structure and risk measurement.
3[6] M. L. Bianchi e A. Chiabrera, «Italian real estate investment funds: market structure and risk measurement,» Questioni di Economia e Finanza, April 2012. Pag. 15
PART 2
PART 2.1 - BUILDING BLOCKS IN CAPITAL BUDGETING
2.1.1 - The Choice To Invest
An individual investor (or a company or any economic agent) according to classical microeconomic theory makes decisions aimed at maximizing his profit, by maximizing the difference between revenues and costs. The ability to generate income passes through the purchase of labor, capital and other inputs in the factor markets to combine them together and produce goods and services, which are "brought" to the market of goods and services to be sold and, through exchange, collect revenues. These steps are depicted in Figure 9. To be able to achieve his goal, the investor will have to make a multitude of choices about the use of the resources at his disposal - which as they are scarce are susceptible to alternative uses - to make sure that the costs that emerge from their use are more than offset by revenues, so as to obtain a profit.4 Investment is a type of economic choice that does not concern the immediate maximization of the well-being of the individual, but on the contrary entails the need to sustain only costs in the present, with the expectation of obtaining greater benefits in the future. In this thesis I will deal precisely with the evaluation of an investment by a private economic agent which has as its object a real estate property, which intends to know if the game is worth the trouble and therefore needs analysis tools that allow him to find an answer. The main elements that constitute an investment can be summarized in:
• The direct cost of the investment
• The indirect cost of the investment, that is the opportunity cost of capital • The time value of money
• A series of future expected risky cash flows
2.1.1.1 - Time Value of Money
Time value of money means that time is money, or that time has a value that can be represented in monetary terms; this means that a euro today is worth more than one euro tomorrow, as is commonly said. This is mainly due to the fact that money has an opportunity cost defined by the interest rate. First of all, we need to define the concept of opportunity cost, which is nothing but "implicit cost of capital, [...] it reflects the income that could have been realized if the capital had been used in its next best alternative way."5 As far as regards the interest rate, it can be defined as the cost paid by the debtor expressed as a percentage of the sum borrowed. If an individual lends money for a certain period of time, we assume 1000 € for a year, at the expiry of the loan the sum returned will be 1000 € plus interest, or the cost that the debtor was willing to bear in order to have the money immediately . This explains why a euro today is worth more than one euro tomorrow, or why having the euro available tomorrow we give up the possibility of being able to use it in the best alternative investment available and the relative profit. Nevertheless, there are two other factors that determine the time value of money6: i) inflation: a euro today is worth more than
4 [23] P. Krugman e R. Wells, Microeconomics, 2th edition, Worth Publishers, 2009. Pag. 6. “Why do individuals have to make choices? The ultimate reason is that resources are scarce.”
5 Ibidem
one euro tomorrow because inflation destroys the purchasing power of real goods and services; ii) cash flow risk: the euro we have today is safe, while the euro we should have tomorrow is risky. Due to these reasons described above it is not possible to directly compare cash flows received and paid in different time periods, but as briefly mentioned above, the interest rate can be used to convert future cash flows to their present value.
Figure 9. The circular flows diagram
Source: [7] N. G. Mankiw, Principles of Microeconomics, 5th edition, Cengage Learning, 2008.
2.1.1.2 - Present Value and Future Value
If it is true that € 1 today does not count as € 1 tomorrow, it is however true that € 1 today is worth (1 + x) € tomorrow. To solve the equation we need to understand what is the opportunity cost of the capital we pay by giving up € 1 today. “The idea of present discounted value arose because we wanted to be able to convert money at one point in time. "The interest rate" is the return on an investment that allows us to transfer funds in this way ";7 in other words, by applying the interest rate to the present value as in equation (1), it is possible to obtain the future value and therefore find that sum of future money equivalent to the sum of current money in the case of an investment lasting only one period.
𝐹𝑉 = 𝑃𝑉(1 + 𝑟) (1)
If we consider investing € 100 for a year at an interest rate of 5%, the future value will be 100(1 + r) = € 105; if this sum is always reinvested for one year at the 5% interest rate, the future value will be 105 (1 + r) = € 110.25. Thanks to this process of continuous reinvestment of the interests earned, the value of the investment grows at a compound rate; the interest rate that describes this dynamic is called compounded interest. After t periods the future value of the investment is given by the formula (2):
𝐹𝑉 = 𝑃𝑉(1 + 𝑟)𝑛 (2)
The procedure that allows to find the present value of a future cash flow is called discounting, while capitalization is used to find the future value of a present cash flow.
2.1.1.3 - Opportunity Cost of Capital
How can these concepts be applied to the evaluation of an investment? We assume that an individual owns a real estate property inherited from the current value of € 300,000 and that with an expenditure of € 70,000 for restructuring he can sell the building for € 400,000; the jobs would last one year and the interest rate in that period is 10%. For simplicity, it is assumed that all cash flows are risk-free. Should the investment be made? At first glance it would seem so, as against an expenditure of € 70,000 it could return a revenue of € 400,000, but our investor did not consider the opportunity cost of capital. First, the value of the property must be considered as a cost of investment, although it is an implicit cost, it’s a fundamental input and it has certainly not rained from the sky without any cost being incurred, it is not a free lunch. Secondly, we must consider the alternative of selling the property in the current state and investing in securities that promise a 10% interest rate and which could therefore give a return of € 30,000 within a year; this is also an opportunity cost, as it is the profit that is renounced by choosing restructuring rather than investing in the financial market. The final value of the property is discounted using the opportunity cost of the capital, or the interest rate of 10%, in order to check which present value would be needed to obtain € 400,000 after a year with a 10% return. The present value is € 363.636 against a total expenditure of € 370,000, so the investment should not be considered, in fact with an investment of € 370,000 in securities with a 10% interest rate, after one year the assets of the investor would amount to € 407,000.
2.1.1.4 - Discounted Cash Flow – DCF
Discounted cash flow, hereinafter DCF, is a method of valuing investments based on the discounting of a series of expected cash flows generated by an asset or investment when the duration is longer than a single period. The fundamental elements are i) the amount of net cash flows, ii) the distribution of flows over time and iii) the discount rate. With regard to the cash flow dimension, it is essentially defined by the calculation of the net cash flows for each period, algebraically adding the cash in-flow and the cash out-flows; distribution is reported based on the income and expenses of each period, while the discount rate is calculated as the opportunity cost of capital. The formula (3) is shown below.
𝑉 = ∑
𝑁𝐶𝐹𝑡 (1+𝑟)𝑡 𝑇 𝑡=0+
𝑅𝐸𝑉𝑡 (1+𝑟)𝑇 (3)V: present value of expected cash flows
NCFt: are the net cash flows expected each year r: opportunity cost of capital
REVt: reversion value, or collection received at the end of the investment from the disposal of the asset T: final year of the investment
2.1.2 - Cash flows Estimation
“The effect of taking a project is to change the firm’s overall cash flows today and in the future. To evaluate a proposed investment, we must consider these changes in the firm’s cash flows and then decide whether they add value to the firm. The first (and most important) step, therefore, is to decide which cash flows are relevant.”8
2.1.2.1 - Relevant Cash Flows
Also called incremental cash flows, the relevant cash flows "consist of any change in the firm's future cash
flows that are a direct consequence of taking the project." 9 Especially if a company is large it could be very difficult to assess all the cash flows if we were to have to evaluate a project, but fortunately it is necessary to evaluate only the incremental cash flows, or the difference between the cash flows obtained by the company with the investment compared to the cash flows obtained without the investment.
Sunk Costs
The sunk costs are costs for which you have already paid or you to which you have already contracted the obligation to pay, so there is no possibility of acting to avoid making that expense. For the definition that has been given of relevant cash flows, the sunk costs do not fall into this category, therefore they should not be considered when analyzing a project.
Opportunity Cost
The opportunity cost, as defined above, is the best possible benefit that you have to give up when you decide to use a resource. Economists usually say "there is no such thing as a free lunch" to express the concept of opportunity cost. From the point of view of identifying relevant cash flows this means that any input that is used for a project is susceptible to alternative uses and therefore its use must be taken into account considering the right cost.
Side Effects
8[11] S. A. Ross, R. W. Westerfield e B. D. Jordan, Fundamentals of Corporate Finance, 10th edition, The McGraw-Hill Companies, Inc., 2013. Pag. 306
It is possible that the introduction of a new product drains demand from the other products of a company, causing a negative impact in terms of cash flows on the entire portfolio. This phenomenon is called erosion or cannibalism and must be recognized as relevant cash outflow caused by the project, as its direct consequence.
Net Working Capital
Usually a project requires to expand current assets such as inventories, account receivables and account payables. An expansion of net working capital must be seen as a loan, since on this immobilized capital no interest is received and if the project is not implemented it would be earned by the company. Once the project is completed, the inventory is generally sold, the account receivables collected and the debts paid, going to eliminate the working capital increase sustained by the company to finance the project.
Financiang Costs
“In analyzing a proposed investment, we will not include interest paid or any other financing costs such as
dividends or principal repaid because we are interested in the cash flow generated by the assets of the project […] our goal in project evaluation is to compare the cash flow from a project to the cost of acquiring that project in order to estimate NPV. The particular mixture of debt and equity a firm actually chooses to use in financing a project is a managerial variable and primarily determines how project cash flow is divided between owners and creditors. This is not to say that financing arrangements are unimportant. They are just something to be analyzed separately.”10 In other words, the important thing is the evaluation of the cash flows generated by the assets and the cost incurred to purchase them; how these cash flows will have to be distributed between equity and debt is another topic that needs to be treated separately.
2.1.2.2 - Project Cash Flows
The free cash flows generated by the assets are given by the following formula:
Project free CF = operating CF − capital spending − changes in net working capital (4)
Operating Cash Flows
The operating cash flow formula is as follows:
Operating CF = EBIT + Depreciation − Taxes (5) EBIT = Revenues − COGS − Opex − Depreciation (5.1)
Since only the cash expenses are considered, the depreciation has to be added back because of iys nature of accrued expense. It should be noted that real estate properties purchased as an investment are not subject to depreciation.
Current and Non-current Capital Expenditures
Capital expenditure includes both investment costs in net working capital and those for the purchase of non-current assets. As far as net working capital is concerned, only the variation is considered, that is the difference between the quantity at the beginning of the year and that at the end; this serves to compensate for the fact that revenues are considered completely cash. A simple example allows to explain the mechanism in the best way.
Income Statement, figures are in €
Revenues 500
Costs (310)
Net income 190
Source: [11] S. A. Ross, R. W. Westerfield e B. D. Jordan, Fundamentals of Corporate Finance, 10th edition, The McGraw-Hill Companies, Inc., 2013
Figures are in € Beginning of Year End of Year Change
Account Receivable 880 910 +30
Account Payableble 550 605 +55
Net working capital 330 305 -25
Source: [11] S. A. Ross, R. W. Westerfield e B. D. Jordan, Fundamentals of Corporate Finance, 10th edition, The McGraw-Hill Companies, Inc., 2013
Assuming for simplicity that the capital expenditure is zero, applying formula (5) we obtain: operating CF = 190 - 0 - (-25) = 215 €. By adding the variation of the net working capital it is possible to compensate the fact that the values of the revenues and costs expressed in the income statement are non-cash. An increase of € 30 in accounts receivables means that of the € 500 of revenues, 470 have been cashed and 30 are yet to be collected, so the total cash inflows are 500 - 30 = € 470. An increase of € 55 in payables accounts means that of € 310 of costs, 255 have been paid and 55 remain to be paid, so the total cash outflows are 310 - 55 = € 255. The net cash flows at the end of the year will therefore be 470 - 255 = € 215, or the same value obtained by applying the formula (5).
Asset Disposition
At the end of the investment period, the assets acquired at the beginning can be sold. In the specific case of real estate investments, the profit component deriving from the terminal value of the asset at the end of the holding period occupies a substantial part of the total returns and is therefore an item that must be considered carefully. The cash flows obtained from the sale of the asset must be considered net of any costs incurred during the sale and taxes. The estimate of the relevant cash flows of the project will be made in the case study.
2.1.3 - Investment Criteria
“An investment is worth undertaking if it creates value for its owners. In the most general sense, we create
value by identifying an investment worth more in the marketplace than it costs us to acquire. […] This is what capital budgeting is all about—namely, trying to determine whether a proposed investment or project will be worth more, once it is in place, than it costs.”11 When we talk about investment that is worth more than the costs, we must consider all the costs, therefore also the opportunity cost, remembering that a euro today is worth more than one euro tomorrow and that a secure euro is worth more than a risky euro. Investments usually promise a risky euro tomorrow in exchange for a certain amount of expenditure today. To compare these two values the discount rate is used, whose estimation will be discussed in chapter 4.
2.1.3.1 - Net Present Value - NPV
The net present value (henceforth NPV) allows us to verify whether the present value of a series of cash flows generated by an investment is greater, less than or equal to the sum used for the investment and therefore to understand if value has been created. The NPV formula (6) is like the DCF formula (3) with the addition of the negative cash flow due to the initial investment expense. This means that for each period we should estimate the net cash flows generated by business activities and discount them by using an adequate discount rate to define their present value. Figure 10 shows the typical pattern of an investment, that consist in a large initial expense, a series of relatively small positive cash flows with respect to the investment and a relatively large cash flow defined as terminal value, calculated as disinvestment of the assets purchased at start of the useful life of the investment or as present value of the cash flows generated beyond the time horizon considered in the capital budgeting.
𝑁𝑃𝑉 = − 𝐼 + ∑
𝑁𝐶𝐹𝑡(1+𝑘)𝑡 𝑇
𝑡=0 (6)
NCFt: expected net cash flow for each period t T: end of the investment period
I: initial investment
k: opportunity cost of capital
The NPV decision rule says that if it is greater than zero, the cash flows generated by the initial investment have a size and distribution over time such as to offset the opportunity cost of the investor, or the required return rate and therefore the investment should be accepted. Conversely, if NPV is lower than zero it is not worth the trouble and the investor should refuse the investment. It should be pointed out that an NPV less than or equal to zero does not mean that the profit obtained from the investment is zero, because the cash flows are discounted so as to be "weighed" for their riskiness. A negative NPV means that the return is not large enough to offset the risk, as it was quantified in the discount rate, so an NPV equal to 0 does not imply the rejection of the investment, as it means that the present value of the flows of cash is large enough to offset the risk incurred, based on the discount rate used. The weaknesses of the NPV are that it does not consider the amount of capital employed of the initial investment relative to the investor's possibilities, it
11[11] S. A. Ross, R. W. Westerfield e B. D. Jordan, Fundamentals of Corporate Finance, 10th edition, The McGraw-Hill Companies, Inc., 2013. Pag. 267
does not give any information about the period in which the investment reaches break-even and requires the estimate of the opportunity cost of capital, which is not always easy.
Figure 10. Typical cash flows pattern of an investment
Source: http://jukebox.esc13.net/untdeveloper/RM/RM_L9_P4/RM_L9_P4_New2.html
2.1.3.2 - Internal Rate of Returns – IRR
L’IRR is the discount rate that equates the discounted cash in-flows and discounted cash out-flows; in other words, it is the discount rate that makes the NPV equal to zero if used as a discount rate. 12 The formula is:
𝑁𝑃𝑉 = ∑
𝑁𝐶𝐹𝑡(1+𝐼𝑅𝑅)𝑡
𝑇
𝑡=0
= 0
(7)In practice, the IRR is the rate of return that, on average, we expect the investment generates in each period. The decision rule is to accept only investments with IRR greater than the opportunity cost of the capital or of the return rate requested by the investor. The IRR decision rule does not always agree with the NPV decision rule: we assume that you are in the situation of having to decide between the two mutually exclusive investments A and B; the IRR can be used to compare the two investments. Looking at Table 3, where the NPV was calculated with a discount rate of 10 percent, the choice would fall on investment B if we were to look at the NPV, while A it would be preferable if we look at the IRR. If we use a discount rate of 25 percent, as described in Table 4, the NPV of alternative B would become negative, since its IRR is less than 25 and the investment A remains the only rational choice. The bottom line is that IRR and NPV can make conflicting judgments. This depends on the reinvestment hypothesis: the NPV assumes that the cash flows are reinvested at the cost of capital and therefore at the discount rate, while the IRR is reinvested at the internal rate of return.13 The fact that the NPV or the IRR prevails in the valuation of an investment depends on the use made of the cash flows received and the return that can be obtained. If, for example, one can expect to obtain a return equal to the opportunity cost of capital from the re-investment of returns,
12[11] S. A. Ross, R. W. Westerfield e B. D. Jordan, Fundamentals of Corporate Finance, 10th edition, The McGraw-Hill Companies, Inc., 2013. Pag. 280
in investments with IRR higher than the cost of capital, the IRR generates an overestimation of the returns on the investment. If the returns are reinvested at the opportunity cost of the capital, the NPV must be used. In a real estate investment, year-end profits cannot be reinvested in the same asset that generated them, due to the specificity and uniqueness of the asset itself, so the NPV should be considered more informative in the selection of alternative projects.
Table 3. IRR e NPV of investments A and B with a discount rate of 10%
Investment IRR NPV
A 28,65% 516.315€
B 22,79% 552.620€
Sources: [12] F. J. Fabozzi, P. P. Peterson, Capital Budgeting: Theory and Practice, John Wiley & Sons, Inc., 2002
Table 4. IRR e NPV of investments A and B with a discount rate of 25%
Investment IRR NPV
A 28,65% 75.712 €
B 22,79% -67.520 €
Sources: [12] F. J. Fabozzi, P. P. Peterson, Capital Budgeting: Theory and Practice, John Wiley & Sons, Inc., 2002
Other information provided by the IRR is the timing of the cash flows: investments with cash flows closer over time generate higher IRR, as a higher discount rate will be required to equal outgoing cash flows to incoming cash flows. With regard to the riskiness of the cash flows, we can assume that we have two alternative investments that produce the same NCF but have two different risks and therefore two different discount rates. The IRR of the two investments will be the same as the cash flows are the same both for timing and size, but the NPV of the less risky investment will be greater. In summary, the IRR cannot see the riskiness of the investments, while the NPV can; the IRR is able to give information about the timing of the cash flows, as well as the NPV. In general, the IRR should be used as the first level of alternative investment screening, to eliminate those with capital costs greater than the rates of return, after which the NPV should be used to select investments that maximize investor wealth.
2.1.3.3 - Profitability Index – PI
The profitability index is calculated with the following formula:
𝑃𝐼 =
𝑃𝑉 𝑜𝑓 𝑓𝑢𝑡𝑢𝑟𝑒 𝑐𝑎𝑠ℎ 𝑖𝑛𝑓𝑙𝑜𝑤𝑠𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 (8)
When NPV is zero, PI is 1. PI tells the investor how many euros his wealth increases for each euro invested. For indices greater than one the investment creates value, for indices between zero and one the investment destroys value. The decision rule of the PI should therefore be to choose the investment with the greatest ratio, but this rule does not always lead to take the alternative that creates greater value, especially when comparing investments with different scales. This fact is represented in Table 5.
Table 5. PI and NPV of investments A, B and C
Investment PV outflows PV inflows PI NPV
A 10.000 € 16.000 € 1.6 6.000 €
B 10.000 € 15.000 € 1.5 5.000 €
C 20.000 € 28.000 € 1.4 8.000 €
Sources: [12] F. J. Fabozzi, P. P. Peterson, Capital Budgeting: Theory and Practice, John Wiley & Sons, Inc., 2002
If one chooses on the basis of the greater PI, the investment A should be undertaken, while if one chooses by looking at the NPV, the choice would fall on the investment C. Looking at investments A and B, which have the same scale, one sees that the PI gives the same information as the NPV. When investments have different scales, the PI should not be used, while on an equal scale it says the same things as the NPV, so it is redundant.
2.1.3.4 – Payback Time
“A project’s payback period is found by counting the number of years it takes before the cumulative cash flow equals the initial investment.”14 The decision rule used is that a shorter payback is better than a longer one. The problem is that this indicator does not tell us anything about the cash flows after break-even, so you cannot know any measure of investment profitability, despite this the payback is useful in industries characterized by extremely high depreciation rates of the assets, such as the electronic equipment industry, which therefore require rapid payback periods since within one or two years it will be necessary to innovate again with new investments.15 In sectors where the investment is long-lasting, such as real estate, repayment is not very useful.
2.1.3.5 - Modified Internal Rate of Return – MIRR
To explain the MIRR it is necessary to return to the hypothesis of reinvestment underlying the IRR: to say that an investment has an IRR of 28.62% means that all net cash flows obtained at the end of each period are reinvested with a compounded rate of return of 28, 62% for the whole life cycle of the investment, in table 6 this situation was hypothesized.
r = √𝑡 𝐹𝑉𝑃𝑉− 1 (9)
In the hypothesis that the NCFs would not be reinvested every year with a compound rate until the end of the life cycle of the investment, the rate of return would be:
FT = 40 € * 5 = 200 €
14[17] R. A. Brealey, S. C. Myers e F. Allen, Principles of Corporate Finance, 10th edition, The McGraw-Hill Companies, Inc., 2011. Pag. 105
PV = 100 €
r = √𝑡 𝐹𝑇𝑃𝑉− 1 = √200 100
5
− 1 = 14.87 %
The return rate of this investment in which the annual NCFs are not reinvested is defined as modified internal rate of return or MIRR. The MIRR can be modified by acting on the return rate assumed for the reinvestment of annual NCFs; in fact the compound return of 14.87 per cent was obtained assuming a reinvestment of 0 per cent, but it could be another value. In this way it is possible to make the hypothesis of reinvestment more likely, for example, assuming that the reinvestment rate is that of an annual government bond. The decision rule of the MIRR is to accept projects with MIRR greater than the opportunity cost of capital.
Table 6. IRR reinvestments assumptions break-down
Years 0 1 2 3 4 5
NCF - 100,00 € 40,00 € 40,00 € 40,00 € 40,00 € 40,00 €
NPV 51,60 €
IRR 28,6%
Each year NCF is reinvested at 28,6% of rate of return
year 1 40,00 € 51,45 € 66,18 € 85,12 € 109,49 € year 2 40,00 € 51,45 € 66,18 € 85,12 € year 3 40,00 € 51,45 € 66,18 € year 4 40,00 € 51,45 € year 5 40,00 € FV (CF at 5th years sum) 352,23 € PV 100,00 €
Compound rate of return – r (using formula 9) 28,6%
PART 2.2 – INVESTMENT RISK
Until now it has been implicitly assumed that the expected cash flows are "safe", that is there are no possibilities that the amount and timing of their collection or payment would be different than expected. However, it is clear that being these cash flow events that belong to the future, they cannot be considered as secure at 100% and, on the contrary, they are much more likely to differ from what was expected. Since the present value of a series of cash flows depends on their size, the timing with which they occur and the discount rate with which they are discounted, a variation in one of this parameters cause a change in the performances of the investment, so it is necessary to understand how the risk impacts on the main elements of the DCF and so on the profitability of an investment.
2.2.1 - Some Definitions About Risk and Risk Management
Risk can be defined as:
• Risk – when an outcome may or may not occur, but its probability of occurring is known. Uncertainty – when an outcome may or may not occur and its probability of occurring is not known.16
• Risk: effect of uncertainty on objectives. Risk is often expressed in terms of a combination of the consequences of an event (including changes in circumstances) and the associated likelihood of occurrence.17
• A risk can be defined as an uncertain event or circumstance that, if it occurs, will affect the outcome of a programme/project.18
• Risk is generally referred to as: the uncertainty expressed through the significance and likelihood of events and their outcomes that could have a material effect on the goals of a real estate development organization over a stated time horizon.19
• Risk is a possible future event combining the probability or frequency of occurrence of a defined threat or opportunity and the magnitude of the consequences of that occurrence.20
Risk management can be defined as:
• Enterprise risk management is a process, effected by an entity’s board of directors, management and other personnel, applied in strategy setting and across the enterprise, designed to identify potential events that may affect the entity, and manage risk to be within its risk appetite, to provide reasonable assurance regarding the achievement of entity objectives.21
16Sloman (1995) cited in[31] P. Loizou e N. French, «Risk and uncertainty in development: A critical evaluation of using the Monte Carlo simulation method as a decision tool in real estate development projects,» Journal of Property Investment & Finance, vol. 30, n. 2, pp. 198-210, 2012
17[34] International Organization for Standardization (ISO), «Risk management — Principles and guidelines. ISO 31000:2009(E),» ISO, 2009
18[16] Royal Institution of Chartered Surveyors (RICS), «Management of risk, 1st edition,» Royal Institution of Chartered Surveyors (RICS), London, 2015
19[13] W. GleiBner e T. Wiegelmann, «Quantitative methods for risk management in the real estate development industry. Risk measures, risk aggregation and performance measures,» Journal of Property Investment & Finance, vol. 30, n. 6, pp. 612-630, 2012 20[32] International Organization for Standardization (ISO), «ISO/IEC Guide 73:2002 Risk management -- Vocabulary -- Guidelines for use in standards,» International Organization for Standardization (ISO), 2002
21[33] Committee of Sponsoring Organizations of the Treadway Commission (COSO), «Enterprise Risk Management — Integrated Framework. Executive Summary,» Committee of Sponsoring Organizations of the Treadway Commission, 2004
• Risk management: coordinated activities to direct and control an organization with regard to risk. Risk management framework: set of components that provide the foundations and organizational arrangements for designing, implementing, monitoring, reviewing and continually improving risk management throughout the organization.22
Risk is defined as a possible event whose probability is known, which causes a deviation of the observed results from those expected and can produce both a negative and a positive impact on the output-related objectives. The uncertainty differs from the risk in that the probability of an event is not known, while for the risk it is. Risk has a quantitative nature, while uncertainty is something more subjective. Risk
management is the entire process of identifying, quantifying, mitigating and monitoring risks.23 According to GleiBner and Wiegelmann (2012) there are some common elements, highlighted in Figure 11,
in the literature analyzed by them regarding risk management: “Four core elements in common […]. The
goal of the risk identification process is to identify possible risks, which may affect, either negatively or positively, the objectives of the business and the activity under analysis. Risk assessment is defined as the overall process of risk analysis and risk evaluation and helps in determining which risks have a greater consequence and impact than others as well as the probability of the event occurring. This is followed by the risk control phase, which evaluates whether the level of risk found during the assessment process requires management attention. Risk monitoring is the periodic tracking of risks and reviews the effectiveness of the treatment plan.”24 In summary, the activities that are part of the risk management process are:
• Risk identification: identification of sources of risk that may have a negative (and positive) impact on the objective of the business.
• Risk assessment: quantification of impact and probability of risks identified • Risk control: decide if avoid, minimize, transfer or accept risk
• Risk monitoring: periodic tracking and check of effectiveness of actions undertaken from feedback. As already specified in the introduction, the perimeter of this thesis will only include the part of identification and assessment of the risk and I will not deal with control and monitoring at all. Looking at Figure 11 three distinct phases can be identified: the definition of objectives, the identification of risks and the management of risks. The objectives of a business activity can be the most diverse and are generally expressed with indicators, both quantitative and qualitative. As stated at the beginning of this chapter, the ultimate goal, the end game of an investor as well as of a company, is to maximize profit; this means that in the preliminary evaluation phase of a project, objectives will be set about the potential gains that this can give. In the risk identification phase it will be necessary to understand which are the sources from which those events could be generated that could lead to a deviation from what was expected. The point is that there will always be forecast errors, but only those that exceed the maximum deviation value set a priori, whose extent defines the risk tolerance, or risk appetite, of the investor must be considered risky. The magnitude of the deviation that you are willing to accept is the price that you have to pay in order to get the profit you are aiming for “is what you must give up in order to get an item you want - the opportunity cost of that item.”25 The definition of opportunity cost tells us that not only obtaining a profit has a cost,
22[34] International Organization for Standardization (ISO), «Risk management — Principles and guidelines. ISO 31000:2009(E),» ISO, 2009
23[16] Royal Institution of Chartered Surveyors (RICS), «Management of risk, 1st edition,» Royal Institution of Chartered Surveyors (RICS), London, 2015
24[4] W. GleiBner e T. Wiegelmann, «Quantitative methods for risk management in the real estate development industry. Risk measures, risk aggregation and performance measures,» Journal of Property Investment & Finance, vol. 30, n. 6, pp. 612-630, 2012 25[23] P. Krugman e R. Wells, Microeconomics, 2th edition, Worth Publishers, 2009, pag. 7
that is the possibility of variance between observations and expectations, but also that the greater the profit that one aims to obtain, the greater the variance that one must be willing to bear. This is why we refer to the relationship between risk and return as a trade-off.
Figure 11. Risk management process
Sources: [13] W. GleiBner e T. Wiegelmann, «Quantitative methods for risk management in the real estate development industry. Risk measures, risk aggregation and performance measures» Journal of Property Investment & Finance, vol. 30, n. 6, pp. 612-630, 2012
2.2.2 - Returns of Real Estate Assets
To understand what returns the best thing to do is solve equation (1) for r:
𝑟 =
𝐹𝑉𝑃𝑉
− 1
(10)Substantially, the returns are the rate of profit on an investment. In real estate, the two sources of income from an investment come from the annual income and from the reversion value, or from the receipt obtained from the disinvestment of the property at the end of the holding period. Adding these elements into the "conceptual framework" of equation (10), we obtain what is reported in equation (11). The first element on the right hand of the equation is profit from the rent, which is generally called income yield, while the second element indicates the return obtained from the price change of the asset, usually defined capital gain.
