The effect of the real estate cycle on investment decisions

Transcription

1 Dept of Real Estate and Construction Management Thesis no. 36 Msc Program in Real Estate Management Master of Science, 30 credits The effect of the real estate cycle on investment decisions An empirical study of Stockholm office market by using DCF cyclical valuation models Author: Dong Jing Stockholm 2010 Supervisor: Hans Lind 1

2 Master of Science Thesis Title: The effect of the real estate cycle on investment decisions An empirical study of Stockholm office market by using DCF cyclical valuation models Authors: Department: Master Thesis number: 36 Supervisor: Dong Jing Department of Real Estate and Construction Management Division of Building and Real Estate Economics Hans Lind Abstract: Property investment decision is subject to real estate market cycle. Start or terminate an investment in different cycle phases will lead to different outcomes. Meanwhile, most of the property investments are decided based on its valuation results. As the most popular valuation method, the traditional Discounted Cash Flow (DCF) valuation method has been proved that it caused bias to its valuation results as it assumes that all variables in trend rather than cycle. This could lead to serious consequences to lots of investments since the valuation results could not reflect the real market condition. The superiority of cyclical DCF model is that it is dynamic, sensitive to market changes, and could reflect variations with different cycle tendencies, but previous cyclical DCF model only assumed the income cash flows to be cyclical but kept the discount rate to be constant. When analyzing the effect of real estate cycle, the cycle is always treated as a whole, but how much that each variable s cyclical variation devoted to the overall effect on the valuation result has been barely analyzed. There is also no record about how different the investment decisions would be if facing different cycle phases, cycle tendencies, and contract lengths. All the unsolved problems that mentioned above are precisely what this paper is going to solve. The empirical study of this thesis is based on the cycle of Stockholm office market, where DCF method is widely used and the cycle is quite stable. The empirical study 2

3 consists of three main analyses, which analyze the investment decision under different period assumptions and different cycle tendencies. Besides, the sensitivity analyses mainly focus on the effects that caused by different variable s cyclical variation. Conclusion and suggestions about what investors should be aware of when making investment decisions based on DCF valuation results could be found after the empirical study. Key words: Real estate cycle, investment decision, cyclical DCF model 3

4 Acknowledgement: I would like to thank my supervisor, Professor Hans Lind, who provided a lot of constructive suggestions and helpful comments on this thesis. His guidance and assistance were very much appreciated. I would also like to thank the Royal Institution of Technology, the Department of Real Estate and Construction Management and all the teachers in the master program of real estate management. They offered me such a great opportunity to study here, and allowed me to learn extensive knowledge and skills on the real estate field. I am also grateful to Nankai University where I not only completed my bachelor degree, but also gained solid theoretical foundation and great passion of economics and finance studies. Finally, I would like to acknowledge my parents who have devoted considerable time and efforts for my over eighteen years of studies. I would never be able to complete this thesis without their constant support and sacrifices. 4

5 List of Figures Figure 1 Phases of the Real Estate Supply/Demand Cycle Figure 2 Real Estate Cycle Phases Figure 3 Real prices of office premises in city centres Figure 4 Prime office rent Stockholm Figure 5 Annual change of office premises in city centre Figure 6 Vacancy rate for office premises in city centres Figure 7 Average yield levels for modern office premises in city centres Figure 8 Results of NOI in Analysis 1 & Analysis Figure 9 Valuation results of Analysis Figure 10 Valuation results of Analysis Figure 11 Valuation results of cyclical scenarios in a fixed and long term period Figure 12 The misinterpretation caused by trend DCF valuation results in Analysis

6 List of Tables Table 1 Assumption of the property to be valued Table 2 Initial inputs for analysis Table 3 Assumptions of cycle tendency, three different scenarios Table 4 Structure of the empirical study Table 5 Assumptions of each variable s range variation in sensitivity analysis I Table 6 An overview of Analysis Table 7 Valuation results ranges of Scenario 2 & 3 in Analysis Table 8 Valuation results ranges of Scenario 2 & 3 of all the tests in Sensitivity Analysis I Table 9 Valuation results ranges of Scenario 2 & 3 in Analysis Table 10 Valuation results ranges of Scenario 2 & 3 of all the tests in Sensitivity Analysis Table 11 Result of Analysis

7 Table of Content 1. INTRODUCTION: Literature Review Purpose and structure THEORETICAL BACKGROUND Theory about real estate cycle Concepts about Cycle Definition of real estate cycle Generation of real estate cycle The phases of real estate cycle Economic characteristics of real estate cycle Theory about Real Estate Valuation Real Estate Valuation and its approaches Traditional DCF model ABOUT STOCKHOLM OFFICE MARKET Historical real estate cycles in Sweden History of real estate valuation in Sweden: DCF method is widely used Introduction of Stockholm office market ASSUMPTION OF EMPIRICAL STUDY Basic assumption of subject property Initial data Input Assumptions of cycle tendency METHODOLOGY Overview Analysis 1 (Invest at 1st year, sell in different cycle phases) Methodology of Analysis 1: Pro forma & Matrix Sensitivity analysis I: How large effect that respectively caused by each variable cyclical variation in Analysis Analysis 2 (Invest in different cycle phases, sell at year 12) Methodology of Analysis 2: Pro forma & Matrix Sensitivity analysis II: How large effect that respectively caused by each variable cyclical variation in Analysis Analysis 3 (Invest at 1 st year, sell at year 12, covers a complete cycle period) RESULTS AND COMPARISON Analysis Sensitivity analysis I

8 6.1.2 Summary of Analysis Analysis Sensitivity analysis II Summary of Analysis Analysis CONCLUSION OF EMPIRICAL STUDY CONCLUSIONS & SUGGESTIONS Short term investment An investment with a fixed investing time: when to sell? An investment with a fixed terminating time: when to invest? Long term investment: what price is the property worth? In terms of Stockholm office market REFERENCES APPENDIX Appendix 1. Cyclical model of DCF valuation method (Pyhrr, Roulac, & Born, 1999) (Born & Pyhrr, 1994) Appendix 2 Variables cyclical assumptions according to different Scenarios Appendix 3. Mathematics models of Analysis Model for Scenario 1 (no cycle existed) Model for Scenario 2 & Scenario 3 (cycle exist) Appendix 4. Mathematics models of Analysis Model for Scenario 1 (no cycle existed) Model for Scenario 2 & Scenario 3 (cycle exist) Appendix 5. Mathematics models of Analysis Test 1 (Scenario 1): Constant cash flow, constant discount rate Test 2 (Scenario 2 & 3): Cyclical cash flow, constant discount rate Test 3 (Scenario 2 & 3): Constant cash flow, cyclical discount rate Test 4 (Scenario 2 & 3): Cyclical cash flow, cyclical discount rate Appendix 6. Valuation results of Scenario 1 in Analysis Appendix 7. Valuation results of Scenario 2 in Analysis Appendix 8. Valuation results of Scenario 3 in Analysis Appendix 9 Results of Sensitivity analysis I (in terms of Analysis 1) Appendix 10 Valuation results of Scenario 2 in Analysis Appendix 11 Valuation results of Scenario 3 in Analysis Appendix 12 Results of Sensitivity analysis II (for Analysis 2) Appendix 13 Results of Analysis

9 1. Introduction: Generally, an investment decision of a property is made mainly based on its valuation price. There are many ways to appraise the property s value, however the most popular valuation method to date is Discounted Cash Flow valuation method (DCF) which discounts the possible incomes that would happen in future, and therefore its result to some extent reflect the reality of the subject property properly. Not only by property appraisal organization, the DCF valuation method is also widely used by commercial banks, investment corporations, and other financial departments when they are making investment decisions. However, risks still existed. Shannon, Reilly and Schweihs pointed out in 2000 that there are two substantial shortcomings of traditional DCF method: 1) Traditional DCF method assumes the discount rate to be constant at the level when the analysis is taken, but it should be supposed to change, sometimes dramatically, over time. 2) The income cash flows are assumed to increase in a straight line rather than cyclical fluctuation in traditional DCF method, which doesn t take cyclical natures into consideration. (Shannon, Reilly, & Schweihs, 2000) As a matter of fact, it is very important for an investor to consider about the cycle conditions when he is making an investment decision. Such shortcomings of traditional DCF method would lead to bias to the valuation result, and then affect the investment decision. For example, a booming in real estate market can always last no more than ten years, and if using traditional DCF method to analyze a property during the booming years would lead to overvaluation, if an investment was made based on the overvalued price at that time, it would be a huge possibility that the investor would lose his money in future. Such phenomenon has attracted many researchers attentions, and some of them contributed to this topic a lot according to previous literatures. 1.1 Literature Review Shannon, Reilly and Schweihs s theory about traditional trend DCF model can be summarized as: in tradition a DCF method, both discount rate and income are supposed to be trend rather than cyclical. The characteristics of traditional DCF model have been detected by other economists earlier too. In 1988, Roulac S.E indicated that a misconception of real estate market 9

10 recovery and overly simplistic measurement method and cash flow streams made the real estate securities overvalued (Roulac, 1988). And Giliberto suggested an empirical study should be done in order to quantify how serious the bias is after concluded from theories that the bias occurred in appraisal-based returns (Giliberto, 1988). Wheaton & Torto researched in how does the appraisal results change respectively according to income and economic circumstances through examining office market data in 1989, and they found that: appraisals were remarkably stable during a period when interest rates fluctuated widely and when expectations about office market income growth probably should have changed quite sharply. (Wheaton & Torto, Income and Appraisal Values: A Re-examination of the FRC Returns Data, 1989) In 1994, Pyhrr & Born indicated that biases existed in DCF valuation models and gave evidence; they concluded that the static model assumptions of trend DCF model which are incompatible with dynamic cyclical market can be presented as below (Born & Pyhrr, 1994): 1). Rent is supposed to change in a constant rate over times. 2). NOI at the end of period is converted by a constant capitalization rate. 3). Vacancy rate is assumed to be stabilized over the periods. And meanwhile, a cyclical DCF model was introduced by them for real estate valuation, which can be found in Appendix 1. In their cyclical DCF model, several cycle factors have been taken into calculation, and they also compared the results from both trend model and cycle model, and proved that the result of cycle model reflected the reality better. Although trend model s shortcomings have been pointed out and the superiority of cyclical model has been introduced, there are still lots of perspectives that previous literatures haven t referred to. For examples: P&B s cyclical model only try to make cash flows to be cyclical but still keep discount rate constant; when analyzing the effect of real estate cycle, the cycle is always treated as a whole, but people barely analyze how much that each variable s cyclical variation devoted to the overall effect on the valuation result; and what is more, in terms of investment decision, there is no record of investors responses to different cycle phases, for example, the different prices that investors would be willing to pay for the same property when facing different cycle tendencies. This paper gives an empirical study that base on Stockholm office market to answer the questions above. 10

11 1.2 Purpose and structure The purpose of this paper is to analyze the effect of real estate cycle on investment decision by using cyclical DCF models, and from which to conclude suggestions for investors who depend on the result of DCF model. The paper analyzes an investor s different responses when he is facing different phases of real estate cycle and different period lengths of investment. Relevant theories of both real estate cycle and real estate valuation would be introduced first; and next would be a brief introduction of historical real estate cycle and history of real estate valuation of Stockholm office market; after that, an empirical study which consists of three main analyses would be carried out based on Stockholm Office Market. The three analyses of the empirical study are organized under different period assumptions: 1) If the investment would begin at year 0, and will be ended at different cycle phases during the coming 12 years. 2) If the investment would begin at different cycle phases during the coming 12 years, and will be ended at year 12. 3) If the investment would begin at year 0, and will be ended at year 12. There are three scenarios in all these analyses as well. Each of the scenarios assumes one possibility of the cycle tendency. After each analysis, a sensitivity analysis is given to measure how large effect that respectively caused by each variable cyclical variation. The analyses focus not only on the differences between trend model and cycle model, but also on the relationship within the cyclical scenarios. From comparing the results, we can conclude what an investor would be aware of when deciding an investment based on DCF valuation result. 11

12 2. Theoretical Background 2.1 Theory about real estate cycle Concepts about Cycle Cycle is interpreted as a periodically repeated sequence of events according to The American Heritage Dictionary (American Heritage Dictionary, 2006). And it is also described as a predictable pattern of occurrences, as in the upward and downward sweep of a sine curve. In some patterns, we see distinct stages of rising, sustaining, falling, and dormancy. (Stout, Nicolai, & Sassover, 1995) Cycle can be found in various fields in our life, and generally, it appeared as a symmetrical and regular sine curve shape in different literatures. But actually, many cycles are asymmetrical in reality. In terms of economics field, there are still lots of economists argue about whether the cycle really exist or just is produced by irrational behavior. However, it cannot be denied that cycle do has influence to human s life, and two of the most important influences can be described as: 1) We could prepare for events that are supposed to happen according to cycle estimation. 2) We could no longer waste time on fighting the inevitable, but adopting and positioning ourselves within the cycles to make optimal strategy. (Stout, Nicolai, & Sassover, 1995) Definition of real estate cycle The Royal Institution of Chartered Surveyors (RICS) gives a definition of real estate cycle on Understanding the Property Cycle, their publication in 1994: Property cycles are recurrent but irregular fluctuations in the rate of all-property total return, which are also apparent in many other indicators of property activity, but with varying leads and lags against the all-property cycle. (RICS, 1994) Generation of real estate cycle According to Glenn Mueller s view in 2006, the original cause of real estate cycle, which can be concluded as the lagged relationship between demand and supply for physical space. (Mueller, 2006) And the same view can be found at Jack C Harries article in 2000, he thought that the market would stay in equilibrium and no cycle would occur if the new supply buildings can be produced or withdrawn immediately, and just because of the existence of the lag 12

13 between before the need for more housing or office space is identified and the time new space becomes available. (Harris, 2000). Pyhrr, Roulac &Born (1999) interpreted this process as in Figure 2. In their article, the interaction of supply and demand forces generated real estate cycle which reached a peak at point B, the equilibrium when supply and demand meet each other at their higher level, and fell to a bottom at point A where supply and demand have an equilibrium at their lower level. If we connect all the A and B together as a curve line, it would be the general shape of real estate cycle in this case The phases of real estate cycle Figure 1 Phases of the Real Estate Supply/Demand Cycle Source: (Pyhrr, Roulac, & Born, 1999) Mueller and Laposa indicated that there are four phases of real estate cycle: Recession, Recovery, Expansion and Contraction/Hypersupply (Mueller & Laposa, 1994), which can be found in Figure 1. Figure 2 Real Estate Cycle Phases 13

14 Generally, when talking about upside cycle, it refers to Recovery and Expansion phases, and downside cycle for Recession and Contraction phases. When the cycle is in phases Recession or Recovery, the vacancy rate is higher than equilibrium; however the trend of the vacancy rate is falling, while in Expansion and Contraction phases the vacancy rate is lower than equilibrium but rising Economic characteristics of real estate cycle The economic characteristics of real estate cycle below concluded from the works of Pritchett (1984), Wheaton (1987) and Witten(1987). 1). Averagely, in a growing economy, the rising and peak phases of the cycle is in dominate position, which means there are more years of good time than bad time for investors. 2). The long-term trend line is upward sloping for both demand and supply cycles in a growing economy. 3). It is more volatile to change supply than change demand in some extent. 4). The demand cycle leads the supply cycle by a period of time. 5). Vacancy rate is the best indicator of the cycle phases. 2.2 Theory about Real Estate Valuation Real Estate Valuation and its approaches Real estate valuation is the task of appraising the prospective price of a site or building in the case of a sale. (Schulz, May 2002) Generally, there are three main kinds of real estate valuation approaches, they are: Sale comparison approach, Cost approach, and Income capitalization approach (Uniform Standard of Professional Appraisal Practice, 2008) Income capitalization approach is considered as the most applicable approach for investment or commercial properties which can produce income. And especially, one main method of this approach, DCF (discounted cash flow) method, which we mentioned at beginning in this paper, has been seen as the most popular used method and is widely used to value larger and more expensive commercial or investment produce-income properties Traditional DCF model A brief concept of DCF model can be presented as: DCF is what someone is willing to pay today in order to receive the anticipated cash flow in future years. (Kaplan, 2004) 14

15 DCF method became popular in finance field since 1929, the Wall Street Crash occurred. It was the first time formally expressed by John Burr Williams in his work The Theory of Investment Value in A basic form of traditional DCF model is as below (Shannon, Reilly, & Schweihs, 2000): Where: PV = Present Value n = The last period for which economic income is expected; n may equal infinity (i.e., ) if the economic income is expected to continue in perpetuity. E i = Expected future economic income in the ith period in the future (paid at the end of the period) k = Discount rate (the cost of capital, e.g., the exit yield available in the market for other investments of comparable risk and other investment characteristics) i = The period (usually stated as a number of years) in the future over which the prospective economic income is expected to be received 15

16 3. About Stockholm office market Stockholm is the capital city of Sweden, and is also the biggest city with the largest population. According to Statistics Sweden, the average number of employees in Stockholm is around 1 million, occupied 25% of the whole country. It is some of these employees who are the primary users of the offices in Stockholm that yield the demand in Stockholm office market. 3.1 Historical real estate cycles in Sweden In Sweden, the commercial rental market had not been subject to market forces until 1972, since the Central Bank (Riksbanken) restricted the market by several macroeconomic tools during 1950s (Gunnelin & Söderberg, 2003). The state played a critical role in three strategic areas of financing mechanisms, access to land, and construction at that time (Jaffee, 1994). In terms of the continuing price falls in late 1970s and early 1980s, except the policy reason, the other main cause was due to continued weakening in the rental market (Uniform Standard of Professional Appraisal Practice, 2008). The boom of the market did not come until 1985, when a tax reduction policy was gradually implemented, and the prices of property began to rise up, and soon, in early 1990s, a commercial real estate crisis occurred in Sweden for there were substantial overbuilt office buildings while the demand had been declined, and the vacancy rate raised disproportionately, reaching the highest peak (22%) in 1993 (Gonzalez, 2004). After that, the real estate cycle in Sweden was more stable, and its varied tendency was consistent with the cycle of Europe and the world but much less fluctuations. Compared with other countries, Sweden s office market performed even better during the Financial crisis recent in years according to data from the companies and organizations IPD, Reuters EcoWin, Riksbank, etc. 3.2 History of real estate valuation in Sweden: DCF method is widely used DCF method is widely used in Sweden according to the real estate valuation history of this country. Real estate valuation was developed in Sweden based on the valuation method that focused on agricultural properties during 1970s. The Institution of Real Estate Economics at the Royal Institute of Technology in Stockholm extent established the theoretical background and basic valuation principles (Samuelsson, 2008). Stellan Lundström introduced the way that uses cash flow analysis as a tool for 16

17 investment analysis of rental properties (Lundström, 1979). Since then, people use valuation method for investment analysis, and the DCF method became popular and widely used in both financial and property investment areas. 3.3 Introduction of Stockholm office market Some basic variables data of Stockholm office market which would be taken as references in next chapters could be found in the figures that are displayed in next page. To summarize these figures, we can get some key points about Stockholm office market: 1) The cycle tendency of Stockholm office market is highly consist with real estate cycle of Sweden which describe in previous section. 2) Compare with other cities in Sweden, the cycle of Stockholm office market always vary ahead of them, which means Stockholm office market is more sensitive to the changes of external environment. 3) Rents varied along with prices, but rent cycle is more stable than price cycle. 4) After the real estate crisis of 1993, there was a dramatically continuing falling of vacancy rate till 2000, and after that, the vacancy rate kept at a less fluctuated and lower level compared with earlier years, which varied between 4% and 10%. 5) The average yield level of Stockholm office market is the least volatile one among all listed variables, and its variation range has been from 4% to 8% since

18 Figure 3 Real prices of office premises in city centres Figure 4 Prime office rent Stockholm Figure 5 Annual change of office premises in city centre Figure 6 Vacancy rate for office premises in city centres Figure 7 Average yield levels for modern office premises in city centres 18

19 4. Assumption of Empirical study 4.1 Basic assumption of subject property The assumed subject property is located in Stockholm center, which has 5 floors and mainly for office use. The rental level of that area can be seen as average office rental level in Stockholm. The investor would like to buy 3 floors of the building at the end of 2007, and is planning to rent them out as offices to other companies. Suppose the investor would make the investment decision only based on the valuation result. The general condition of the subject property can be found in Table 1. The property to be valued floor 3 (floor 3-5 of a building) area/floor 300 sqm total area 900 sqm Contract period 1-12 years (one complete cycle: ) Table 1 Assumption of the property to be valued 4.2 Initial data Input The empirical study will be carried on mainly based on the historical data as displayed in previous chapter, according to which, the initial inputs are assumed as below: Estimate market rent (at year 0) Rent 3500 sek/sqm/y Inflation rate inflation rate=0% Estimate operating &maintenance cost o&m cost sek/sqm/y (be constant over time) Estimate vacancy rate (at year 0) 1 In Sweden, most of rental lease are gross leases, which makes the operation & maintenance cost in Sweden to be higher than other countries who use net lease instead. 19

20 vacancy rate 7% Exit yield (at year 0) Exit yield 6% 2 Discount rate (at year 0) Discount rate 6% (constant in all cash flows) Table 2 Initial inputs for analysis 4.3 Assumptions of cycle tendency There is a complete cycle that consists of 4 quarter periods. Each period covers 3 years. Three Scenarios are built to represent three different cycle tendency assumptions. In Scenario1, there would be no cycle happens, this is a trend scenario; but the other two scenarios are supposed to be cyclical. All the scenarios begin with an initial level at year 0, but after then, in the cyclical scenarios, the cycle will be assumed in different cycle phases during different quarter periods. Scenario 1 Scenario 2 Scenario 3 Year 0 Quarter 1 Quarter 2 Quarter 3 Quarter Initial Constant Constant Constant Constant level (No cycle) (No cycle) (No cycle) (No cycle) Initial Recession phase Recovery phase Expansion phase Contraction phase level (Downward cycle) (Upward cycle) (Upward cycle) (Downward cycle) Initial Expansion phase Contraction phase Recession phase Recovery phase level (Upward cycle) (Downward cycle) (Downward cycle) (Upward cycle) Table 3 Assumptions of cycle tendency, three different scenarios 2 According to Godon Formula, Exit yield=r-g, since we assumed inflation rate is zero in this case, we got Exit yield=r. 20

21 5. Methodology 5.1 Overview The main structure of this empirical study can be seen in Table 3. Analyses Analysis 1 Assumptions -Sensitivity Analysis I Analysis 2 -Sensitivity Analysis II Contract Contract period Contract type Scenarios Involved Scenarios Floating: year 1 - year n (n=2,3, 12) Short term Trend Scenario Floating: year n - year 12 (n=1,2, 11) Cyclical Scenarios Analysis 3 Fixed: year 1 - year 12 Long term Cyclical Scenarios Table 4 Structure of the empirical study There are three analyses which are built according to different assumptions, and the details of these analyses would be introduced in later sections. Scenario names Scenario 1 Scenario 2 Scenario 3 Three scenarios are built according to different assumptions of cycle tendencies: No cycle exist, Down-up-down cycle, and Up-down-up cycle. Variables data inputs are supposed to vary along with different cycle tendencies over time in different scenarios, and all the data can be found in Appendix Analysis 1 (Invest at 1st year, sell in different cycle phases) Analysis 1 is used to test how much would an investor be willing to pay at the first year when he facing different contract length and different cyclical tendencies. Analysis 1 will focus mainly on the possible contracts which would all begin at the first year, but will end in different years during a complete cycle period. The results of this analysis will indicate how different prices that an investor would be willing to pay for the same building at the first year, while the contract is supposed to end at different phases of a cycle. This analysis includes all three scenarios, through which we can compare the results not only between trend DCF model and cyclical DCF model, but also between two different cyclical models with different assumptions of cycle tendency. After that, a sensitivity analysis would be applied to test the effects that come from each variable s cyclical variation Methodology of Analysis 1: Pro forma & Matrix At first, a pro forma would be built in each scenario to calculate net operating income (NOI) and the property s price at one year s end (equal to Salvage value) for each year. 21

22 After that, the results that we got from the pro forma would be put in a corresponding matrix in time sequence in each scenario, so that the valuation result for each year can be calculated through the matrix. The result of year i during the cycle period in this case, for example, means the price that an investor would be willing to invest at the first year when the investment is supposed to end at year i. The mathematics models for Analysis 1 can be found in Appendix Sensitivity analysis I: How large effect that respectively caused by each variable cyclical variation in Analysis 1 From the mathematics models we can see there are three main variables in the models: Market rent, Vacancy rate, and Exit yield. This sensitivity analysis is used to test each scenario s response to different variable s variation. Table 4 shows the assumptions of each variable s variation range in sensitivity analysis I: Variables original range Test new range Variation Test a (3000,4000) More fluctuated Market rent (3200,3800) Test b (3400,3600) More stable Vacancy Test c (2%, 12%) More fluctuated (4%, 10%) rate Test d (6%, 8%) More stable Test e (3%, 9%). More fluctuated Exit yield (4%, 8%) Test f (5%, 7%) More stable Table 5 Assumptions of each variable s range variation in sensitivity analysis I 5.3 Analysis 2 (Invest in different cycle phases, sell at year 12) Analysis 2 is used to test how much would an investor be willing to pay at different years in different cycle phases if he has been told the investment would end at a certain year whenever he invests. Unlike Analysis 1, Analysis 2 will focus on the possible contracts which will all ends at year 12, but begin at different year during a completely cycle period. The results of this analysis will show different investment decisions an investor would make for the same property when he standing at different cycle phases. A sensitivity analysis would also be carried out thereafter Methodology of Analysis 2: Pro forma & Matrix The pro forma in this section would be as same as in Analysis 1, but after which, the 22

23 matrixes would be built in converse way, in order to calculate the valuation result for each year when investment would be made and would be ended at year 12. The result of year i in this case means the price that an investor would be willing to invest at year i when the investment is supposed to end at year 12, the last year Sensitivity analysis II: How large effect that respectively caused by each variable cyclical variation in Analysis 2 The design of Sensitivity analysis II is as same as Sensitivity I, but to test Analysis Analysis 3 (Invest at 1 st year, sell at year 12, covers a complete cycle period) This analysis is used to test how much the investor would be willing to invest when facing a long term and fixed contract period with different cycle assumptions of cash flow & discount rate and cycle tendencies. In this analysis, the contract length would be assumed as 12 years equal to a complete cycle period. Table 5 shows an overview of Analysis 3: Constant Discount rate Cyclical Discount rate Constant NOI cash flow Test 1 (Scenario 1) Cyclical NOI cash flow Test 2 (Scenario 2 & 3) Table 6 An overview of Analysis 3 Test 3 (Scenario 2 & 3) Test 4 (Scenario 2 & 3) The mathematics models for each test could be found in Appendix 5. After that, a comprehensive analysis would be carried out by combining all the valuation results which last for the whole 12 years from all the analyses above, in order to analyze from a long term aspect that how much effects caused by different variable, different cycle tendencies, different variation ranges, etc. 23

24 6. Results and Comparison 6.1 Analysis 1 The details of pro forma and matrix of Analysis 1 can be found in Appendix 6-8. Figure 8 Results of NOI in Analysis 1 & Analysis 2 The pattern in Figure 8 is completely symmetrical. In Scenario 1, which assumes no cycle will happen in the coming 12 years, the values of NOIs are shown as a horizon line, which means they are constant at the initial level till the end. In terms of Scenario 2 and Scenario 3, the different cycle tendencies did not change the values of NOIs, but just make the curves directions to be conversed. Figure 9 Valuation results of Analysis 1 According to Figure 9 we can find out that the valuation results of Scenario 1 is still a horizon line, the values are constant at 41,325,000 SEK. 24

25 As mentioned in last chapter, the valuation result of year i means the price the investor would be willing to pay for the subject property at year 0 while the investment would be ended at year i. Maximum Minimum Value (SEK) Change (% from initial level) Value (SEK) Change (% from initial level) Scenario 2 56,145, % 28,350, % Scenario 3 67,594, % 34,544, % Table 7 Valuation results ranges of Scenario 2 & 3 in Analysis 1 To compare the results in Scenario 2 and Scenario 3, as shown in Table 6, taking the value of 1 st year as a baseline, we can see that: 1) Above the baseline, the values of Scenario 3 are much more fluctuated than Scenario 2, which reached a peak at 2011 that is 63.57% higher than the baseline; but below the baseline, the values of Scenario 2 are more fluctuated than Scenario 3. We can also say the curve line of Scenario 3 is higher than the symmetrical position of Scenario 2, in terms of curve shapes. 2) In terms of time, the values in the first half period ( ) as a whole are more fluctuated than in the rest half period ( ). It means that: 1). If the investment would be ended during Quarter 1 and Quarter 2 ( ), when the cycle is expected to be in Expansion phase in Quarter 1 and Contraction phase in Quarter 2, like what happened in Scenario 3, the investor would be willing to pay much more for the subject property than the initial level; when the cycle is expected to be in Recession phase and Recover phase during Quarter 1 and Quarter 2, as assumed in Scenario 2, the investor would not invest in this case as the value of the same property is depreciated in this case. 2). If the investment would last for longer than that, which would be ended during Quarter 3 and Quarter 4, and in terms of year 0, when facing a coming Expansion cycle phase, the investor would not invest as he know the cycle would fall down when the investment is ended; he would even invest more while facing a Recession phase in Quarter 1, but the extra price he would be willing to pay in this case would not be as much as mentioned in the previous point Sensitivity analysis I There are 6 tests in this section, two tests for one variable, to test what the results are going to change if the variable s variation range changed in different way. The assumptions of each variable s variation can be found in Table 4. 25

26 Tests All the results of Sensitivity analysis I can be found in Appendix 9. There are two variables directly relate to NOI, Market rent and Vacancy rate. According to the results of Sensitivity analysis I, the fluctuations range of NOIs in both cyclical scenarios could be sorted as a descending order as below: Test a > Test c > Original NOIs > Test d > Test b It means NOI is more sensitive to Market rent, when the range of market rent became slightly wider, like what happened in Test a, the range of NOIs was significantly amplified more than other tests; and while the range of market rent shrank slightly down, such like in Test b, the range of NOIs were narrowed more than other tests. The effects also come from Vacancy rate, but not as significant as Market rent. Value Maximum Minimum Scenario 2 Scenario 3 Scenario 2 Scenario 3 % Change (from initial level) Value % Change (from initial level) Value % Change (from initial level) Value % Change (from initial Test a 58,330, % 71,439, % 26,542, % 33,617, % Test b 53,959, % 63,750, % 30,157, % 35,471, % Test c 57,022, % 69,115, % 27,706, % 34,228, % Test d 55,268, % 66,074, % 28,993, % 34,860, % Test e 68,388, % 88,603, % 25,693, % 33,308, % Test f 48,922, % 54,984, % 31,763, % 36,242, % Table 8 Valuation results ranges of Scenario 2 & 3 of all the tests in Sensitivity Analysis I The valuation results ranges of both cyclical scenarios of all the six tests are shown in Table 7. All the tests are sorted in a descending order below according to the fluctuation ranges of their results of both the cyclical scenarios: Test e >Test a > Test c > Original > Test d > Test b > Test f The valuation results are most sensitive to Exit yield in this case. The result is most fluctuated when the range of Exit yield become slightly wider in Test e, and is most stable when the range of Exit yield become slightly more narrow in Test f. level) The variables that cause less effect on the valuation results are Market rent and Vacancy rate, they are, as mentioned above, directly related to NOI. We can conclude that in terms of valuation results, the effect from Exit yield/discount rate is more than the variables that involved in NOI Summary of Analysis 1 The results of Sensitivity analysis 1 indicate that the effect of Exit yield/discount rate is much more than the effect of NOI, which can explain why the valuation results become less fluctuated if the investment will be terminated during the second half cycle period. 26

27 If an investor has to make a decision at initial year, the optimal situation for him is an approaching Expansion phase and a short period before selling time; it would be even better that the investment can be terminated successfully at the peak point of the cycle. The second good choice for him is an approaching Recession phase and a long period before selling time, longer than the half-cycle period, so that he can also benefit from the investment if it can be ended during the Expansion or Contraction phases that after. 6.2 Analysis 2 The valuation results of Analysis 2 are shown in Figure 10. More details of pro forma and matrix of Analysis 2 can be found in Appendix NOIs in Analysis 2 are supposed to be as same as in Analysis 1. Figure 10 Valuation results of Analysis 2 In this analysis, the value of year i means the price that the investor would to pay at year i if the investment will be ended at Value(SEK) Maximum Change (% from initial level/sell price) Value(SEK) Minimum Change (% from initial level/sell price) Scenario 2 44,402, % 40,527, % Scenario 3 42,276, % 38,477, % Table 9 Valuation results ranges of Scenario 2 & 3 in Analysis 1 Compare with the valuation results of Analysis 1, the range of Analysis 2 s valuation results become much narrower. According to Table 9, the value of the peak point of the most fluctuated scenario is 44,402,012 SEK, increased by 7.45% compare with the initial level/sell price, but this number in Analysis 1 is 63.57%, almost nine times than in Analysis 2. 27

28 As showed in Figure 10, the shapes of the results curves are not like typical cycle, for each scenario, only the results in Quarter 1( ) are at the opposite site of the baseline compare with other quarters; the shapes of the results curves are neither symmetrical, the curve of Scenario 2 is slightly higher than the symmetrical position of Scenario 3. The valuation results are much more stable during Quarter 1, which means that to the investor, since the investment will be ended at 2020, he will be cautious to invest during Quarter 1, in spite of which cycle phase it would be in this period. In Quarter 2, the cycle of Scenario 2 is in the Recovery phase, and the signs of recovery inspired the investor, he would like to invest more money than the initial level on the subject property even the cycle just left the bottom and is still at a low level. In contrast, the Contraction phase in Scenario 3 makes the property s value falling down even though the cycle just left the peak and is still at a high level. The cycle of Scenario 2 will experience an Expansion phase during Quarter 3, but in Figure 10 we found that although the value is increasing, but the growth rate is lower than in Quarter 2. Similarly, the recession phase of Scenario 3 didn t make the value decrease as sharp as in Quarter 2, but slow down the pace of declining. Since the time is so limited during Quarter 4, the values of both scenarios have an accelerating increasing/decreasing according to their different cycle phases. To conclude from above: 1) A Recovery cycle phase always makes investors to be confident about their investment, while a Contraction cycle phase is always treated as a threaten. 2) During an Expansion cycle phase or a recession cycle phase, investors are always cautious, they are neither as excited as in Recovery cycle phase, nor as worried as in Contraction phase. That s why the values in an Expansion phase are still growing but not as rapid as in Recovery phase and the values in a Recession phase are still declining but not as fast as in Contraction phase. 3) The point that is similar to Analysis 1 is: the results would be more fluctuated if the period of the investment is shorter than that in Analysis 1 half-cycle period, and three quarter periods in Analysis 2. 4) The cycle tendency that assumed in Scenario 2 is more welcome in this case as its curve line is slightly higher than the symmetrical position of Scenario Sensitivity analysis II Like Sensitivity analysis I, there are also 6 tests in this section. All the results of Sensitivity analysis II can be found in Appendix 12. NOIs of Analysis 2 are as same as in Analysis 1, so we don t talk about NOI in this 28

29 Tests section. Value Maximum Minimum Scenario 2 Scenario 3 Scenario 2 Scenario 3 % Change (from initial level) Value % Change (from initial level) Value % Change (from initial level) Value % Change (from initial Test a 44,849, % 42,426, % 40,426, % 38,261, % Test b 43,954, % 42,127, % 40,629, % 39,015, % Test c 44,576, % 42,343, % 40,499, % 38,502, % Test d 44,227, % 42,210, % 40,556, % 38,774, % Test e 45,554, % 42,640, % 40,272, % 37,746, % Test f 43,288, % 41,932, % 40,800, % 39,561, % Table 10 Valuation results ranges of Scenario 2 & 3 of all the tests in Sensitivity Analysis 2 The sequence of the fluctuation ranges of all the test results for both cyclical scenarios stays the same as in Analysis 1, which is: Test e >Test a > Test c > Original > Test d > Test b > Test f It indicates again that the variable which affects valuation results most is Exit yield/discount rate", and the other variables which directly affect NOI, like Market rent and Vacancy rate, caused less effects than it Summary of Analysis 2 Focus on the valuation results again after got the results of Sensitivity analysis II. Exit yield/discount rate is still the variable that affects the valuation results most, which can explain why the investor is willing to invest more on the property in Scenario 2 at the last quarters even he knows the net operate incomes will reduce as the period becomes shorter; and he invest much less on the property in Scenario 3 at the last quarters because both NOIs and Discount rate are in a disadvantageous conditions. It can also explain why the range of the valuation results in Analysis 2 is much narrower than in Analysis 1, because the sell time is fixed, and then the sell price is fixed as well, since the sell price is not influenced by the cyclical variation of Exit yield, the effect of Exit yield/discount rate is actually just Discount rate in this case. level) 6.3 Analysis 3 In Analysis 3, the investment period is supposed to be fixed and long-term. 29

30 Test 1 Test 2 Test 3 Test 4 Scenario 1 41,325,000 kr Scenario 2 41,105,278 kr 40,778,939 kr 40,573,071 kr Scenario 3 41,590,974 kr 41,941,395 kr 42,222,970 kr Table 11 Result of Analysis 3 The assumptions of different tests can be found in Table 6. According to Table 7, the most obvious phenomena we can point out are: 1) Unlike in other analyses, the values in this analysis are very close to each other. 2) All values of Scenario 2 are lower than the initial level while in Scenario 3 are higher than it. 3) The values of Scenario 2 are descending from Test 2 to Test 4 while in Scenario 3 are ascending. The phenomena above indicate that: 1) The effect of cycle on long-term investment is less than on short-term. 2) The investment decision for a fixed, long-term period is to a great extent affected by the coming cycle phase (the cycle phase that is expected to happen in Quarter 1). When the cycle is expected to fall down during Quarter 1, as assumed in Scenario 2, the investor would be willing to invest less than the initial level no matter which test it is. Contrary situation happened in Scenario 3, the coming Expansion cycle phase inspired the investor, and he would like to spend more in this case. 3) Since the investment decision is largely affected by which cycle phase it is in Quarter 1, the investor has different attitudes towards cyclicity. In terms of Scenario 2, when adding more cyclical factors in (from Text 1 to Text 4), the values are descending. It means that the cyclicity is treated as a risk when the investor is facing a coming Recession phase of the cycle, because the cyclicity causes uncertainty. However, such uncertainty becomes welcome in Scenario 3. The values of Scenario 3 are ascending from Text 1 to Text 4. Figure 11 lists all the results which assumed the investment would last for the whole 12 years from all the analyses above. Compare all these values, we can also find that all the values in Scenario 3 are higher than the initial level while values in Scenario 2 are lower. It confirms again what we concluded above that the expected cycle phase in Quarter 1 largely affects the investment decision making. 30

31 Figure 11 Valuation results of cyclical scenarios in a fixed and long term period Sort the tests a-f in a descending order as following in terms of the difference between two scenarios values. Test e >Test a > Test c > Test 4 (Origin) > Test d > Test b > Test f The sequence is as same as we got in previous sensitivity analyses. It indicates that in spite of the length of term, Exit yield/discount rate is the most influential variable in the valuation process. That explains why the values in Test 3 (assumed constant NOI, cyclical discount rate) are higher than Test 2 (assumed cyclical NOI, constant discount rate) in Scenario 3, and lower than it in Scenario 2. 31

32 7. Conclusion of Empirical study Analysis 1 considered the possible investments that would begin at year 0, and will end at different cycle phases; Analysis 2 focus on the possible investment that would begin at different cycle phases, and will end at year 12; Analysis 3 just take the investment that cover the complete cycle period (12 years) into consideration. Generally, investor would like to invest at Recovery phase and sell at Expansion phase, but if one of the deal times cannot be decided freely, for example, there is a fixed investing time or fixed selling time, or both fixed investing time and selling time, like we assumed in the empirical study, the investment decision would be much different. In terms of cycle tendencies, neither the curve shapes of the valuation results of the short term analyses (Analysis 1 & Analysis 2) are symmetrical. The cycle tendency that assumed in Scenario 3 is more welcomed in Analysis 1 while the cycle tendency in Scenario 2 is more welcomed in Analysis 2. In the long term analysis (Analysis 3), Scenario 3 is more welcomed as well. Scenario 3 is more welcomed in the analyses which make the investment decision at year 0, because in such analyses, the first two phases are always important to the investor, and Scenario 3 offered an Expansion phase in Quarter 1; in the analysis that has a fixed selling time, the last two phases are more important to the investor, that s why Scenario 2 is more welcomed in Analysis 2. The variable that affects the valuation results most is Exit yield/discount rate 3 independent of a short term or long term perspective. That explained why the valuation result is dramatically high at the peak point where there is an Expansion or Contraction phase with a short-term investment contract, and becomes more stable in a longer period investment even there are more NOIs; and why the results of Test 3 which assumed NOI to be constant and Discount rate to be cyclical are more fluctuated than the results of Test 2 which has the converse assumptions. Compared with the short term investment, the valuation results of the long term investment are much more stable. 3 Growth rate is not taken into consideration here, so Exit yield is equal to Discount rate here, according to Gorden formula: r=y+g. 32

33 8. Conclusions & Suggestions In terms of the investor, some implications of the analysis results are interpreted as below: 8.1 Short term investment As mentioned above, a short term investment is more likely to be affected by cycle conditions than a long term investment. To the investor, it is important to understand when to invest as well as when to stop An investment with a fixed investing time: when to sell? 1) If the cycle is going to cheer up, the value of a property should be technically higher 4 than the trend model valuation price. The return of this investment would be rather positive if the property can be sold out before the cycle begins falling. But if the property would not be sold out before the cycle falling back to the initial level, it would be better to hold it at present and make it to be a long term investment. 2) If the cycle is going to fall, the valuation result of trend DCF model would be overvalued in this case. The decision of investment would be cautious, not only for the overvalued result, but also because that even if the property could be sold at a peak point after the falling, the present value of the property is still much lower than the value that sell the property at the peak point that comes soon after investing An investment with a fixed terminating time: when to invest? 1) Not all the Recovery cycle phases are profitable to make an investment, although a Recovery cycle phase is always regarded as a good chance to invest. If it comes a Recovery cycle phase, but the investment will be terminated soon after, it is very risky to invest especially according to the valuation results of traditional trend DCF model. 2) Similarly, not all the Contraction cycle phases are bad times for investing. If it comes a Contraction cycle phase and the investment will be terminated soon after, it is still very profitable to invest since the value of the property is still at a high level. 3) The possible chances for investment are misinterpreted by the valuation results of traditional trend DCF model. According to Figure 12, the gray shadow areas (A2, A3) are treated as the unprofitable invest prices by trend DCF valuation results, but actually they are good chances to invest since the value of the property should be higher in the cyclical market according to the valuation results of the cyclical models; and the yellow shadow areas (B2, B3) are considered as good chances to invest in trend DCF valuation results since the prices in this areas are below the valuation prices, but under 4 The conditions of property (location, age, popularity, etc) are not taken into consideration here. 33

34 the cyclical environment, to invest at a price within these areas is quite dangerous since the property value should be much lower in the cyclical market according to the valuation results of cyclical models. Figure 12 The misinterpretation caused by trend DCF valuation results in Analysis 2 Actually, in terms of each scenario, the prices that under the valuation results curve line are all profitable and could be accepted for the investment. 8.2 Long term investment: what price is the property worth? The effect of market cycle on long-term investment is less than on short-term. However, the valuation result is still subject to Exit yield/discount rate most. The decision of a long term investment is subject to short term cycle tendency. The coming cycle phase would influence the investment decision to some extent. If the cycle is expected to rise up soon, the price that the investor would be willing to invest is higher than facing a falling cycle, even the investor knows that the cycle is fluctuated, and will change its tendency during the long-term investment period. Based on the different cycle tendencies, the Cyclicity is treated in different ways. If the cycle is expected to rise up soon, the Cyclicity is a welcomed factor, the value of the property is higher to the investor if more variables are supposed to be cyclical; oppositely, if the cycle is going to fall soon, the Cycilicity would be treated as a threaten, the value of the property becomes lower to the investor if more variables are supposed to be cyclical. In brief, to the investor, when the cycle is going to rise, the property becomes more valuable if the cycle is more fluctuated; and when the cycle is going to fall, the property becomes less valuable if the cycle is more fluctuated. 34

35 8.3 In terms of Stockholm office market From the historical data we can see, under the influence of world-wide financial crisis, the real estate market was not that optimistic at 2008, and the cycle kept falling till the middle of 2009 when the economy started to warm up again. If an investor planned to make a short term investment (1 year for example) at 2008 and depended on the result of trend DCF model, the property would be very possibly overvalued as the cycle would still fall down during the coming year; if an investor made a long term investment at 2008, according to analysis above, the property value estimated by trend DCF model would be undervalued as a rising cycle was coming. 35

36 References American Heritage Dictionary. (2006). The American Heritage Dictionary. Houghton Mifflin. Barot, B., & Yang, Z. (2002, July). House Prices and Housing Investment in Sweden and the United Kingdom, Econometric Analysis for the period Review of Urban & Regional Development studies (RURDS), No.2 Vol.14. Born, W. L., & Pyhrr, S. A. (1994, Fall). Real Estate Valuation: The Effect of Market and Property Cycle. Journal of Real Estate Research. Englund, P., Quigley, J. M., & Redfearn, C. L. (1998). Improved Price Indexes for Real Estate: Measuring the Course of Swedish Housing Prices. Journal of Urban Economics, 44, pp Fernandez, E. (2005, April). Fair Valuation of Real Estate. BIS Papaers, No.21, part 27. Giliberto, S. M. (1988). A Note on the Use of Appraisal Data in Indexes of Performance Measurement. AREUEA Journal, 16:1, Gonzalez, A. (2004). Office Rental Index for Stockholm CBD. Master thesis No.264 of Department of Building and Real Estate Economics,Royal Institute of Technology, Sweden. Gunnelin, Å., & Söderberg, B. (2003). Term Structures in the Office Rental Market in Stockholm. Journal of Real Estate Finance and Economics, 26(2/3): Harris, J. C. (2000, July). Real Estate Cycle,Riding out ups and down. Tierra Grande Real Estate Center Journal. Jaffee, D. M. (1994). The Swedish Real Estate Crisis. SNS,Stockholm, Sweden: Studieförbundet Näringsliv och Samhälle, Center for Business and Policy Studies. Kaplan, D. (2004). Franchise value a multiple-choice question. Sports Business ournal, May 17, p03. Lundström, S. (1979). Avkastningsvärdering av hyresfastigheter, Värdering genom analys av betalningsströmmar - cash flowanalys. KTH, Institutionen för fastighetsekonomi, Stockholm. Mueller, G. R., & Laposa, S. P. (1994). The Path of Goods Movement. Real Estate Finance, 11:2. MuellerRGlenn. (2006). Real Estate Space Market Cycles. Committee on Financial Services, United States House of Representatives. PritchettPC. (1984). Forecasting the Impact of Real Estate Cycles on Investment. Real Estate Review, 13:4, Pyhrr, S. A., Roulac, S. E., & Born, W. L. (1999). Real Estate Cycles and their Strategic Impications for Investors and Portfolio Managers in the Global Economy. Journal of Real Estate Research, Vol 18, No.1. PyhrrAS, WebbRJ, & BornLW. (1990). Analyzing Real Estate Asset Performance During Periods of Market Disequilibrium Under Cyclical Economic Conditions: A Framework for Analysis, In S.D.Kapplin and A.L.Schwartz, Jr. Research in Real Estate, Vol 3, Renaud, B. (1997.5). The 1985 to 1994 Global Real Estate Cycle: An Overview. Journal of Real Estate Literature, pp RICS. (1994). Understanding the Property Cycle. Riksbank Sweden. (26 November 2009). Financial stability report. Roulac, S. E. (1988). How to Value Real Estate Securities. Journal of Portfolio Management, 14:3, Samuelsson, P. (2008). Official and Unofficial Valuation Standards in Sweden. FIG Working Week June. TS 5D-Tools and Methods in Land Valuation. Schulz, R. Valuation of Properties and Economic Models of Real Estate Markets. Unpubilished doctor dissertation. CASE of Humboldt University. Shannon, P., Reilly, R. F., & Schweihs, R. P. (2000). Valuing a Business. McGraw-Hill Professional. Statistics Sweden. (2009). Regional Gross Domestic Product (BRP), number of employed and compensation of 36

37 employees (ENS95) by region (NUTS1-3). Year Stout, J. H., Nicolai, M. M., & Sassover, N. (1995). The Human Lifebook. Omniview Pr, Uniform Standard of Professional Appraisal Practice. (2008). Appraisal Foundation, Standards Rule 1-4 (b). Ventolo, W. L., & Williams, M. R. (2005). Fundamentals of real estate appraisal (Edition 8 ed.). Dearborn real estate education. WheatonCW. (1987). The Cyclic Behavior of the National Office Market. AREUEA Journal, 15:4, WheatonCW, & TortoGR. (1989). Income and Appraisal Values: A Re-examination of the FRC Returns Data. AREUEA Journal, 17:4, WittenGR. (August 1987). Riding the Real Esate Cycle. Real Estate Today, WolmanWilliam, & KleinRoger. (1975). The Beat Inflation Strategy. Simon and Shuster.,. 37

38 Appendix Appendix 1. Cyclical model of DCF valuation method (Pyhrr, Roulac, & Born, 1999) (Born & Pyhrr, 1994). Where NPV = Net Present Value of Cash Flows NOI = Net Operating Income DS = Debt Service CE = Capital Expenditures MV = Market Value of Property ( Assumed Selling Price) MB = Mortgage Balance SE = Selling Expenses EI = Equity Investment (Initial Cost of Equity) R = PV Discount Rate ( Required IRR in Equity Investment) GPI = Gross Possible Rental Income VAC = Vacancy and Credit Loss OI = Other Income OE = Operating Expenses DS = Debt Service CR = Selling Expense as a Percent of Market Value CAP = Overall Market Capitalization Rate (for Converting NOI into Market Value) K = Mortgage Constant for Remaining Balance of Loan t = Year, 1,2,,n θ = Inflation Cycle m = Market Supply and Demand Cycle λ = Property Life Cycle (Aging Cycle) n = Ownership Life Cycle (Holding Period of Investment) 38

39 Appendix 2 Variables cyclical assumptions according to different Scenarios Marke t rent Vacan cy rate discou nt rate Scenari o 1 Scenari o 2 Scenari o 3 Scenari o 1 Scenari o 2 Scenari o 3 Scenari o 1 Scenari o 2 Scenari o 3 Quarter 1 Quarter 2 Quarter 3 Quarter % 7.00 % 7.00 % 7.00 % 7.00 % % % % % % % % % % % % % % % % % % % % % % % % % % 7.00 % 7.00 % 7.00 % 7.00 % 7.00 % 7.00 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 39

40 Appendix 3. Mathematics models of Analysis 1 Model for Scenario 1 (no cycle existed) N = NOI 0 + r + NOI NOI NOI 0 + ( 0 ) r y r 0 = [Re 0 Ar V 0 OM] [ + r + r r r0 ] r + r Where: NPV n = Net Present Value at year n. Re 0 = Rent level at year 0 Ar = Total area V 0 = Vacancy rate at year 0 OM = Operating & Maintenance cost r = Discount rate n = No. n year y 0 = Exit yield at year 0 Model for Scenario 2 & Scenario 3 (cycle exist) N NOI + r NOI + NOI NOI + ( 2 + r y ) 2 + r {Re α, Ar [ V β, OM]} r r θ, } r Where NPV = Net Present Value of Cash Flows Re = Rent level Ar = Total area V = Vacancy rate OM = Operating & Maintenance Cost y r = Exit yield r = Discount rate α = Rent cycle factor β = Vacancy rate cycle factor θ = Exit yield cycle factor φ = Discount rate cycle factor n = year No. n, n=1,2,3 13 i = year No. i, i n, i=1,2, {Re α, Ar [ V β, OM]} r φ 40

41 Appendix 4. Mathematics models of Analysis 2 Model for Scenario 1 (no cycle existed) N = NOI 0 + r + NOI NOI NOI 0 + ( 0 ) r y r 0 = [Re 0 Ar V 0 OM] [ + r + r r r0 ] r + r Where: NPV n = Net Present Value at year n. Re 0 = Rent level at year 0 Ar = Total area V 0 = Vacancy rate at year 0 OM = Operating & Maintenance cost r = Discount rate n = No. n year y 0 = Exit yield at year 0 Model for Scenario 2 & Scenario 3 (cycle exist) N NOI + r + NOI + r NOI 2 + ( NOI 2 y ) r 2 2 {Re α,year 2 Ar [ V β,year 2 OM]} r r θ,year 2 + [ r φ,year 2 ] 2 Where NPV = Net Present Value of Cash Flows Re = Rent level Ar = Total area V = Vacancy rate OM = Operating & Maintenance Cost y r = Exit yield r = Discount rate α = Rent cycle factor β = Vacancy rate cycle factor θ = Exit yield cycle factor φ = Discount rate cycle factor i = year No. i, i n, i=1,2, {Re α, Ar [ V β, OM]} [ r φ, ] 41

42 Appendix 5. Mathematics models of Analysis 3 Test 1 (Scenario 1): Constant cash flow, constant discount rate N NOI 0 + r + NOI 0 + r 2 + NOI 0 + r NOI 0 + r + r 3 Test 2 (Scenario 2 & 3): Cyclical cash flow, constant discount rate N NOI + r + NOI 2 + r 2 + NOI 3 + r NOI 3 + r + r 3 Test 3 (Scenario 2 & 3): Constant cash flow, cyclical discount rate N NOI 0 + r + NOI 0 + r + r + NOI r + r 2 + r + + NOI 0 + r 3 + r + r 2 + r 3 Test 4 (Scenario 2 & 3): Cyclical cash flow, cyclical discount rate N NOI + r + NOI 2 + r + r + NOI r + r 2 + r + + NOI 3 + r 3 + r + r 2 + r 3 42

43 Appendix 6. Valuation results of Scenario 1 in Analysis 1 year Year PGI 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 3,150,000 vacancy rate 7% 7% 7% 7% 7% 7% 7% 7% 7% 7% 7% 7% 7% EGI 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 2,929,500 Operating & maintenance cost 450, , , , , , , , , , , , ,000 NOI 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 rate of return 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% 6.0% property price at year end 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 in terms of 1st year Cash flows per year ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479,500 2,479, ,804,500 2,479,500 2,479, ,804,500 2,479, ,804,500 discounted rate 6% PV 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 41,325,000 43

44 Appendix 7. Valuation results of Scenario 2 in Analysis 1 year Year PGI 3,150,000 3,060,000 2,970,000 2,880,000 2,970,000 3,060,000 3,150,000 3,240,000 3,330,000 3,420,000 3,330,000 3,240,000 3,150,000 vacancy rate 7.00% 8.00% 9.00% 10.00% 9.00% 8.00% 7.00% 6.00% 5.00% 4.00% 5.00% 6.00% 7.00% EGI 2,929,500 2,815,200 2,702,700 2,592,000 2,702,700 2,815,200 2,929,500 3,045,600 3,163,500 3,283,200 3,163,500 3,045,600 2,929,500 Operating & maintenance cost 450, , , , , , , , , , , , ,000 NOI 2,479,500 2,365,200 2,252,700 2,142,000 2,252,700 2,365,200 2,479,500 2,595,600 2,713,500 2,833,200 2,713,500 2,595,600 2,479,500 Exit yield 6.00% 6.67% 7.33% 8.00% 7.33% 6.67% 6.00% 5.33% 4.67% 4.00% 4.67% 5.33% 6.00% property price at year end 41,325,000 35,478,000 30,718,636 26,775,000 30,718,636 35,478,000 41,325,000 48,667,500 58,146,429 70,830,000 58,146,429 48,667,500 41,325,000 analysis 1 year Cash flows per year (at the end) ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,843,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365, ,971,336 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252, ,917,000 2,142,000 2,142,000 2,142,000 2,142,000 2,142,000 2,142,000 2,142,000 2,142,000 2,142, ,971,336 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252,700 2,252, ,843,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365,200 2,365, ,804,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479,500 2,479, ,263,100 2,595,600 2,595,600 2,595,600 2,595,600 2,595, ,859,929 2,713,500 2,713,500 2,713,500 2,713, ,663,200 2,833,200 2,833,200 2,833, ,859,929 2,713,500 2,713, ,263,100 2,595, ,804,500 discounted rate 6.00% 6.67% 7.33% 8.00% 7.33% 6.67% 6.00% 5.33% 4.67% 4.00% 4.67% 5.33% 6.00% PV 41,325,000 35,808,962 31,599,619 28,350,036 31,358,910 34,742,060 38,638,579 43,254,749 48,912,336 56,145,115 49,190,520 44,224,812 40,573,071 44