Regulating the Mid-rental Segment in Amsterdam: implications for Institutional Investors

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Regulating the Mid-rental Segment in Amsterdam:

Implications for Institutional Investors

Master Thesis

Frank van Breukelen

University of Amsterdam, Amsterdam Business School MSc Real Estate Finance

Supervised by: prof. dr. J.B.S. Conijn

August 14, 2018

Abstract

This paper aims to estimate the effect of rent regulations targeting the mid-rental seg-ment in Amsterdam. Although existing literature on the effects of rent regulations on the housing market is extensive, the knowledge of the quantitative effects of these regulations on the business case of investors is much less so. This study constructs a conceptual framework in order to allow for heterogeneous effects between eight districts within the municipality of Amsterdam. By exploiting a Monte Carlo Simulation model, the effects of such regulations on the internal rate of return of investors in Dutch residential real estate are estimated. The results suggest that all new regulations combined will have a critical effect on the returns, even with the proposed land value compensations. However, by optimising the residential plans and constructing smaller dwellings the impact might be alleviated.

Keywords: Real Estate, Unregulated Rental Market, Rent Regulation, Monte Carlo Simula-tion, Institutional Investor

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This document is written by Student Frank van Breukelen who declares to take full respon-sibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Contents

List of Figures

1 Overview Map Districts of Amsterdam . . . 7

2 Structure of DCF Simulation Model. Author modification. Source: French and Gabrielli [2005] . . . 13

3 Visualisation of Optimisation Effective Floor Area . . . 28

4 Historical series of inflation, rent growth and the resulting increment . . . 38

5 Histogram of IRR Distributions Noord vs. Scenario 1 (grey) . . . 48

6 Adapted EFA of β After Optimisation . . . 51

7 Visualisation Possible Predicted Inflation Paths . . . 60

8 Histogram of IRR Distributions Within Ring vs. Scenario 1 (grey) . . . 66

9 Histogram of IRR Distributions IJburg vs. Scenario 1 (grey) . . . 66

10 Histogram of IRR Distributions Ring West vs. Scenario 1 (grey) . . . 67

11 Histogram of IRR Distributions Zuidas vs. Scenario 1 (grey) . . . 67

12 Histogram of IRR Distributions Buitenveldert vs. Scenario 1 (grey) . . . 68

13 Histogram of IRR Distributions Nieuw-West vs. Scenario 1 (grey) . . . 68

14 Histogram of IRR Distributions Zuidoost vs. Scenario 1 (grey) . . . 69

List of Tables

1 Division of the Project . . . 24

2 Scenario Characteristics . . . 36

3 Descriptive Statistics Time Series . . . 39

4 District Specific Input Variables . . . 43

5 Results IRR . . . 45

6 Investment Value Effect . . . 49

7 Effect asking price for land . . . 50

8 Assumptions used for Example Calculation . . . 60

9 Example Calculation of Base Case Scenario IRR . . . 61

10 Descriptive Statistics . . . 62

11 Sensitivity Analysis Adjusted Exit Yield . . . 63

12 Detailed IRR Results . . . 64

13 Sensitivity Analysis Adjusted GIY . . . 70

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Introduction

1 Introduction

After the global financial crisis of 2008, the housing market in Amsterdam has seen a strong recovery. This conclusion can be drawn when analysing several factors. The most prominent indicator is the transaction price of dwellings in the region of Amsterdam. Residential real estate has faced an average year-on-year increase of 13.5% in 2017 [NVM, 2017]. Due to these steep increases housing prices are now close to the peak of average transaction prices of before the crisis. Moreover, the recovery is observed when looking at rents. Average rents in Amsterdam, including both regulated rents as well as market rents, have increased on average in the past three years by 210 basis points above the consumer price index. Which is almost 90 basis points per year higher than the Dutch average transaction price increase for these years [CBS, 2017b,c].

The increased attractiveness of the Amsterdam housing market, together with favourable market conditions, has caused scarcity of supply. The number of transactions of owner-occupied homes has dropped by 13.3% since the last quarter of 2016 [NVM, 2017]. The scarcity on the owner-occupied market, however, is much less debated than the scarcity in the rental market. Rising rents have initiated a rent gap between dwellings in the regulated segment and the free market segment. The shortage of homes in the mid-rental segment is the most prominent. The mid-rental segment is the part of the unregulated rental market with base rents between the e710.68 and e971 per month. Currently, only 6.4% of homes in Amsterdam are rented within this segment [Amsterdam, 2017b].

As a solution for the current problems with regard to the supply of mid-segment rental hous-ing, the municipality has introduced the ”Actieplan Middeldure Huur” [Amsterdam, 2017a]. This can be loosely translated to ”Action plan mid-segment rent” and will be referred to as the AMR in this research. The AMR consists of a set of new regulations that have been introduced in order to increase the supply. The new regulations consist of constraints for newly built stock with regard to the assignment of housing to certain renters, the initial rent setting, the rent growth, the conversion restrictions and house size.

These new regulations impact the business case for investors in the private rental sector as well as the Amsterdam housing market as a whole. New regulations that are similar to these are

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Introduction

now more widely considered by Dutch municipalities to increase the supply in the mid-segment rental market. Investors and other active parties in the residential market of Amsterdam are concerned about their ability to endeavour in future investment opportunities [IVBN, 2018], which might affect the future addition of new stock.

Although the topic of scarcity in the mid-rental segment is widely discussed in the media, no clear picture can be constructed with regard to the implications that these new regulations have for the investors. It is of importance for both parties to comprehend the consequences of implementing new regulations in a previously unregulated market. This paper will elaborate on the effect of these new regulations on the business case of institutional investors and will aim at answering the following research question: ”What are the implications of the new regulations aimed at the mid-rental segment in Amsterdam for the business case of institutional investors?”.

1 2 3 4 5 6 7 8

Figure 1: Overview Map Districts of Amsterdam

To model the effect of the new regulations this paper makes use of a model that calculates the internal rate of return (IRR). However, in addition to standard calculation models, the model will be adapted to take into account the uncertainty of particular input variables. This is done by introducing Monte Carlo simulations to the method of analysis. After empirically estimating the input variables and the uncertainty of those, the model will run 10,000 times. This will give a reliable insight in the possible outcomes for these projects in numerous predicted environments.

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Literature Review

The simulations will be run based on real world information of projects that were recently built or are to be delivered in the near future in Amsterdam. As heterogeneous outcomes are expected between the districts in Amsterdam, the simulation will be run for example projects in eight different districts of Amsterdam. These districts are equivalent to the eight districts that are referred to in the AMR. The eight districts that the municipality has defined are: (1) Within the ring road, (2) Zuidas, (3) Buitenveldert, (4) Ringzone West, (5) IJburg,

(6) Noord, (7) Nieuw-West, and (8) Zuidoost. The overview of the districts is shown in

Figure 1.

In Section 2, this paper will elaborate on existing literature and current debates in this

field of study. Section 3 will further elaborate on the structure of the housing market of

Amsterdam and develop the context of the new regulations that will be implemented. These new regulations, as described in the AMR, will be extensively presented in Section 4. This section will also discuss the mechanisms through which these regulations might affect the business case of investors. Section 5 presents a comprehensive explanation of the methodology used to assess the effects of the regulations on the business case of investors. In Section 6, the data used for the quantitative analysis will be described. Then, Section 7 will elaborate on the results collected from the analysis. In Section 8, conclusions will be drawn from the results. Finally, Section 9 will reflect on these results and positions those in the context to contribute to the debate.

2 Literature Review

In presenting the current academic literature this paper divides the literature in two parts. The literature with regard to the effects of regulations on investments will be presented first. Thereafter, the literature concerning the inclusion of uncertainty into the calculation models will be discussed.

2.1 Regulation and Investments

Contemporary forms of rent regulation have established on historical foundations. Willis [1950] has found that the earliest rumours of rent control date back to ancient Rome. In times of Julius

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Literature Review

Caesar it is thought that the first rent ceiling was adopted to avoid excessive price increases imposed by landlords. Moreover, this was an attempt to stabilise housing prices in the Roman empire. More recently, in 1916, rent control legislation was first adopted in the Netherlands during the first World War. Although the Netherlands declared themselves neutral, the war affected the housing market due to rising construction prices and the inflow of Belgian refugees

[Holzhaus, 2017]. Throughout the 20th century, the Dutch legislation with regard to rents has

changed considerably. However, the means for which they are implemented are quite the same. The fact that anyone should be able to afford housing is the most common argument in favour of regulation [Arnott, 1995].

Currently, international literature divides rent control in two main dimensions as described by Arnott [1995]. The ”first-generation” rent control is defined by measures that freeze nominal rents periodically. Nominal rent freezes cause real rent decreases in inflationary environments. The first rent control measures in the Netherlands were of this nature. First-generation rent controls became relatively common practice in the aftermath of both World Wars, driven by housing shortages and high construction prices. The second-generation of rent controls con-cerns annual rent increases that are linked to inflation indices. Arnott [1995] argues that these second-generation rent controls are less rigid and allow for more flexible implementation. The Dutch regulated rental segment currently possesses these second-generation regulations. The maximum rent increase for these regulated contracts is currently set by the government at infla-tion with an addiinfla-tional 250 basis points [Tweede Kamer, 2018]. As these types of rent controls differ substantially, it is of importance to correctly identify which types of new regulation are imposed by the municipality of Amsterdam.

The currently available literature provides insight in the possible side effects of rent control regulations. Studies into the effects of first-generation rent control have found many side-effects of nominal rent freezes. Evidence shows that these forms of rent control adequately decrease real rents [Fallis and Smith, 1984]. However, existing literature quite unanimously considers the side-effects of such regulation to be costlier than the benefits. Coleman [1988] describes in his study concerning rent control in Britain, that the share of households renting from a private landlord has decreased since the introduction of these rent control measures. In 1914,

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Literature Review

it was estimated that more than 95% of households privately rented their home. Since the introduction of the rent control in 1915, this figure had decreased towards only 8% in 1985. He attributes this decrease in market share to the lack of construction of new supply in this segment.

This decrease in supply is supported empirically in a study of Sims [2007]. In this research, the effects of rent control in Boston are analysed by investigating the abrupt end of rent control measures in the state of Massachusetts in 1995. Besides the decreasing supply, Sims addresses the negative relationship between rent control and maintenance in rent-controlled market seg-ments. In a quantitative analysis he finds that rent control measures not only affect the quantity of supply, but also the quality. This effect might be the consequence of reduced maintenance. This confirms the suspicion that Moon and Stotsky [1993] had, but they could not support this with conclusive evidence on the matter. In further research, Arnott and Shevyakhova [2014] find that rent control causes postponement of maintenance. Stating that the incentive to maintain deteriorates under rent-controlled circumstances. Thereby, the negative relationship between rent control and maintenance seems to be apparent.

Moreover, academic literature states that rent control tend to increase rents of the uncon-trolled stock [Early, 2000; Fallis and Smith, 1984]. Fallis and Smith [1984] state that rents in the uncontrolled market rise due to controlling rents in the regulated segment. This might be explained by the misallocation of housing resulting from rent control as found by Glaeser and Luttmer [2003]. They find that misallocation is a consequence of rents below market level. Housing with controlled rents might be used for other purposes than providing for the low-income households, affecting the overall benefit of rent control. An overwhelming number of articles is, thus, found that criticise the nominal rent freezes. On the opposing side, no articles have been found that clearly support these measures.

Research into the effects of second-generation rent control has posed far less conclusive re-sults. Arnott [1995] states that the flexibility of second-generation rent controls leads to largely heterogeneous effects and limited generalisability and should, thus, be analysed individually. The proposed regulations for the mid-rental segment in Amsterdam seem to be of a very unique nature. Mainly due to the fact that it combines first- and second-generation rent controls.

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Fur-Literature Review

thermore, a factor of interest is the fact that only the newly built housing stock will be subject to the new rent regulations. It is therefore of importance to identify what the measures exactly are and who they affect. This will be the topic of interest in Section 4.

In spite of the heterogeneous characteristics of second-generation rent control, some research is done comparing rent control between different countries. De Boer and Bitetti [2014] have compared rent regulations between OECD countries and have done this by constructing a composite index. Using this measure, they tested whether rent control leads to lower average rents, while controlling for quality. As they found no evidence of this they stated that this could be possible due to landlords compensating for their eroded returns by setting higher initial rents and accepting lower future rent growth. Whereas Andrews et al. [2011] found that home-ownership rates are negatively affected by rent regulations and other tenant protecting measures. As a possible explanation the lock-in effect of rent regulation in heavily regulated rental markets is identified. They do note that this will have other negative side-effects which are to be capitalised into housing prices.

Weber [2017] has made a similar attempt to compare different rent control regimes. In his study, he compares 18 rental markets in a quantitative study. His findings show that markets with very strict rent control systems show lower real rent growth. However, he also finds that in free rent regimes real rents only marginally appreciate. Furthermore, the study shows that tenure security regulations have a positive impact on real rents. As landlords are limited in the freedom to increase rents during tenancy they might be triggered to set higher initial rents, which cause the higher rent dynamics.

The academic knowledge regarding the effect of rent controls on the housing market has become profound over the past decades. Far less research has focused on the topic from the investor’s point of view and the impact that such regulations can exert on the feasibility of acquisition of new assets. In a briefing paper Wilson [2017] has shortly covered the subject of the reduced appetite of investors under rent-controlled environments. Intuition would imply that artificially controlled rents below the market rent would decrease investor appetite. However, the paper does not elaborate on the actual effects of rent control on the project returns of investors. Although investment appetite could be affected, it might still be a viable investment

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Literature Review

opportunity. It is of importance to understand the magnitude of the effects of such regulations on the business case of investors to balance out the gains for the tenant and the losses for the investor.

The effects of rent regulations are overall well examined. However, the quantitative backing of the effects of such regulatory measures on investments is much less elaborated upon. After having established a broader understanding of the available international literature on the side effects of rent regulations it essential to expand on the literature behind the construction of the model.

2.2 Uncertainty and Valuation

In order to correctly estimate the effect of such regulations, a model should be constructed which allows for adjusting the input variables easily. Appraisers currently make use of discounted cash flow models to determine market values in the Netherlands. These models are completely dependent on the input variables, which are determined by the expert opinion of the appraiser. However, many of the input variables are uncertain. Instead of completely depending on the expertise of the appraiser, Li [2000] combined the standard DCF model with the use of Monte Carlo Simulations. He states that implementation of Monte Carlo simulations in a common DCF model allows for uncertainty in the predicted input variables and gives a more scientific insight in the results of valuations.

The importance of uncertainty in real estate valuation is supported in other academic liter-ature. Baroni et al. [2006] state that the main weakness of DCF modelling is the lack of proba-bility distributions in the free cash flows. They find that introducing Monte Carlo simulations will add robustness to valuations in real estate and give a more comprehensive interpretation to outcomes. French and Gabrielli [2005] have developed a modelling process to introduce un-certainty in DCF calculations by way of converting to a simulations model. This model will be used as a base for the presented simulations model. The visualisation of the model structure they constructed is depicted in Figure 2.

The usage of DCF simulation models has been explored in academic research. However, it has not yet been implemented in the current practice of appraisers. As this paper specifically

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The Current Housing Market Introduction of uncertainty Data DCF Inputs Output Inflation Rent growth Exit yield Expectations Simulation Assumption

Iteration Range of _outputs

Analysis

Figure 2: Structure of DCF Simulation Model. Author modification. Source: French and Gabrielli [2005]

examines the effects of regulations on the prospected cash flows of a property it seems convincing to address the problem of uncertainty in the modelling of investor returns. Therefore, this paper will account for uncertainties in future cash flows by exploiting the Monte Carlo Simulation model in the method of quantitatively analysing the investor returns.

The literature discussed above aims to derive the market value using the Monte Carlo Simulation models. This paper introduces uncertainty in future cash flows in a model that calculates the internal rate of return. In contrast to calculating the current market value, this paper will estimate the current market value under the uncontrolled environment. Instead of estimating the discount rate, the proposed model estimates the current market value. The output of the model will therefore be the IRR. The IRR denotes the discount rate for which the net present value of the property is zero. Thereby, the model will estimate the investors return on the project, rather than the current market value. As the estimation of the current market value of objects is not an exact science, sensitivity analyses with regard to this variable will be performed.

3 The Current Housing Market

The current housing market can be viewed upon from different perspectives. This section will first elaborate on the national housing market conditions. After that the focus will shift towards the local housing market of the municipality of Amsterdam. Then to complete the context of

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The Current Housing Market

the regulatory changes the view of institutional investors on the local housing market will be discussed.

3.1 The Dutch Housing Market

The tenant structure of the Dutch rental market is separated in two main segments. These two rental segments are determined by the type of rental contracts underlying the use of the property. Firstly, there is a regulated rental segment. This segment is defined by contracts

with an initial rent that is set below thee710.68 per month. This segment is strictly regulated

by the Dutch government with regard to setting initial rents, the rent increases that can be implemented, and the tenant protection.

The second segment defined is the unregulated rental segment. The rental contracts that

have an initial rent of above the threshold ofe710.68 per month belong to this segment. These

rental contracts are subject to far less regulations. These rental contracts are not restricted with regard to the rent setting and rent growth. However, renters in this segment are still protected by law to a certain extend. The most important factor is the protection of renters from eviction without legitimate cause.

Whether dwellings may be rented out in the unregulated rental segment is dependent on the so-called ”Woning Waarderings Stelsel (WWS)”, which is established in the Dutch law. This law includes a system in which independent dwellings are assigned points for quality, size, and the tax assessed value. The Dutch government has identified a conversion table that links the points assigned to a maximum rent that can be charged. In the case that a dwelling is assigned a total of 145 points or more, it is allowed to be rented out with unregulated rental contract [BHW, 2017]. Renting out dwellings with unregulated contracts allows for freely setting the initial rent and the maximum annual rent increase can be agreed upon between renter and landlord within the contract. There are no restrictions imposed by the government with regard to these matters.

The mid-rental segment, a sub-segment of the unregulated rental market, is defined by a

monthly rent between e710.68 and e971.00 [Amsterdam, 2017a]. This segment aims to serve

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[Middelkoop, 2017]. This income group is defined as the middle-income households. This

segment is one which is much debated in the media as shortages are rising. In order to explain the shortages in this segment we have to identify both national and the local causes.

On a national level there are some other explanations could be presented to explain the high current demand for specifically the mid-rental segment. Firstly, as the financial crisis of 2008 was largely triggered by the issuance and repackaging of sub-prime mortgages in the US. As a result, some profound changes in the Dutch mortgage market have been observed as well. Most importantly the criteria for the issuance of new mortgages have been tightened over the past years with regard to the loan-to-value (LTV). The Dutch government has decreased the maximum LTV over the past five years gradually with 1%-point per year. Home buyers were able to issue a loan for 105% of the value of the home in 2013. This has now decreased to only 100% since the start of 2018 [DNB, 2015]. This implies that home buyers need to invest their own savings in order to pay for buyer’s costs and possible improvements to the newly bought homes. This capital requirement has influenced the purchasing power of potential households with low to middle-incomes. These households now often divert to renting instead of buying.

Another pressurising factor on the popularity of home-ownership is the decreased mortgage-interest deductibility. Since 2013, the rate at which homeowners are allowed to deduct mortgage interest has decreased from 52% to a current level of 49.5% in 2018. With the decreasing mortgage interest deductibility, the tax advantage of owning a home is slowly evaporating. The Dutch government has stated in the latest coalition agreement that the rate at which mortgage interest can be deducted will drop even further towards 37% in 2041 and, thus, decreasing the tax incentive of home-ownership [Tweede Kamer, 2018].

After having identified these pressurising factors on the mid-rental segment in the Nether-lands it is critical to assess the local housing market of Amsterdam as well. Housing markets are highly diverse and show heterogeneous characteristics between municipalities and even districts. The next subsection will elaborate on the local housing market and the issues it faces.

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3.2 The Amsterdam Housing Market

The Amsterdam housing market has shown signs of increasing shortages. House prices are rising rapidly in the owner-occupied segment. Rents are rising accordingly. Investors are willing to compress yields in order to acquire assets as they see very limited risk in renting out homes. Understanding the issues of the market requires to look at both the available stock within the city as well as the proportions of housing stock in relationship to the proportion of household incomes.

The housing shortage in the Netherlands is currently more acknowledged by consumers, market parties and regulators. Amsterdam is considered to be the most problematic region with regard to shortages in the market. It is estimated that the housing market of the metropolitan area of Amsterdam was short of almost 45,000 houses in 2016. The housing shortage is estimated to increase towards a peak shortage of 60,000 homes in 2020 [ABF Research, 2017]. The urgency of increasing the housing stock is unambiguously present with the municipalities and market parties.

Tackling these shortages efficiently requires analysing the type of housing that is most needed within the city. In Amsterdam, this is done annually by the municipality and reported amongst other information in the ”Wonen in Amsterdam” report. This report compares the distribution of household incomes in Amsterdam with the distribution of the housing stock.

As of 2017, the rental market of Amsterdam is about 67.5% of the total housing stock. The vast majority of these rental dwellings falls within the regulated rental segment (52.7%). The remaining rental housing stock in Amsterdam is divided over the mid-segment rental housing (6.4%) and the top-rental segment (8.4%) [Amsterdam, 2017c]. Comparing this with the in-come of households, the municipality of Amsterdam has concluded that there is a surplus of inexpensive housing facilities in relationship to the number of low-income households. This surplus has been slowly decreasing over the past years and is predicted to decline even more. The greatest shortage of housing is observed in the housing for middle-income households. In 2017, the share of middle-income households was 19.6%, whereas the share of mid-rental and mid-priced owner-occupied housing was only 15.6%. This discrepancy might seem insignificant; however, this would come down to an estimated 18,500 households that do not live in suitable

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housing facilities. They either over-consume with regard to housing or under-consume. The available housing in relationship to the number of households with a high income is almost equal.

The misallocation of housing is for the largest part due to the under-consumption of middle-income households by living in inexpensive regulated rental housing with artificially low rents. These artificially low rents originate a lock-in effect for renters. As incomes grow, households have no obligation to move out from their regulated rental dwelling. The low rents in combina-tion with the costs of moving are obstacles in the process of moving out. This creates a skewing effect in the balance between income and rent. In 2015, it was estimated that in Amsterdam 14.5% of the renters of unregulated rental dwellings had an income above the threshold at that time [VNG, 2015; Rijksoverheid, 2017].

The regulated rental market of Amsterdam is sensitive to this skewed balance as the average rents in the unregulated rental segment are the highest of the Netherlands. The maximum regulated initial rent is constant over the Netherlands as a whole and the gap is therefore larger. Hence, the lock-in effect becomes larger as well. As a result, the regulated rental sector has a waiting list of more than a decade for assignment of a regulated rental dwelling. In turn, misallocation by over-consumption of lower-income households is created.

The most critical segment, therefore, is currently considered by the municipality to be the housing segment serving the middle-income households. The problems for these households can be attributed into three causes. Firstly, these households have a very limited access to the regulated rental segment due to the income restrictions in the assignment of these dwellings. Secondly, the rises in rent and housing prices have made the expensive segments unaffordable. Finally, the supply of mid-rental or mid-priced housing is very limited.

By ways of new regulations with regard to the construction of housing for the middle-income households, the municipality tries to expand the supply. The expansion of the supply is aimed at increasing the affordability and stimulating the flow of under-consuming renters from the regulated rental segment towards the mid-rental segment. From the perspective of the investor these regulatory changes might affect their business case. Knowing the investment analysis framework will give an improved insight in which factors play an important role in the

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investment decision.

3.3 Investment Analysis Framework

Putting the regulatory changes into perspective requires not only to look at the current market conditions, but also to discuss the framework that institutional investors use to analyse in-vestment opportunities. For most of the larger Dutch institutional investors in residential real estate these are, at least partially, discussed in fund summaries or annual reports. This analysis is based on the annual reports, fact sheets or fund summaries of; Altera [2018], Amvest [2018], ASR [2018], Bouwinvest [2018], Syntrus Achmea [2017], and Vesteda [2018]. Decision-making on a property level in residential real estate is dependent on a multi-criteria analysis. Fac-tors taken into account are, amongst others; market conditions, location, rent levels, property typology, and the minimum expected return.

Looking at these decision factors the institutional investors seem to agree on the market conditions and the location. Although yields are compressing, investment funds show high indirect returns on their residential property. Together with positive direct returns, these figures resulted into a double-digit total return of the IPD benchmark in 2017 of 16.9% [Bouwinvest, 2018]. As can be deducted from the compressing yields, the appetite for investments is still high.

Likewise, the investors agree on the location. Amsterdam is considered as one of the best local housing markets of the Netherlands. The capital gains, as reported in the annual reports, are almost solely the highest in the Amsterdam area. Furthermore, some of the investors state that their strategy is aimed at investing in the big cities to build a core portfolio. The market conditions and location will not, or not directly, be affected by the introduction of the new regulations.

The property typology can be reviewed for aesthetics, rent levels, target group and practical-ity. In their annual reports and fund summaries, these investors are not always fully transparent about their strategies. This will most probably be due to competition in the market. Currently, for the largest part, the properties developed fit into the portfolios of the investors as prop-erties within the Amsterdam area still attract investors. As a result of the new regulations,

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Regulations for the Mid-rental Segment in Amsterdam

the property typology might be affected. Rent levels might decrease which attract other target groups. Furthermore, it could be expected that lower rent levels introduce the incentive to create different types of housing.

Finally, the minimum long-term return or IRR will be analysed. The institutional investor takes into account the return they would have to make on these investments. The annual reports used for this analysis show that goal returns of the fund can be divided in two approaches. Either investors set goals relative to the benchmark or absolute goals regarding the long-term return or IRR for the fund. The goal for the expected long-term return or IRR as discussed in the annual reports varies between the 5% and 8%. The IRR is expected to be affected by the introduction of the new regulations. The magnitude of these effects are still unidentified and therefore the most important topic of the research. The impact on the property return might directly impact the feasibility of the project or the asset typology.

4 Regulations for the Mid-rental Segment in Amsterdam

To combat the predicted shortages in the near future, the municipality of Amsterdam has introduced a set of new regulations that aim to increase the supply of mid-segment rental homes. These new regulations are documented in the AMR which was published in 2017. Furthermore, they express that with this scheme the ambition is to increase the projected addition of mid-rental dwellings to the market. They aim to add at least 1.500 dwellings per year until 2025. This would come down to an increase of more than 60% in contrast to 2017.

The proposed regulations will only apply to newly built residential projects for which a new issuance or transformation of ground rent conditions is required. Moreover, these regulations will only involve the mid-segment rental units within a residential project [Amsterdam, 2017a]. With regard to allocation of future developments the municipality aims at a so-called ”40-40-20” division.

This division intends that these projects should have 40% of the homes in their project to be rented out as regulated rental units or to be sold as social owner-occupied dwelling. These social

owner-occupied homes are priced up to e152.000 and help households with lower incomes to

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Furthermore, there should also be 40% of homes in the rental segment or to be sold as

mid-priced owner-occupied home, between e152.000 and e249.000. The remainder can be rented

out in the top-segment with rents above thee971 per month or to be sold as expensive home,

with a purchase price abovee249.000 [Amsterdam, 2017d]. The new regulations imposed by

the municipality of Amsterdam, as stated in the AMR, are divided in six separate requirements.

4.1 Assignment Former Regulated Renters

The Amsterdam housing market has a relatively large share of regulated rental housing. Social housing associations in the Netherlands should currently assign 80% of their regulated rental

dwellings to household with an income below the threshold of e36.798. These homes have

artificially low rents to be affordable for the lowest income households of society. Currently,

another 10% should be assigned to households with an income of belowe41.056 [Rijksoverheid,

2018a].

To tackle the long waiting lists for the regulated dwellings, the municipality mainly tries to stimulate the flow through of under-consuming renters in the regulated rental segment. Hereby, these middle-income households do not occupy the inexpensive regulated rental dwellings any-more, while being provided new housing. Therefore, they state in the new regulations that half of the mid-segment rental homes should be assigned to these, so-called, skewed renters. In the case that not enough households apply for these homes the rest should be assigned to other households with middle-incomes.

4.2 Assignment Middle-income Renters

In addition to the first rule of assigning the mid-segment homes, the AMR states that all homes within this segment should be assigned to the middle-income households during the first 25 years of continued operations. Moreover, homes with three rooms or more should prioritise assignment to households with at least one minor and one adult [Amsterdam, 2017a].

In essence, this does not significantly increase the risk of the investor. Currently, insti-tutional investors often demand a income to rent ratio of 3.5 or above. When calculating the

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the most expensive mid-rental segment dwelling (e971) this would yield about 3. However, on

average the assignment of middle-income households to average mid-segment dwellings would result in a rent to income ratio of above 4, which is not uncommon in the sector.

4.3 Maximum Initial Rent

The new regulation with regard to initial rent setting that is discussed in the AMR states that

initial basic rents for this segment cannot exceed the e971 per month. Furthermore, should

average rents for the mid-rental homes not exceed e850 per month. Landlords are also not

allowed anymore to oblige renters to rent parking spaces with their homes to increase gross potential income from residential projects.

A natural reaction of an investor would be to allow for lower initial rents by creating smaller

homes. Hence, they would be able to still obtain the market rent. For some districts in

Amsterdam this would, however, come down to creating homes which are very small. This would bear other risks for investors as the marketability decreases herewith. It is therefore of importance to analyse the investment criteria of institutional investors to determine the minimum size of a dwelling they are willing to incorporate in their portfolio.

4.4 Inflationary Rent Growth

Whereas, in the past the rent growth of the unregulated rental segment was only subject to contractual agreements, the new AMR regulations state that in the first 25 years the annual rent growth is capped by inflation. In the Netherlands the most common inflation index to link rent growth to is the consumer price index (CPI). As stated in the AMR, the annual rent increases landlords are allowed to apply are often based on the CPI June to June year-on-year mutation. The CPI index growth will be the maximum rent increase landlords may charge in July each year [Amsterdam, 2017a].

The unregulated rental sector had no limits with regard to annual rent increases before. Such agreements were normally documented in the rental contracts. Common practice was to link rent increases to the CPI as well and set a maximum increment on this figure in the

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registered by the CBS [2017b], the average increment on inflation has been 80 basis points with peaks of 350 and lows of -150 basis points. It is expected that implementation of capping rent growth by inflation will have an effect on the returns of institutional investors. These effects can best be modelled using expected future cash flows in the calculation model. However, due to uncertainty in future inflation as well as the rent increase increment it would be desirable to run Monte Carlo simulations to extrapolate the effect within different environments.

4.5 Conversion Restriction

The municipality of Amsterdam also wants to ensure that the stock of the mid-rental segment will grow and that these homes will not be converted to owner-occupied homes in the medium

term. Therefore, they extended the conversion restriction for these dwellings by 10 years.

Instead of the prior standard conversion restriction of 15 years, landlords will not be allowed to convert these dwellings for the first 25 years of continuous operation.

The possibility of conversion is a real option for an investor in real estate. The ratio between values of investment properties and owner-occupied properties is not constant over time. The possibility to convert rental homes to private ownership adds substantial value. The extension of such a restriction will have no impact in the typical 10-year time horizon of residential real estate appraisals. However, when constructing a model that analyses returns, one has to account for the value of this option in the net sales proceeds (NSP) that are taken into account at the end of the appraisal horizon.

4.6 Monitoring House Size

In order to monitor the quality of life within this segment, the AMR shows the ambition of the municipality to monitor the house size. However, not all mid-segment rental homes are aimed at families and, therefore, it is not necessary to monitor the size of all homes. Almost a quarter of the mid-rental homes are rented out to families, who need more space than couples or individuals [Amsterdam, 2017a].

The AMR does not provide strict regulations with regard to the house size. The example calculations show that they expect between the 20 and 30% of homes to be between 65 and

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Methodology

75m2 of effective floor area, depending on the district. These homes will therefore be restricted

in both maximum rent and minimum size. As a consequence, there is a high possibility that in some of the areas with higher market rents in the city, the balance between size and rent will become skewed.

5 Methodology

To extract the quantitative effects of these regulations on the business case of institutional investors, it is of importance to construct a conceptual framework which enables generalisation towards future investment opportunities. This section puts forth a framework that enables quantitative analysis of the effects of such regulations and extensively describes the modelling. The framework allows for heterogeneous effects between the eight districts of Amsterdam while generating results that can be generalised towards future projects within the districts. This section divides the effect of the new regulations into four components and describes how these components are put together in a model.

First, the effect of the regulation that limits the average initial rent of the mid-rental

dwellings to be e850 will be discussed in Subsection 5.1. In the subsequent Subsection, 5.2,

the modelling of the second effect will be debated. This effect arises from the ambition of the municipality of Amsterdam to control the size of a portion of the mid-rental dwellings. In Sub-section 5.3, the modelling of capping the rent growth will be discussed. The last regulation that directly influences the investor is the prolonged restriction on converting the rental homes to owner-occupied homes. The method of estimating the magnitude of the resulting effect on the exit value of the property will be discussed in Subsection 5.4. In Subsection 5.5 the construc-tion of the base IRR calculaconstruc-tion model will be discussed together with the established input variables. Finally, in Subsection 5.6, the Monte Carlo Simulation model is elaborated upon.

5.1 Rent Cap Effect

Before all else, a new residential project has to account for the ’40-40-20’ proportions with regard to the tenure structure [Amsterdam, 2017d]. As earlier noted, this rule implies that new residential developments in Amsterdam should account for 40% in regulated rental housing,

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Methodology

40% in either the mid-rental or mid-priced owner-occupied housing and the remaining 20% in the top rental segment or expensive owner-occupied segment.

As the regulated rental units are not the main investment segment for institutional investors and the newly implemented rent control regulations do not affect these dwellings, these are ignored in the framework. In the following, the other 60% of the dwelling will be acknowledged as to total project as these are the segments institutional investors mainly invest in. Hence, the total effective floor area of these unregulated dwellings comprises 100% of the project. This paper, furthermore, assumes that the institutional investor only invests in rental housing. The division of the rental units will be assumed to be constant with the 40% and 20% stated in the regulations of the municipality. The investor is able to acquire a package deal which

consists for1₃ out of top-rental segment dwellings, which are not affected by the new regulations.

The remaining 2₃ of the project regards mid-rental housing, which part is prone to the new

regulations.

In order to achieve average rents of on average e850, the mid-segment rental dwellings are

rent-controlled. From the AMR it is also deducted that a portion of the mid-rental segment should be built bigger than the market size is about 25% of the mid-rental dwellings. This gives us a new division of the unregulated program as depicted in Table 1.

Table 1: Division of the Project

Segment Proportion Variable

Top-rental 331₃% α

Mid-rental 50 % β

Mid-rental with monitored size 162

3% γ

Total 100%

Notes: This table shows the unregulated rent division of a stan-dardised residential real estate development in Amsterdam and the corresponding variables allocated to each group. This divi-sion will be the foundation for the conceptual framework that underlies the method.

In order to estimate the effect of the new regulations on the initial rent it is established that the total gross potential income from the project equates 100%. The total income corresponds with the 100% of the original total effective floor area, EFA. From this point onward, it is

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Methodology

desirable to measure the initial rent of the project under the new market conditions. The model therefore needs input variables concerning market information of the districts within Amsterdam. The input variables that need to be assessed are both the average monthly market rent per unit within the district and the corresponding average effective floor area per unit. As the new regulations apply to the newly added stock the market data should include data from recently completed residential real estate or residential projects that will be delivered and put in the market soon.

It is then possible to calculate the effect of the rent cap on the initial rent of the mid-rental dwellings per district, d, using the following formula:

∆Initial rentdβγ = e850 − Avg. Market rentd

Avg. M arket rentd

(1) Where,

d = District

β = Proportion mid-rental

γ = Proportion mid-rental monitored in size

For example, it could be illustrated that the change in initial rent for the proportion β and

γ in a certain district with an average market rent ofe1,000 should be calculated as follows:

∆Initial rentdβγ = e850 − e1, 000

e1, 000 = −15.0% (2)

As this regulation only applies to the mid-rental dwellings, the change in initial rent should only be administered to that part of the total project, β and γ. It is then possible to establish the new initial rent for the whole property in proportion to the initial market rent of the project for each district. This is then done by:

N ew initial rentd= α + (β + γ)(1 + ∆Initial rentdβγ) (3)

With the proportions taken from Table 1, and progressing with the example from Equation 2, it is possible to establish that for the example project that the new initial rent of this project in proportion to the original initial rent would be the following:

N ew initial rentd= 33

1

3% + (50 % + 16

2

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Methodology

5.2 Size Effect

Besides lowering initial rents, the municipality of Amsterdam has indicated that they desire a portion of the mid-rental dwellings to be constructed with an EFA that is above the market standard. In the example calculations of the AMR [Amsterdam, 2017a], they show that they expect 20 to 30% of the mid-rental dwellings to be constructed with an effective floor area

between 65 and 75m2. For simplicity of the model, the median of these ranges will be used.

Thus, 25% of the mid-rental dwellings will have to increase in size towards 70m2.

The first assumption we have to make in modelling the effects of such regulation is that the total floor area of a project cannot be increased. Hence, increasing the size of part of the residential program will not be possible without sacrificing floor area in other parts of the plans. Developers and investors should decide on which square meters they should sacrifice in order to

enlarge 25% of the mid-rental dwellings towards 70m2. As these market parties would evaluate

this decision on the basis of profitability of these square meters they would not sacrifice floor area of the top-segment dwellings which are not limited by initial rent setting and rent growth. Thus, in order to increase the size of these mid-rental dwellings the mid-rental dwellings that are not forced in size would shrink.

In order to determine the increase of floor space of the mid-rental dwellings belonging to the γ proportion, the average size of the dwellings in the district, d, should be gathered. Then, using the following formula, the increase in effective floor area is calculated:

∆EF Adγ =

70m2− Avg. EF A_d

Avg. EF Ad

(5) For example, it could be calculated that the effective floor area of the γ proportion of a

project in a certain district with an average effective floor area of 60 m2 would need to be

adapted by: ∆EF Adγ = 70m2− 60m2 60m2 = 16 2 3% (6)

In the specific case that the average floor area of the projects within a district would be

greater than the 70m2_{, the effective floor area would not need to change for proportion γ.}

In the search for the floor area required for the growth of these homes, real estate developers and investors would optimise the plans. The most probable solution for this would be to shrink

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the other mid-rental dwellings as the new regulations do not set special requirements with regard to the size of the residential units in proportion β of the project. In the optimisation of the total program one could expect that corresponding with the decrease in the average initial rent the size would also decrease following:

∆EF Adβ= ∆Initial rentdβ (7)

To clarify this assumption, one could think of a project with an average initial rent ofe1,000

and an average effective floor area per home of 60m2. Following Equation 2, it is calculated

that the change in the initial rent for proportion β would then be approximately -15.0% to

achieve an average rent ofe850 per dwelling. Equation 7 then represents the assumption that

in case of a rent decrease of 15.0% an investor would decrease the size with 15.0% as well.

They would then create rental dwellings of approximately 51m2 and put those in the market

ate850 per month. This mechanism would allow them to still charge market rents under the

new regulatory environment.

This optimisation should, however, be implemented with care. In some districts in Ams-terdam it will not be possible to decrease the size of the dwelling by the same rate as the rent decreases. This factor should thus need complementary analysis. However, for the districts where optimisation of the residential program is possible, the calculation of the change in effec-tive floor area for these dwellings leaves a discrepancy for optimisation of the project depicted in Equation 8. This discrepancy is calculated in a percentage of the total EFA of the property.

Optimisable f loor aread= −[β(∆EF Adβ) + γ(∆EF Adγ)] (8)

From the example property earlier noted, it could be calculated that the optimisable floor area of the property in proportion to the total EFA would be:

Optimisable f loor aread= −[50%(−15.0%) + 16

2

3%(16

2

3%)] ≈ 4.7% (9)

The floor area that is unlocked using the optimisation can then be rented out at the same rent rate as the other floor area is rented out. As it was established that the rent obtained from each floor area is assumed to be constant over the whole property, it is possible to calculate

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Methodology

the new initial rent after optimisation in proportion to the original initial rent. By combining Equation 3 and 8, it is possible to compute the ratio between the original rent and the rent after EFA optimisation. This is done using the following formula:

N ew initial rent incl. optimisationd=

N ew initial rentd

1 − Optimisable f loor aread

(10) From the example project used in the prior example calculations we could now calculate a new initial rent after optimisation. This would then yield the following:

N ew initial rent incl. optimisationd=

90.0%

1 − 4.7% ≈ 94.5% (11)

This shows that after optimisation of the example property the new initial rent would be possible to increase from 90.0% of the original market rent towards 94.5%. Therefore, when optimisation is possible, the initial rent would not be impacted as heavily by the new regulations.

Figure 3: Visualisation of Optimisation Effective Floor Area

Figure 3 visualises the optimisation process of the effective floor area. The initial division of the total EFA is depicted in the tree map on the left. The middle tree map shows the decrease of the effective floor area of the β proportion. The size of this discrepancy, rectangle 1, is calculated in Equation 7. The creation of this vacant floor area allows for the growth of the residential units of the γ proportion. This is shown in the third tree map. The growth of the γ proportion is indicated by rectangle 2. The size corresponding to this increase is calculated in Equation 5. The remainder, indicated with rectangle 3, is effective floor area that can be redistributed. The redistribution of this floor space will yield the average rent per EFA of the combination of the proportions α, β, and γ. The size of this fraction is calculated in

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Equation 8. The initial rent of the project changes from the left tree map, 100%, to the newly calculated initial rent including optimisation as calculated using Equation 10. The modelling of the returns of investors will include calculations based on the initial rent with rent restriction on mid-rental homes, and the initial rent with the restriction and optimisation. By comparison with the return of the investor in an environment without these restrictions it is possible to deduct the effect of these regulations affecting initial rents.

5.3 Rent Growth Effect

Having constructed the effects of the regulation on the initial rents, another important issue is the future prospects with regard to rent growth. In current appraisal practices, the future prospected cash flows in discounted cash flow models does not take into account the uncertainty. In order to accurately estimate the effect of the rent growth restriction, the constructed model will account for uncertainty in the prediction of both inflation and the increment of rent growth. The prediction of both will be based on historical series. By exploiting this method, we can estimate the effect of the rent growth restriction on the predicted internal rate of return.

5.4 Conversion Restriction Effect

To understand the impact of the lengthening of the conversion restriction on the return of investors, a framework is constructed which calculates the loss of value based on the market value gap observed in common appraisal technique. Appraisal of the market value of Dutch residential real estate is based on the highest value of two different scenarios. For the first scenario appraisers value based on continued operation, in which the whole property will be kept as rental property over the full 10-year appraisal horizon. In case of turnover of a dwelling the dwelling will again be rented out. The second, the conversion scenario, accounts for individual sales of units within a property within the appraisal horizon. The appraiser establishes a sales turnover rate at which the dwellings will be sold over the appraisal horizon. The sales proceeds of a unit will be based on the vacant value of the property. Both scenarios will yield a market value for a property, the highest will be used as the actual market value [Buffing et al., 2014].

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own-Methodology

ership has no value in case of vacant values equal or lower than investment values. Typically, vacant values in the Netherlands are lower than the investment value for investors. This is due to the restrictions involving tenancy with regard to tenant protection and the fact that tax treatment is skewed in favour of owner-occupancy. However, market conditions might arise in which elevated market rents close this gap. This is currently the case in Amsterdam. Com-mercial brokers report that for some districts in the city it is not uncommon to find vacant values exceeding investment values [Colliers International Nederland BV, 2017; Cushman & Wakefield, 2017; Syntrus Achmea Real Estate & Finance, 2017]. In the specific case that the vacant values keep rising, whereas rents stabilise, this gap might increase again. As the ratio between these values changes over time this will correspond to inconsistencies with regard to the value gap between both appraisal scenarios.

In case of a conversion restriction, the investor is not able to exploit the potential added value of the conversion scenario. The perceived property value can therefore only be the value of continued operation. By comparing the highest value of both scenarios to the value of the continued operation scenario alone a difference will occur. This gap in value will be the basis for establishing the effect of an extended conversion restriction and will be addressed as the value gap.

This value gap is, therefore, defined as the average gap in value over several years between taking the highest of both the conversion and the continued operation scenario versus always taking the continued operation scenario. To establish the size of the value gap, a historical data set of properties in Amsterdam should be analysed. For simplicity and generalisability, it is assumed that the value gap will be rather similar for the districts within Amsterdam. To account for the time inconsistency of this gap a long-term average will be used to calculate the average effect over the investment horizon.

As the market values in both scenarios reflect the discounted value of future cash flows, it allows for spreading the value gap over the whole investment horizon in annual losses. The average value gap is then presented as a percentage showing the loss in value in the case that conversion is not possible or allowed. The value gap and the eventual losses per year are both presented in proportion to the total value of the property. In order to spread the losses over the

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Methodology

10-year appraisal horizon, a discount rate, d, needs to be applied. The discount rate applied will be IRR obtained in the base case, as this is the initial required return on equity estimated for the project. The annual losses in proportion to the total property value are then computed as follows:

Average annual lossi,t =

Average value gapi∗ di

1 −_(1+d1

i)t

(12) For example, the average value gap over time between these valuations is found to be 5% and the discount rate for a property is assumed to be 7%. The valuations used in this analysis are assumed to be with a 10-year valuation horizon, which is market practice. It is, therefore, assumed that t = 10. Using Equation 12, the average annual loss in value can be calculated for this property as follows:

Average annual lossi,t =

5% ∗ 7% 1 −_(1+7%)1 10

≈ 0.71% (13)

After having computed the annual loss in value, it is possible to quantify the effect that such an extension has on the net sales proceeds taken into account in the IRR model in year 10. Prior to the implementation of the new regulation, investors would be able to sell of individual properties after 15 years. After the implementation this will only be possible after 25 years. Therefore, up to year 15 there is no difference observed. After that the annual loss in value is taken into account, as calculated in Equation 12 for the extended conversion restriction.

By discounting the loss in value from year 16 until year 25 towards year 10 the effect of this new regulation on the exit value of the property can be estimated. This is done in the following fashion:

N P V annual loss10−25,i =

Average annual lossi,t

(1 + di)6

+ ... + Average annual lossi,t

(1 + di)15

(14) Continuing from the example shown in Equation 13, it is now possible to calculate the net present value of the annual losses between year 15 and year 25 for the property. This yields the following:

N P V annual loss10−25,i=

0.71% (1 + 7%)6 + 0.71% (1 + 7%)7 + ... + 0.71% (1 + 7%)15 ≈ 8.3% (15)

The last step in the process of estimating the effect of the extended conversion restriction on the IRR involves translating this into an adjusted exit yield. By calculating the adapted

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exit yield it is possible to take the effect into account in the IRR calculation. This is done using the following formula:

Adjusted exit yieldi =

Exit yieldi

1 − N P V annual loss10−25

(16) It is assumed that the example property has an exit yield of 5% prior to the introduction of the conversion restriction. Together with the outcome of Equation 15 we can now calculate the adjusted exit yield after the introduction of the conversion restriction. Due to the extension of the conversion restriction the exit yield should be adapted to the following:

Adjusted exit yieldi=

5%

1 − 8.3% ≈ 5.21% (17)

5.5 IRR Model and Input Variables

Combining the above effects will involve constructing a straightforward IRR Monte Carlo Simu-lation model, which has the flexibility to adapt to the new reguSimu-lation conditions. In accordance with valuation standards the constructed model has a time horizon of 10 years. At time t = 0, the initial investment is included in the model. From t = 1 to t = 10, the model takes into account the net cash flows from operations. Furthermore, the net sales proceeds at t = 10 are included as exit value of the property. This subsection will elaborate on the method of calculation of the project IRR and will exhibit an example calculation. Moreover, the method of establishing the input variables is discussed.

5.5.1 Initial Investment

Calculating project returns, in this case the IRR, demands to establish an initial investment in the property done by the investor in year t = 0. Determination of the acquisition price by institutional investors is a process of analysing the cash flows, rather than analysing the costs the real estate developer has made. Hence, the initial investment of the investor is normally not based on the combination of the land value, the development costs, and the construction costs.

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Methodology

is the gross income multiplier (GIM) method. This method shows the ratio between the gross potential income in year t = 1 and the value of the investment property. It is of importance to notice that the aim of this research is not to determine market values accurately. The aim of estimating the initial investment is to determine a reference point of the IRR. The topic of interest in this paper is estimating, as accurately as possible, the effect of the regulations on the IRR. Therefore, estimating the initial investment by means of the gross potential rent income and relating this to the estimated market gross initial yield (GIY), the inverse of the GIM, suffices for this research. Predictions of the gross initial yield are commonly mentioned by real estate brokers and investors in the market. However, it might be of value to include sensitivity analysis with regard to the GIY as this is an estimated variable and regards a sizeable cash flow at t = 0.

5.5.2 Net Cash Flow

To calculate the impact of these regulations the model needs several input variables. As a basis for the initial rent level, market data will be collected from properties in the districts within Amsterdam. The required input from these projects are the average market rent together with the average EFA. With the method shown in Subsection 5.1 and 5.2, the model predicts the gross potential income separately for the mid-rental dwellings and the top-rental units. This allows for differentiated rent growth over time. By simply subtracting the vacancy, which is empirically derived, the gross income is determined. To calculate the net cash flow, the operating expenses are subtracted. An assumption of the operating expenses can be based on the annual reports of investors.

5.5.3 Inflation Series

Part of predicting the development of the net cash flows is dependent on the inflation series. Estimating the effect of the rent growth cap involves predicting inflation figures as well as predicting the possible rent growth in an environment without the rent cap. Both series will account for uncertainty in the predictions. This will be based on historical data, which is to be collected from the Dutch Central Bureau of Statistics. The predicted series will be normally

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Methodology

distributed.

In order to accurately predict these series, the means, standard deviations and correlation coefficient need to be collected and used as input variable for the simulations. The model will then randomly select values for the rates from the probability function in each of the simulated environments.

To create the uncertain time series for inflation a set of 10 random numbers with a normal

distribution are created with a mean of zero, x. These random numbers will develop the

stochastic path of the inflation time series. The path will simulate as many different possible paths for the inflation time series as the number of simulations that are run. In Appendix A.2, a visualisation can be found of some of the inflation paths within the performed simulations.

The path, πt, will be simulated using the following formula:

πt=πt−1∗ e

√ σ∗x1

x1∼ N (0, 1) (18)

5.5.4 Rent Growth Series

The rent growth in the unregulated rental segment is not only dependent on inflation. Scenarios in which rent growth is not capped by inflation might have rent growth series deviating from the inflation series. In the model, this series is established by simulating the rent growth increment series.

As input for this series, the difference between the historical inflation and rent growth should be analysed over time. Then, similar to the inflation series this analysis must generate a mean, a standard deviation, and the correlation coefficient between both.

In order to randomly generate rent growth increment values, which are correlated with the inflation values, the model draws from the simplified relation as described by Heston [1993]. In the simplified relation described in the Heston Stochastic Volatility Model, the created

random numbers for the inflation series, x1, as noted in Equation 18, are correlated with the

random numbers, x2, in order to provide the correlated number series on which the rent growth

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Methodology

correlated number series is created by:

1 = x1 2 = ρx1+ x2 p 1 − ρ2 ₍₁₉₎ Where, 1 = Inflation value

2 = Rent growth increment value

ρ = Correlation coefficient

The prediction of the rent growth increment time series is then created by the model similar

to Equation 18. However, the normally distributed random numbers of x1 will then be replaced

by the correlated random numbers, 2, created in Equation 19.

5.5.5 Exit Value

The final part of calculating the internal rate of return for a project involves estimating the net sales proceeds at the end of the investment horizon. Determining the exit value will be done using the exit yield. The exit yield is a similar ratio method as the gross initial yield. The exit yield shows the ratio between the projected gross potential rent income in year t = 11 and the predicted exit value. The exit yield will be derived from theory.

To test whether the exit yield is viable for the properties, the capital growth will be analysed as well. Comparing the capital growth figures to historical observations of capital growth in the market presents a more profound overview of the value increase. Furthermore, sensitivity analysis will be added along with the earlier noted initial investment sensitivity analysis.

5.5.6 The Internal Rate of Return

All the variables for determining the IRR have now been established. The combination of the variables yields the project IRR. To give an overview of the constructed model, a calculation of a base case scenario IRR is included in Appendix A.3 and A.4. This IRR calculation model will be the foundation for all the quantitative analyses. By adapting the input variables as discussed, the model will yield the effect of the regulatory measures on the project return.