A DYNAMIC BOOLEAN MODEL OF ROLLOVER FINANCING FOR RESIDENTIAL REAL
ESTATE DEVELOPMENT IN CHINA
Nga-Na Leung1, Kevin Grosskopf2, Lezhou Zhan3, Raja R.A. Issa4
ABSTRACT
During the past two decades, China has maintained strong growth in residential real
estate development, which has become increasingly attractive to foreign investors.
However, the People's Bank of China released new housing loan regulations in June
2004 effectively eliminating development subsidies, raising interest rates and equity
requirements for both developers and buyers, making debt and public equity
expensive and rarely accessible. As a result, developers with limited private equity
increasingly have to rely on internally generated cash flow for roll-over development.
Roll-over financing means using sale proceeds from buildings completed and sold
early in the project life-cycle to finance later construction phases.
The key issue for successful roll-over is to determine the optimal interval between
construction phases. However, quantitative analysis of optimal interval would require
tremendous work in the traditional discounted cash flow (DCF) models. As a result,
this study proposes a dynamic model with Boolean variable constraints, which
defines cash flows as Boolean variables, and enables them to change with
construction intervals. The dynamic model not only simplifies quantitative analysis
for optimal interval, but also depicts a complete picture for decision making in
various scenarios.
The model is applied to a hypothetical project consisting of four (4) high-rise
residential condominiums developed in sequence in Shenzhen, China. It easily
computes optimal intervals in both cash-constraint and cash-sufficient situations.
KEYWORDS
Residential real estate development, roll-over financing, dynamic modeling, boolean
variable constraints
1
Rinker School of Building Construction, University of Florida, Gainesville, FL, 32611; PH (352) 273
1179; nnleung@ufl.edu
2
Rinker School of Building Construction, University of Florida, Gainesville, FL, 32611; PH (352)
273 1158; kgro@ufl.edu
3
Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611;
PH (352) 392 1464 Ext 2031; zhan@ufl.edu
4
Rinker School of Building Construction, University of Florida, Gainesville, FL, 32611; PH (352)
273 1152; raymond-issa@ufl.edu
1
INTRODUCTION
Leading China’s emergence as a world economic power is the real estate sector, one
of the most profitable industries attracting foreign investment. Although financial
crises and SARS caused recession throughout much of Asia from 2001-2003, China’s
residential market grew 6-7% annually while generating speculative returns of 1525%. (Asia Pulse, 2004). The average price for residential real estate rose 6.5% to
¥2,481/m2 (US$30/sf), with Shenzhen reaching ¥5,780/ m2, or approximately
US$70/sf (China Daily, 2004). Fearing that much of this growth and price escalation
had been artificially driven by speculative turnover, the People's Bank of China
released new housing loan regulations in June 2004 effectively eliminating
development subsidies and raising interest rates and equity requirements for luxury
property developments, a sector where much of China’s residential market growth
was concentrated. Debt financing in China is more expensive and difficult to obtain,
forcing developers to increasingly rely on internally generated cash flow.
“Roll-over” financing, a term given to the use of income generated early in the
project cycle to finance construction in later stages, allows developers to meet
increasing cash flow requirements while minimizing reliance on costly debt and
external equity. To maximize profit and effectively utilize revenue from presales and
early sales proceeds, the optimal interval between construction phases must be
carefully determined in advance. If the interval is too short, income might not be
realized early enough to cover the cash outflow of sequential stages. If the interval is
too long, income is spread over an extended period of time, stranding working capital
and reducing the project return on investment.
However, quantitative analysis of optimal interval would require tremendous
work in traditional discounted cash flow (DCF) models. The assumption of changing
construction interval change many cash flow items and requires separated spread
sheets for each interval. This study proposes a dynamic model with Boolean variable
constraints, which defines cash flows as Boolean variables responding to the change
of one single variable: the construction interval. The dynamic model not only
simplifies quantitative analysis for optimal interval to one spread sheet, but also
depicts a complete picture for decision making in various scenarios.
The rest of the paper highlights the differences between multi-family residential
real estate development in the US and China. Based on the characteristics of Chinese
real estate development, a dynamic model with Boolean variable constraints is
proposed, which is incorporated into a hypothetical project consisting of four highrise residential condominiums developed in sequence. The model easily solves the
problem of optimal interval for efficient roll-over financing by satisfying all the
constraints imposed.
COMPARISON OF RESIDENTIAL DEVELOPMENT IN US AND CHINA
As shown in Table 1, residential project developments in China differ considerably
from those in developed countries, such as in the US, in the following aspects: source
of income; income recognition cycle; land property right; and debt financing ratio.
2
Table 1: Differences between residential project developments in the US and China
US
China
Source of income
Unit lease, project sales
Unit sales
Income recognition cycle
(holding period)
5-10 years or longer
2-5 years
Land acquisition
Property right
Land-use right
Debt financing
70-80% of value; income
capitalization
70-90% of estimated development
costs
Source of Income
A large percentage of multi-family residential projects in the US, for example, are
developed for unit lease and project sales. The developer’s income includes monthly
cash flows and one-time sale proceeds. In China, however, most residential projects
are developed for unit sales, which generate the sale proceeds as the major income.
Income Recognition Cycle
Income recognition cycle is defined as the period from land acquisition to design and
construction, holding, until the project’s titles are completely turned over. In China,
however, the cycle ends when the buildings are built and sold. Subsequently, income
recognition cycles in China are much shorter, from 2-5 years for turnkey sales
projects compared to 10-30 years for leasing projects in the U.S. The short income
recognition cycle enables roll-over financing in China for large projects having
multiple completion phases.
Land Acquisition
The property right of land can be bought In US, in the form of fee simple absolute.
In China, however, all property right of land belongs to the states. Developers can
only purchase land-use right for maximum of 70 years (PRC State Council, 1990).
This would not affect too much of property possession for the developer, since the
proportion of land-use right attached to the structure is transferred to each individual
buyer when an apartment unit is sold. However, it does affect significantly the price
and availability of land for development, since all land-use right can only be obtained
openly and limitedly through the following three sources: tender, auction, and license
(PRC Ministry of Land and Resources, 2002).
Debt Financing
In the US, the value of an income producing property is usually determined by the
first year’s net operating income divided by the capitalization rate. The loan amount
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is then determined by loan-to-value (LTV) ratio, usually up to 70%-80% of value. In
contrast, the ceiling on construction loans in China is determined by the loan-to-cost
(LTC) ratio, usually 70%-80% of total estimated costs. Equity should be invested into
the project before construction loans are in use (Bank of China, 2004). Underwriting
loans based on LTC rather than LTV is much stricter, because actual cost is usually
much less than the estimated value.
Valuation methods
The timing of cash flows is considerably different between typical multifamily
residential projects in the U.S. and in China (Table 2). In US, there are 3 major cash
flow phases: cost during acquisition and construction, net income from lease, and
gain from project sales proceeds. All estimated costs and benefits are discounted to
time 0 to get the project’s net present value (NPV) (Ling and Archer, 2003). In China,
however, there are only 2 major cash flow phases: cost during construction, and gain
from unit sale proceeds. In a roll-over financing model, cost and gain are interlaced,
and the net before tax cash flows of each month are discounted to time 0 to get the
project NPV. In either case, if NPV is equal to or greater than 0, the project is
financially acceptable; otherwise, it should be financially rejected.
Table 2: Cash flow valuation methodologies in US and China
Formulas
US
Construction related cost
Revenue from lease
Gross Potential Income from Rental
- Vacancy & Collection Loss
= Effective Gross Income
- Operating Expense
= Net Operating Income
- Debt Service
= Before Tax Cash Flow
Gain from sale proceeds
Sales Value
- Adjust base
= Gain (loss) from Sales
China
Gross Potential Sales Income
- Vacancy & Collection Loss
= Effective Gross Income from Sales
- Construction related Cost
= Earning Before Interest & Taxes
- Debt Service
= Before Tax Cash Flow
Cash flow
Sales
Proceeds
DP
Construction
Cost
Lease Revenue
Construction Cost
4
Sales
Proceeds
BOOLEAN MODEL FOR ROLL-OVER FINANCING
Given the limited debt financing available in China, roll-over financing, or the use of
sales proceeds early in the project life-cycle to sustain working capital through project
completion is considered a necessity for both domestic and foreign developers. The
key issue for successful roll-over is to determine the optimal interval between
construction phases, which is determined by the dynamic Boolean model in this study.
Simply defined, Boolean logic is a form of algebra in which all values are reduced to
either True or False, which fits a binary value of either 1 or 0. Boolean logic variables
are used to express constraints and profit objectives. The output, optimal time
interval α, is then generated from a series of responses to a sequence of constraint and
objective arguments. If an argument is true, a value of 1 is assigned to the variable;
and if false, 0 is assigned. For illustration purposes, the model assumes costs and
revenues in each phase can be divided evenly, and no resource constraints on the
construction of the buildings exist.
Calculation of monthly cost Ci
For simplicity, the total project cost is divided into only 2 major categories: the cost
for acquisition and design (C0i), and the cost for building construction (Cji). All direct
and indirect costs are included.
Assume the acquisition and design of the whole project takes Da months. The
cost of each month C is C a N / Da , where C is the cost of acquisition and design for
0i
a
one building, and N is number of buildings in the project. Therefore
If 1  i  Da
1  C a N / Da
C 0i  
(1)
0  C a N / Da If i  Da
Assume the construction of one building takes Db months, and the interval
between two construction phases is α months. For the jth building, construction starts
D  1   ( j  1)
D  Db   ( j  1)
in month a
, and ends in month a
, during which the
Cb / Db
cost per month is
, where Cb is the total cost for the construction of one
building. For other months the cost is 0. Therefore,
1  Cb / Db If Da  1   ( j  1)  i  Da  Db   ( j  1)
C ji  
(2)
0  Cb / Db Otherwise
Where j = 1, 2, 3, … N
For the whole project, the total cost of the ith month Ci is
N
Ci  C0i   C ji
j 1
(3)
Calculation of the monthly revenue Ri
Presales typically begin when the building is two-thirds completed, which is
usually when the structure and building envelope is finished. For the jth building,
D  1   ( j  1)
construction starts in month a
, therefore, presale can start as early as
5
in month Da  1   ( j  1)  2 / 3Db , and end in month Da  Dd   ( j  1)  2 / 3Db ,
where Dd is the projected duration of sales proceeds. The revenue per month
is Rd / Dd ; for other months the revenue is 0, where Rd is the total sales revenue for
one building. Therefore,
If Da  1   ( j  1)  2 / 3Db  i  Da  Dd   ( j  1)  2 / 3Db
1  Rd / Dd
R ji  
(4)
0  Rd / Dd Otherwise
Where j = 1, 2, 3, … N
Therefore, total revenue of the ith month Ri is
N
Ri   R ji (5)
j 1
Performance indicators
The objective of the roll-over model is to reduce working capital, preserve bonding
capacity, and maximizing project net present value. Working capital includes initial
equity invested and monthly interests paid for the cumulative principal borrowed.
The line of credit requirement (LCR), which is the maximum amount borrowed from
the bank, is the indicator of bonding capacity used in the project. The net present
value (NPV), internal rate of return (IRR), and return on equity (ROE) are the major
performance indicators of a project. To obtain these performance indicators, earnings
before interest and tax (EBIT) and before tax cash flow (BTCF) for each month must
be calculated.
Earnings before interests and tax (EBIT) is the difference between revenue and
cost for each month, given by
EBITi  Ri  Ci (6)
Before tax cash flow is the difference among EBITi, working capital (Wi), loan
(Li), interest obligation (INTRi), and one-time balloon payment (BP) at maturity,
given by
BTCFi  EBITi  Wi  Li  INTRi  BP (7)
At the beginning of the project, EBITi is negative, and working capital (Wi) is
required to pay for project costs, since it is required that equity must be invested
before loan can be used. When the cumulative Wi reaches E, the required equity,
loan from the bank (Li) is used to pay costs. At the same time, interest payment for
all cumulated principal borrowed up to month i (INTRi) is paid from working capital.
Later when EBITi becomes positive, interest payment is deduced from EBITi. The
one-time balloon payment (BP) is deducted from EBITi at maturity, usually when the
last building is substantially completed.
The project’s before tax NPV is estimated by discounting BTCF at the cost of
capital Kc
n
BTCFi
(8)
NPV  
i
i 1 (1  K c / 12)
6
Where n  Da  3   ( N  1)  2 / 3Db  Dd , the projected sales proceeds closure
date of the last building; Kc is the before tax cost of capital depends on the cost of
debt and equity.
The internal rate of return (IRR), which is the discount rate that sets the NPV of
BTCF to 0, is given by
n
BTCFi
(9)
0
i
i 1 (1  IRR / 12)
The total equity investment is equal to the working capital invested, which is the
sum of initial equity investment and the interests paid during construction. Different
values of α can significantly change the project duration and the value of the project.
Therefore, monthly time value is considered in the calculation of equity investment,
discounted at the cost of equity (Ke)
n
Wi
(10)
PVe  
i
i 1 (1  K e / 12)
The return on equity investment is calculated by dividing the present value of
total equity investments (PVe) by the NPV of the project.
PVe
(11)
ROE 
NPV
The line of credit requirement (LCR) is defined as the maximum cumulated
principal (CPi) required in any month,
LCR  Max(CPi ) (12)
Both the NPV and the LCR decrease when α increases. To measure the LCR at
unit NPV for different α value, a new variable, β, is introduced. β is given by
  LCR / NPV (13)
CASE STUDY
The following case study is based on the information provided by a real estate
developer in Shenzhen, China. The project is located in downtown Shenzhen, and
consists of 4 high-rise residential condominiums, each having 100 apartment units.
The project consists of 3 phases; land acquisition and design, construction, and sales.
Land acquisition and design of the four buildings are done at the same time, while
construction and sales are done in sequence. Additional assumptions are listed in
Table 3. Based on these assumptions, the proposed roll-over financing model is
developed in MS Excel. By changing the construction interval α between buildings,
the NPV, Equity, LCR, IRR, ROE, and β are calculated and shown in Table 4.
Changes in equity and LCR with respect to monthly time intervals are plotted in
Figure 1. The model indicates that equity changes only slightly with α, since initial
equity, which is the major part of the total equity investment, does not change in
relation to α. The LCR, however, reduces rapidly when α increases from 0 to 4
months, from $7,200,000 to $3,654,000, a reduction of almost 50%. When α is
greater than 4, however, the LCR becomes relatively stable ranging from $3,960,000
to $2,880,000.
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Table 3: Case assumptions
General Assumptions
For one Building ($ in thousand)
Average Area per Unit
900sf
Number of Units
Price per sf
$65/sf
Potential Sales Income
A&D*
$11/sf
A&D*
Construction
$24/sf
Construction
Sales
90%
Sales
Vacancy
10%
Vacancy
Duration (in months)
100 Units
$5850
-$990
-$2,160
$5,265
A & D*
3
Construction
12
Sales
10
$0
Loan Assumptions
Loan-to-Cost
Term
80%
Substantial
Completion
Loan Amount
$10,080
Type of Loan
Interest Only
6%
Cost of Equity
Cost of Debt
15%
Equity Investment
$2,520
Cost of Capital
7.80%
* Acquisition and design for the whole project is -$3,960K, 12 months.
A& D: Acquisition & Design
DP: Down Payment
Table 4: Project Performance Indicators (US$ in thousands)
Interval

0
1
2
3
4
5
6
7
8
9
10
11
12
NPV
6,494
6,408
6,319
6,228
6,135
6,050
5,965
5,880
5,796
5,717
5,640
5,572
4,812
Equity
2,589
2,581
2,576
2,573
2,573
2,540
2,512
2,511
2,510
2,510
2,510
2,539
2,572
LCR
7,200
6,314
5,427
4,541
3,654
3,447
3,240
3,060
2,880
2,880
2,880
3,420
3,960
IRR
80%
76%
72%
67%
63%
61%
59%
57%
55%
54%
53%
53%
52%
ROE
251%
248%
245%
242%
238%
238%
237%
234%
231%
228%
225%
219%
187%
1.11
0.99
0.86
0.73
0.60
0.57
0.54
0.52
0.50
0.50
0.51
0.61
0.82
β
Interval vs. Equity & LCR
$8,000
$7,000
$6,000
$5,000
$4,000
$3,000
$2,000
$1,000
$0
0
1
2
3
4
5
6
7
8
9
10
11
12
Months
Equity
LCR
Figure 1: Time Interval vs. Equity and LCR
On the other hand, reducing the LCR correspondingly reduces the NPV and the
IRR. Increase of α from 0 to 12 months results in a reduction of the NPV from
$6,494,000 to $4,812,000, and the IRR from 80% to 52% (Figure 2). This suggests
that without debt financing constraint, i.e., if the developers are able to borrow as
much as they need, it is optimal to build all buildings at once. However, in reality,
bonding capacity constraint is the largest problem to overcome.
8
The trade-off of NPV and LCR suggests using a new variable to measures LCR
given the same NPV. Thus β is introduced, which is defined as the LCR divided by
the NPV. The objective is to minimize β within the developer’s line of credit limits.
Figure 3 shows that the optimal α is either 8 or 9 months that yields a minimum β of
0.50, which means to generate every one dollar of NPV only requires to borrow $0.50
from the bank. However, β does not change much when α is in the range of 4 to 10
months. In practice, any value in this range is optimal, and developers probably
prefer a shorter life cycle to generate higher NPV, therefore, a smaller α, such as 4
months, is preferred.
Interval vs. NPV, IRR
90%
80%
70%
$6,000
$5,000
60%
50%
40%
30%
20%
10%
0%
NPV
$4,000
$3,000
$2,000
$1,000
$0
0
1
2
3
4
5
6
7
8
9
10
11
IRR
$7,000
12
Months
NPV
IRR
Figure 2: Time Interval vs NPV and IRR
Interval vs. NPV, LCR & β
$8,000
1.20
1.00
$6,000
0.80
$5,000
$4,000
0.60
$3,000
β
NPV, LCR
$7,000
0.40
$2,000
0.20
$1,000
$0
0.00
0
1
2
3
4
5
6
7
8
9
10
11
12
Months
LCR
β
NPV
Figure 3: Time Interval vs NPV and LCR
CONCLUSION
Cash flow management in the booming construction and real estate market in China
is extremely essential, especially for new developers and those implementing rapid
expansions. The characteristics of residential project developments in the US and
China are compared from 5 aspects, namely source of income, income recognition
cycle, land acquisition cost, debt financing, and presale or pre-lease performance. A
dynamic model with Boolean variable constraints is proposed. The objective is to
optimize construction interval to effectively utilize revenue from early sales proceeds
to finance later construction within a project, thus reserve bonding capacity for
9
developing other projects. The following conclusion can be drawn from the
hypothetical case in Shenzhen, China: roll-over financing has little effect on total
equity investment, given the short project cycle and low interest rate; both the project
NPV and LCR decrease with the increase of interval α, but the optimal interval is in
the range of 4 to 10 months; without bonding capacity constraints, the optimal
strategy is to build all buildings at once.
The MS Excel model proposed in this paper is suitable to evaluate roll-over
financing of all kinds of commercial projects for sales with little modification.
Design-and-build developers can customize the model to evaluate the feasibility of
their potential projects.
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