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#### Flashcard 1729653247244

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#topology
Question
In geometry, an affine transformation preserves [...objects...].
points, straight lines and planes

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In geometry, an affine transformation, affine map [1] or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes.

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Affine transformation - Wikipedia
s related to each other leaf by an affine transformation. For instance, the red leaf can be transformed into both the small dark blue leaf and the large light blue leaf by a combination of reflection, rotation, scaling, and translation. <span>In geometry, an affine transformation, affine map [1] or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line. Examples of affine transformations include translation, scaling, homothety, similarity transformation, reflection, rotation, shear mapping, and compositions of them in any combination

#### Flashcard 1731730476300

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#stochastics
Question

The Wiener process starts at [...

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The Wiener process is characterised by the following properties: [1] a.s. has independent increments: for every the future increments , are independent of the past values , has Gaussian increments: is normally distributed with mean and variance ,

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Wiener process - Wikipedia
Brownian motion 4.3 Time change 4.4 Change of measure 4.5 Complex-valued Wiener process 4.5.1 Self-similarity 4.5.2 Time change 5 See also 6 Notes 7 References 8 External links Characterisations of the Wiener process[edit source] <span>The Wiener process W t {\displaystyle W_{t}} is characterised by the following properties: [1] W 0 = 0 {\displaystyle W_{0}=0} a.s. W {\displaystyle W} has independent increments: for every t > 0 , {\displaystyle t>0,} the future increments W t + u − W t , {\displaystyle W_{t+u}-W_{t},} u ≥ 0 , {\displaystyle u\geq 0,} , are independent of the past values W s {\displaystyle W_{s}} , s ≤ t . {\displaystyle s\leq t.} W {\displaystyle W} has Gaussian increments: W t + u − W t {\displaystyle W_{t+u}-W_{t}} is normally distributed with mean 0 {\displaystyle 0} and variance u {\displaystyle u} , W t + u − W t ∼ N ( 0 , u ) . {\displaystyle W_{t+u}-W_{t}\sim {\mathcal {N}}(0,u).} W {\displaystyle W} has continuous paths: With probability 1 {\displaystyle 1} , W t {\displaystyle W_{t}} is continuous in t {\displaystyle t} . The independent increments means that if 0 ≤ s 1 < t 1 ≤ s 2 < t 2 then W t 1 −W s 1 and W t 2 −W s 2 are independent random variables, and the similar condition holds for

#### Flashcard 1731736767756

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#stochastics
Question

The Wiener process has [...]: is normally distributed with mean and variance ,

Gaussian increments

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ad> The Wiener process is characterised by the following properties: [1] a.s. has independent increments: for every the future increments , are independent of the past values , has Gaussian increments: is normally distributed with mean and variance , has continuous paths: With probability , is continuous in . <html>

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Wiener process - Wikipedia
Brownian motion 4.3 Time change 4.4 Change of measure 4.5 Complex-valued Wiener process 4.5.1 Self-similarity 4.5.2 Time change 5 See also 6 Notes 7 References 8 External links Characterisations of the Wiener process[edit source] <span>The Wiener process W t {\displaystyle W_{t}} is characterised by the following properties: [1] W 0 = 0 {\displaystyle W_{0}=0} a.s. W {\displaystyle W} has independent increments: for every t > 0 , {\displaystyle t>0,} the future increments W t + u − W t , {\displaystyle W_{t+u}-W_{t},} u ≥ 0 , {\displaystyle u\geq 0,} , are independent of the past values W s {\displaystyle W_{s}} , s ≤ t . {\displaystyle s\leq t.} W {\displaystyle W} has Gaussian increments: W t + u − W t {\displaystyle W_{t+u}-W_{t}} is normally distributed with mean 0 {\displaystyle 0} and variance u {\displaystyle u} , W t + u − W t ∼ N ( 0 , u ) . {\displaystyle W_{t+u}-W_{t}\sim {\mathcal {N}}(0,u).} W {\displaystyle W} has continuous paths: With probability 1 {\displaystyle 1} , W t {\displaystyle W_{t}} is continuous in t {\displaystyle t} . The independent increments means that if 0 ≤ s 1 < t 1 ≤ s 2 < t 2 then W t 1 −W s 1 and W t 2 −W s 2 are independent random variables, and the similar condition holds for

#### Flashcard 1737354251532

Question
[...] command updates all packages in an environment
conda update --all

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Before you proceed to conda update --all command to update all packages in an environment, first update conda with conda update conda command if you haven't update it for a long time.

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python - Bulk package updates using Conda [Anaconda] - Stack Overflow
add a comment | up vote 4 down vote <span>Before you proceed to conda update --all command, first update conda with conda update conda command if you haven't update it for a long time. It happent to me (Python 2.7.13 on Anaconda 64 bits). share|edit|flag edited Dec 26 '17 at 4:42 [imagelink]

#### Flashcard 1738856074508

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#metric-space
Question
the Banach fixed-point theorem is also known as [...]
the contraction mapping theorem

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In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive metho

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Banach fixed-point theorem - Wikipedia
Banach fixed-point theorem - Wikipedia Banach fixed-point theorem From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points. The theorem is named after Stefan Banach (1892–1945), and was first stated by him in 1922. [1] Contents [hide] 1 Statement 2 Proofs 2.1 Banach's original proof 2.2 Shorter

#### Flashcard 1739934797068

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#forward-backward-algorithm #hmm
Question

In the forward-backward algorithm, the formula for posterior marginals is [...]

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bserving the remaining observations given any starting point , i.e. . These two sets of probability distributions can then be combined to obtain the distribution over states at any specific point in time given the entire observation sequence<span>: The last step follows from an application of the Bayes' rule and the conditional independence of and given . It remains to be seen, of course, how the forwar

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Forward–backward algorithm - Wikipedia
cific instance of this class. Contents [hide] 1 Overview 2 Forward probabilities 3 Backward probabilities 4 Example 5 Performance 6 Pseudocode 7 Python example 8 See also 9 References 10 External links Overview[edit source] <span>In the first pass, the forward–backward algorithm computes a set of forward probabilities which provide, for all k ∈ { 1 , … , t } {\displaystyle k\in \{1,\dots ,t\}} , the probability of ending up in any particular state given the first k {\displaystyle k} observations in the sequence, i.e. P ( X k | o 1 : k ) {\displaystyle P(X_{k}\ |\ o_{1:k})} . In the second pass, the algorithm computes a set of backward probabilities which provide the probability of observing the remaining observations given any starting point k {\displaystyle k} , i.e. P ( o k + 1 : t | X k ) {\displaystyle P(o_{k+1:t}\ |\ X_{k})} . These two sets of probability distributions can then be combined to obtain the distribution over states at any specific point in time given the entire observation sequence: P ( X k | o 1 : t ) = P ( X k | o 1 : k , o k + 1 : t ) ∝ P ( o k + 1 : t | X k ) P ( X k | o 1 : k ) {\displaystyle P(X_{k}\ |\ o_{1:t})=P(X_{k}\ |\ o_{1:k},o_{k+1:t})\propto P(o_{k+1:t}\ |\ X_{k})P(X_{k}|o_{1:k})} The last step follows from an application of the Bayes' rule and the conditional independence of o k + 1 : t {\displaystyle o_{k+1:t}} and o 1 : k {\displaystyle o_{1:k}} given X k {\displaystyle X_{k}} . As outlined above, the algorithm involves three steps: computing forward probabilities computing backward probabilities computing smoothed values. The forward and backward steps m

#### Flashcard 1739942661388

Tags
#poisson-process #stochastics
Question
For a collection of [...] subregions of the underlying space, the number of points of a Poisson point process in each bounded subregion will be completely independent of all the others.
disjoint and bounded

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For a collection of disjoint and bounded subregions of the underlying space, the number of points of a Poisson point process in each bounded subregion will be completely independent of all the others. </h

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Poisson point process - Wikipedia
sed to define the Poisson distribution. If a Poisson point process is defined on some underlying space, then the number of points in a bounded region of this space will be a Poisson random variable. [45] Complete independence[edit source] <span>For a collection of disjoint and bounded subregions of the underlying space, the number of points of a Poisson point process in each bounded subregion will be completely independent of all the others. This property is known under several names such as complete randomness, complete independence, [21] or independent scattering [46] [47] and is common to all Poisson point processes.

#### Flashcard 1741150358796

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#measure-theory #stochastics
Question
A set Ω equipped with a sigma-algebra $$\mathcal{A}$$ is called a [...]
measurable space

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A set Ω equipped with a sigma-algebra  is called a measurable space and usually denoted as a pair (Ω,). In this context, the elements of  are called measurable sets.

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#### Flashcard 1741389171980

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#topology
Question
topology concerns the properties of space that are preserved under [...]
continuous deformations

i.e. homeomorphisms. Remeber scrub

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In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Topology - Wikipedia
ogy (disambiguation). For a topology of a topos or category, see Lawvere–Tierney topology and Grothendieck topology. [imagelink] Möbius strips, which have only one surface and one edge, are a kind of object studied in topology. <span>In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into what is known as a topological space. Important

#### Flashcard 1741390744844

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#topology
Question
topology is concerned with [...] that are preserved under continuous deformations
the properties of space

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In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

#### Original toplevel document

Topology - Wikipedia
ogy (disambiguation). For a topology of a topos or category, see Lawvere–Tierney topology and Grothendieck topology. [imagelink] Möbius strips, which have only one surface and one edge, are a kind of object studied in topology. <span>In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into what is known as a topological space. Important

#### Flashcard 1744160820492

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#lebesgue-integration
Question
the Lebesgue definition of integration considers [...] that are not necessarily just rectangles
horizontal slabs

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While the Riemann integral considers the area under a curve as made out of vertical rectangles, the Lebesgue definition considers horizontal slabs that are not necessarily just rectangles, and so it is more flexible.

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Lebesgue integration - Wikipedia
es, Fourier transforms, and other topics. The Lebesgue integral is better able to describe how and when it is possible to take limits under the integral sign (via the powerful monotone convergence theorem and dominated convergence theorem). <span>While the Riemann integral considers the area under a curve as made out of vertical rectangles, the Lebesgue definition considers horizontal slabs that are not necessarily just rectangles, and so it is more flexible. For this reason, the Lebesgue definition makes it possible to calculate integrals for a broader class of functions. For example, the Dirichlet function, which is 0 where its argument is

#### Flashcard 1752711171340

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#banach-space
Question
a Banach space is a [...] vector space.

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a Banach space is a complete normed vector space.

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Banach space - Wikipedia
Banach space - Wikipedia Banach space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, more specifically in functional analysis, a Banach space (pronounced [ˈbanax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly. [1]

#### Annotation 1756308311308

 you will be buying low , or investing when other peo- ple don ’ t see the value. That positions you to sell high — in other words, when other people think you ’ re crazy for selling too soon.

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#### Annotation 1756309884172

 There are emerging markets for commercial properties all around the United States at any given time.

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#### Annotation 1756311457036

 different types of commercial property follow different paths in the market cycle. Simply because a market is emerging for apartments does not mean that it is emerging for retail space.

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#### Annotation 1756313029900

 retail space generally lags behind apartments:

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#### Annotation 1756314864908

 #emerging #markets First come the announcements that new job opportunities will be opening up in an area. That creates a demand for ofﬁ ce space.

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#### Annotation 1756317486348

 #emerging #markets Then the people who will work in those ofﬁ ces begin to move into town. Because homes can ’ t be built fast enough, the apartment market suddenly heats up.

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#### Annotation 1756319845644

 #emerging #markets Many people want to see if their job will work out, and they want to get a good feel for the community. They check things out by rent- ing ﬁ rst. After their leases expire, they start to buy single - family houses.

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#### Annotation 1756328234252

 Retail space tends to follow housing surges, as merchants realize they can make money by moving closer to where people live and work.

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#### Annotation 1756329807116

 Discovering how to recognize the signs of emerging markets — and then acting on that knowledge — will make you a very rich person.

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#### Annotation 1756331379980

 Forced Appreciation This is one of the fastest ways to make money with commercial prop- erties. The concept is also called a value play . Whenever you look at a deal, always look for ways to force appreciation beyond what the local market may naturally generate.

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#### Annotation 1756333214988

 To force appreciation, you must ﬁ nd a deal with a slight problem.

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#### Annotation 1756335049996

 the previous owner. Maybe he ’ s been afraid to raise rents, so his rents are under market. Maybe he is charging the correct amount for rent, but has higher - than - normal vacancies. Perhaps his expenses are running high. These are all opportunities to buy a property with a built - in reward, as long as you buy based on the actual numbers . That is the key to buying right with commercial properties.

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#### Annotation 1756336885004

 Most sellers try to sell based on projected or pro forma numbers. This means that they are basing their price on what they think you can earn after you buy the property. The problem with pro forma numbers is they are not real. You are buying based on future cash ﬂ ows that may never materialize.

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#### Flashcard 1756364934412

Tags
#topological-properties
Question
In topology, a homeomorphism is a continuous function between topological spaces that has a [...]
continuous inverse function.

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In topology, a homeomorphism is a continuous function between topological spaces that has a continuous inverse function.

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Homeomorphism - Wikipedia
formation between a coffee mug and a donut (torus) illustrating that they are homeomorphic. But there need not be a continuous deformation for two spaces to be homeomorphic — only a continuous mapping with a continuous inverse function. <span>In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word homeomorphism comes from the Greek words ὅμοιος (homoios) = similar or same (French pareil) and μορφή (morphē) = shape, form, introduced to mathematics by Henri Poincaré in 189

#### Flashcard 1756366507276

Tags
#topological-properties
Question
In topology, a homeomorphism is a continuous function between [...] that has a continuous inverse function.

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In topology, a homeomorphism is a continuous function between topological spaces that has a continuous inverse function.

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Homeomorphism - Wikipedia
formation between a coffee mug and a donut (torus) illustrating that they are homeomorphic. But there need not be a continuous deformation for two spaces to be homeomorphic — only a continuous mapping with a continuous inverse function. <span>In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word homeomorphism comes from the Greek words ὅμοιος (homoios) = similar or same (French pareil) and μορφή (morphē) = shape, form, introduced to mathematics by Henri Poincaré in 189

#### Flashcard 1756368080140

Tags
#calculus
Question
[...] establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
Euler's formula

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Euler's formula establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

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Euler's formula - Wikipedia
s formula half-lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann–Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel's conjecture v t e <span>Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more

#### Annotation 1756369653004

 #fourier-analysis the process of decomposing a function into oscillatory components is often called Fourier analysis

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the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis.

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Fourier analysis - Wikipedia
, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, <span>the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize t

#### Flashcard 1756371225868

Tags
#fourier-analysis
Question
the process of [...] is often called Fourier analysis
decomposing a function into oscillatory components

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the process of decomposing a function into oscillatory components is often called Fourier analysis

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Fourier analysis - Wikipedia
, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, <span>the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize t

#### Annotation 1756380925196

 you will be buying low , or investing when other peo- ple don ’ t see the value. That positions you to sell high

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#### Annotation 1756382760204

 Back to forced appreciation: All you have to do is raise rents up to market levels.

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#### Annotation 1756384595212

 raise rents up to market levels. You ’ ll ﬁ rst have to wait until leases expire, because leases transfer with ownership.

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#### Annotation 1756386430220

 Apartments usually have one - year leases.

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#### Annotation 1756388265228

 Ofﬁ ce buildings and other commercial properties have 3 - year to 20 - year leases.

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#### Annotation 1756390100236

 raising rents also raises your property value: Commercial properties are primarily valued on multiples of their cash ﬂ ow.

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#### Annotation 1756391935244

 for each notch that you raise your net operating income , you ’ ve just raised the value of your property by multiple notches.

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#### Annotation 1756393770252

 #plays #value One of my favorite value plays is to ﬁ nd a property with higher - than - normal expenses. Most properties operate with expenses of about 50 percent of gross income. When you see the actual ﬁ nancials of a property with higher expenses, determine if you can lower those expenses to the average level.

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#### Annotation 1756395605260

 #lagrange-multiplier #optimization the method of Lagrange multipliers finds the local extrema of a function subject to equality constraints.

Lagrange multiplier - Wikipedia
[imagelink] Figure 1: The red line shows the constraint g(x, y) = c. The blue lines are contours of f(x, y). The point where the red line tangentially touches a blue contour is the maximum of f(x, y), since d 1 > d 2 . <span>In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange [1] ) is a strategy for finding the local maxima and minima of a function subject to equality constraints. For the case of only one constraint and only two choice variables (as exemplified in Figure 1), consider the optimization problem maximize f(x, y) subject to g(x, y) = 0. We assum

#### Annotation 1756397702412

 #plays #value Repositioning This is a special type of value play, and one of my favorites. When you reposition a property, you change the tenant base or signiﬁ cantly alter the appearance of the property. Sometimes you do both.

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#### Annotation 1756400061708

 #lagrange-multiplier #optimization We assume that both f and g have continuous first partial derivatives.

Lagrange multiplier - Wikipedia
maxima and minima of a function subject to equality constraints. For the case of only one constraint and only two choice variables (as exemplified in Figure 1), consider the optimization problem maximize f(x, y) subject to g(x, y) = 0. <span>We assume that both f and g have continuous first partial derivatives. We introduce a new variable (λ) called a Lagrange multiplier and study the Lagrange function (or Lagrangian or Lagrangian expression) defined by

#### Annotation 1756401634572

 #plays #value You may ﬁ nd a property that needs some tender loving care. We call this deferred maintenance . Maybe it ’ s an okay property, but it hasn ’ t been upgraded in over a decade. It may look tired and out - of - date. There may also be the wrong type of tenant leasing the space.

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#### Annotation 1756406353164

 #plays #value For years the mall had languished as a working - class shopping center. In the meantime, the demographics in Hingham had changed. The city could now support higher - end enterprise. The working - class mall gained a new life and was repositioned as the nation ’ s ﬁ rst lifestyle center . In place of the blue - collar stores, high - end shops like Williams Sonoma, Whole Foods, and Panera Bread moved into the refurbished spaces. The place took off, and is now one of the most popular shop- ping centers in the area.

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#### Annotation 1756407926028

 #lagrange-multiplier #optimization Thus, the method of Lagrange multipliers yields a necessary condition for optimality in constrained problems.

Lagrange multiplier - Wikipedia
where the partial derivatives of L {\displaystyle {\mathcal {L}}} are zero). However, not all stationary points yield a solution of the original problem. <span>Thus, the method of Lagrange multipliers yields a necessary condition for optimality in constrained problems. [2] [3] [4] [5] [6] Sufficient conditions for a minimum or maximum also exist. For the general case of an arbitrary number n of choice variables and an arbitrary number M of constrai

#### Annotation 1756410285324

 #plays #value Apartments are sometimes great candidates for repositioning. Let ’ s say that you ﬁ nd a tired apartment building in a good area. This prop- erty has not been kept up well, so it ’ s attracting tenants who are even less well - kept. To reposition the building, you ﬁ rst spruce up the exterior, focusing on the siding, rooﬁ ng, and parking lot. You upgrade the landscaping, put new signage on the property, and create a nice leasing ofﬁ ce. You then work on certain strategic improvements inside the property. With the property now looking much better, it ’ s time to reposition those tenants. You get rid of the tenants who pay slowly, never pay at all, or are criminally inclined. Replace them with the tenant proﬁ le that you are targeting.

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#### Annotation 1756412644620

 #plays #value To reposition the building, you ﬁ rst spruce up the exterior, focusing on the siding, rooﬁ ng, and parking lot. You upgrade the landscaping, put new signage on the property, and create a nice leasing ofﬁ ce. You then work on certain strategic improvements inside the property. With the property now looking much better, it ’ s time to reposition those tenants. You get rid of the tenants who pay slowly, never pay at all, or are criminally inclined. Replace them with the tenant proﬁ le that you are targeting. This is a process that can take several months, absorbing more time and money than the simple value - play of raising rents. The rewards can be quite spectacular, though. Not only can you ﬁ ll your vacant units, but soon all of the units are paying substantially more in rent. Because your property value is calculated at a multiple of the net operating income, you ’ ve just skyrocketed the worth of the property. When you come across a property that ﬁ ts the proﬁ le I just described, you should deﬁ nitely consider it for repositioning.

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#### Annotation 1756422868236

 #lagrange-multiplier #optimization Solving contrained optimization by direct substitution can be difficult becausing finding analytic solution of the constraint equation is not easyundesirable because the natural symmetry between the variables is spoiled

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#### Annotation 1756424441100

 #lagrange-multiplier #optimization The method of Lagrange multipliers relies on the intuition that at a maximum, f(x, y) cannot be increasing in the direction of any neighboring point where g = 0 . If it were, we could walk along g = 0 to get higher, meaning that the starting point wasn't actually the maximum.

Lagrange multiplier - Wikipedia
s of problems without the need to explicitly solve the conditions and use them to eliminate extra variables. Single constraint[edit source] Consider the two-dimensional problem introduced below maximize f(x, y) subject to g(x, y) = 0. <span>The method of Lagrange multipliers relies on the intuition that at a maximum, f(x, y) cannot be increasing in the direction of any neighboring point where g = 0. If it were, we could walk along g = 0 to get higher, meaning that the starting point wasn't actually the maximum. We can visualize contours of f given by f(x, y) = d for various values of d, and the contour of g given by g(x, y) = 0. Suppose we walk along the contour line with g = 0. We are int

#### Annotation 1756438859020

 when we asked questions and got answers that justified going on, we asked for commitments. We ask questions like: "Is that what you want?" or "Is there anything else we should cover?" or "Are you willing to pay a ten per cent premium for a glossy finish?" or "If we show you we can meet your requirements, what will you do?"

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 WE NEVER ASK FOR THE ORDER!

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 High Probability Selling process is a closing process. We focus on finding out what's necessary to do business, right from the start. We use an orderly process that's thorough and professional. Our approach is designed to have the prospect commit to do business with us if what we have is what he wants.

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 we don't move to a new phase without a commitment. When we reach a point where a prospect won't make commitments, we end the meeting and move on to someone else.

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 NEVER ASK FOR THE ORDER! Just negotiate mutual commitments. In a situation where our company can't fulfill the prospect's Conditions of Satisfaction, acknowledge that promptly and make a swift, courteous exit.

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 You don't ever try to convince a prospect that he needs and wants what you have to sell. If he clearly understands the benefits you're offering, and they're not what he wants, it's time to end that visit. If he really wants what you have, he won't let you go

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#### Annotation 1756925660428

 get money partners to put up the cash for your deals. Depending on how the deal is structured, you should get between 25 and 50 percent of the monthly cash flow. If you got 50 percent of the cash flow, you’ll now need to accu- mulate 168 units to be free as a bird. That’s double the number of units compared to our earlier example, but the good news is you put no money down. Not a bad trade-off.

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 tenants are paying down your mortgage! That means even in a real estate market with no appreciation, your property is building equity.

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#### Annotation 1756928806156

 12 Multi-Family Millions tenants are paying down your mortgage! That means even in a real estate market with no appreciation, your property is building equity. If you’re investing in emerging markets, your property will be appre- ciating rapidly at the same time your mortgage balance is dropping

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 every month you can enjoy a cash flow that supports your lifestyle.

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 your tenants are going to work each day to pay you rent, which is paying down your mortgage.

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 you might buy a building for $1 million and hold it for 10 years. You’re retired and using the cash flow to live on. After 10 years, that property might be worth$1,500,000 and your mort- gage principal may be down to $700,000. Notice that even though you reached your cash flow goal 10 years ago and you’re living very com- fortably, you’re actually$800,000 richer now! You have the option to take out a loan against the property and pull some of that equity out.

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 Most small real estate investors chase single-family houses. Most very large (corporate) investors chase commercial properties like office buildings and big shopping centers. That leaves a comfortable and profitable gap for you and me to step up and make our fortunes in between!

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 There is simply less competition when you buy apartments. The reason is obvious: Most people are scared away by the fear of dealing with tenants.

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#### Annotation 1756938243340

 investors most likely avoid apartments because they think it takes big money to get started.

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#### Annotation 1756939816204

 Investors making fortunes in apartments treat the business like a business. Each property is handled separately: It has its own ownership

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 Each month, separate financial reports are created and reviewed. That’s where investors should be spending their time—reviewing reports and doing more deals—not in rolling up their sleeves and dealing with tenants.

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 I personally do not stay in contact with tenants; but I insist that my property managers do!

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 If you are too much of a do-it-yourselfer, and think you’ll save a few bucks by managing the property yourself, I have news for you: You’ll be a burned-out statistic within two and a half years, on average. You’ll hate your tenants, they’ll hate you, the property will be deteriorating, and so will your former profit.

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#### Annotation 1756946369804

 buy from these landlords, and not be one of them.

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 Banks will indeed finance only about 80 percent of the money needed to buy a property

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 there are a great many ways to get other people to put up the remaining 20 percent, for a share of the cash flow and profits.

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#### Annotation 1756951350540

 118-unit apartment complex in Decatur, Georgia. They purchased it for $4,860,000. But first, they put together a group of partners and raised$1,400,000 needed to close the deal.

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 walked away with $140,000 to do repairs to the property, and another check for$170,000 just for putting the deal together!

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 Apartment deals are a profit multiplier.

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#### Annotation 1756963147020

 With an apartment building, you’ve at least got other tenants paying while your property manager is working to fill the vacancies. If you have one empty unit in a three-unit building, you may not have any cash flow for that month, but you’re probably covering your expenses and mortgage.

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 If you have a ten-unit building and a couple of tenants decide to leave, not only will the other eight make the mortgage payment but you’ll still have some cash flow that you can spend or reinvest in other properties.

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#### Annotation 1756966292748

 Your apartment buildings should never be more than 95 percent occupied. Why? Because if they’re 100 percent occupied, you might very well be charging rents that are too low. But at 95 percent, you’re getting the maximum level of rents on pretty much the maximum number of units. (Naturally, this logic applies only to properties with lots of units; a three-unit property would not fit into this rule of thumb.)

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#### Annotation 1756967865612

 For every renewal and every new tenant, you should be asking higher rent. You keep up this policy until your occupancy gets below 95 percent. Now you’ve found out what the market is willing to pay for rent in your building. You should now level off, and hold it there until your occupancy climbs above 95 percent, at which time you start the process again

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 You must get enough knowledge so when you do that first deal, you’re taking a calculated risk.

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 Know what the numbers mean and how to analyze them. Know what to expect before the closing, how to do your due diligence, how to get the property inspected, and how to find your property manager. Know the best strategies to exit the deal. Have an exit plan before you enter!

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#### Annotation 1756973632780

 internalize these princi- ples. Once you’ve got them down, you’re ready to spread your wings and fly.

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 You can have all the skill and knowledge, but if you don’t take action, it’s worthless. In case you’re wondering how you’ll do in those first tentative tries to fly, I’ll tell you: You will fall a few times. That’s right: You’ll screw up. But so what! After all, you’re taking calculated risks, and not betting the farm.

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 Get out there and take action. Get started and then stumble. But then you get up, dust yourself off, and again move down the road in the direction of your dreams.

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#### Annotation 1756979399948

 apartments are no more complicated than other real estate investments, or most other skills, for that matter.

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 Just reconcile yourself that when you’re starting out, you’ll be bad at the beginning. Then you’ll get better and—if you stick with it—will be on the road to mastery.

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 why not make it a type of real estate investing that can make you so much wealthier, so much faster than your typical single-family home investments?

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#### Annotation 1756984380684

 Hunt for lenders to do new deals.

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 If I could get into the deal with no money out of my pocket and get cash flow every month, I wanted in. That was my philosophy. I wanted enough cash flow each month so I could pay all my bills and not have to worry all the time.

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 The market was exhausted. Builders had overbuilt, the market was oversupplied, and demand was at its lowest point.

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#### Annotation 1756989885708

 buy a property, fix it up, and find a seller for the property. Sometimes it can be quick, but six months are usually required to complete that cycle. (Trust me: I know. I later got my contractor’s license and rehabbed hundreds of deals.)

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#### Annotation 1756991458572

 buy properties two hours away—and eventually 2,000 miles away.

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 If you start by investing in multi-family properties the right way, you can become wealthier, faster.

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 When you discover how to find multi-family deals, they will jump into your consciousness, and beckon you to buy!

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#### Annotation 1756996177164

 there are many types of multi-family housing. Properties for low-income families are usually government-subsidized housing. Then there’s housing for working people who can’t afford a house. There is also housing for the working people who simply choose to rent instead of buy. Finally, there is luxury rental housing.

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 #property #types Grade: A, B, C, and D. A properties are the luxury ones. They are usually less than 10 years old. White-collar workers live in them. These people are usually renters by choice: They don’t want the hassle of home ownership. Maybe they’ve been transferred to the community recently, or are soon to be married. Some of them travel a lot and have yet to settle down. Class A properties are the most expensive and are usually bought up by institutions (corporate investors).

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 #property #types B properties were built within the last 20 to 30 years. Their tenant base is a mixture of white-collar and blue-collar workers. Some are renters by choice and others rent by necessity.

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 #property #types C properties were built within the last 30 to 40 years. This is where you’ll find many tenants that are renters for life. On the other hand, some tenants (like me at one point) are just starting out in life. As they get better jobs, they work their way up the rental scale.

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 #property #types C properties are where you’ll find many Section 8 or government- subsidized housing tenants. Many investors are afraid of subsidized housing. They fear that the tenants are really rough. Well I’m here to tell you . . . they are! But only if you don’t screen them properly. It just stands to reason: If you don’t look at people’s background when you rent to them, you’re going to get tough tenants.

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 You are more likely to get good tenants if you: r Screen for prior evictions r Require that they have been working for two years before renting from you r Require that they have lived in the same residence for at least two years before moving into your property Yes, you will have to screen more applicants to get the good ones, but it’s worth it.

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 #property #types D properties are the worst. They are in bad areas and have bad tenants. There are usually drug dealers in the units and as soon as you get rid of one, another shows up to reopen the store. You see beat-up cars in the parking lot and bars on the windows. It’s not a place where you (or your property manager) will want to go to collect rents, even in the daytime. You can make a lot of money with D properties. I’ve done it. They are management-intensive and to be honest, involve many more headaches than rewards.

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#### Annotation 1757011119372

 Determine the property class you want to invest in and start driving around the neighborhoods.

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 Multi- family properties get foreclosed on just like homes. Some fantastic deals are to be had, all across the country.

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 #foreclosure Multi- family properties get foreclosed on just like homes. Some fantastic deals are to be had, all across the country. The owners have a thousand stories to tell: r Perhaps they were too aggressive when they bought and the num- bers didn’t really make sense. r Some tried to manage tenants themselves. r Others went into the death spiral of holding off on repairs, only to have the good tenants leave and rents drop, which resulted in delaying repairs even longer. The bottom line is the property went upside down. Now there is an opportunity to buy it at a discount and make some real money, real quickly.

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 I bought a three-family at foreclosure for $41,000 and resold it for$160,000 nine months later. I put $22,000 worth of work into it, but didn’t do the work myself. The profit was still a home run! I once bought a two-family for$2,000! I put $60,000 into it and resold that one for$140,000. I bought a six-family foreclosure for $125,000, put a little work into it and resold it for$295,000. There is big money in multi-family foreclosures.

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 Many of the best deals are from burned-out landlord-owners. They never learned that multi-family investing is a business

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#### Annotation 1757020294412

 business has systems. If you follow the systems, you’re usually successful. If you don’t, you’re usually not.

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 Find good property managers, and then ensure that they do their job. They must follow certain specific processes to keep them accountable for maximizing your profit and maintaining your property.

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 #buying #process Reposition properties for great wealth. But my conservative process for buying means that you’ll also have two other investment options for that same deal: Buy and flip, or buy and hold.

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 If you buy right, you’ll have several alterna- tives for realizing your profits.

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 #buying #process The 14 Steps to Acquiring a Property These are the steps you must take if you want to invest with the least amount of time, money, and risk—and for the most profit: 1. Decide what size buildings you want to start investing in. 2. Decide where you want to invest. 3. Determine what types of multi-family properties you’ll buy. 4. Put your team in place. 5. Market to get your deal. 6. Analyze the deals. 7. Create the offer or letter of intent. 8. Negotiate the deal. 9. Create and sign the purchase-and-sale agreement. 10. Do your due diligence. 11. Renegotiate the deal. 12. Start your financing. 13. Choose a management company. 14. Close the deal.

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 #buying #process 1. Decide What Size Buildings You Want to Start Investing In What size building are you comfortable investing in?

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 start moving and take action by doing a small deal. You just need to get in the game. It doesn’t matter where you start.

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 Once you have a comfort level with how all the pieces of this puzzle go together, you might graduate to medium-size deals—20 to 75 units. As I’ve already said, some people actually go out and do multi-hundred-unit deals as their very first one!

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 the faster you go big, the faster you’ll become wealthy. That’s because it takes just as much effort to do the big deals as it does to do the little ones.

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 whatever you do, keep your eye on that goal and do what it takes to get some deal—however small—under your belt and in your bank account.

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 start focusing on larger properties. Before you know it, you’ve got a portfolio of apartment complexes that are spinning off cash flow

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 #buying #process 2. Decide Where You Want to Invest Do you want to invest in your own town? Looking at the demograph- ics can help you decide which cities to focus on, or avoid.

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 #buying #process I was buying in the good areas of a bad city. I was also buying for much less than replacement cost and my buildings were cash-flowing.

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 decide where you want to invest; it doesn’t have to be a city down on its luck to be a profitable investment. It does have to be an area you’re comfortable with.

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 #emerging #markets investing beyond your backyard, in emerging markets. Sometimes your local area just does not hold much current promise. Fortunately, by using management companies, you can invest anywhere.

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 Invest in cities that will give you the highest return. You don’t have to be a big company to do that.

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 #emerging #markets At any given time, 20 to 30 markets in the United States are emerg- ing. That means they look like beat-up, low-potential markets now, but the stage is set for them to explode. Investing in these markets will explode your wealth, too.

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 The farther away the property is, the less likely you will go over there and work on it

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 You should run these properties like a business, and I don’t mean the landlording business.

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 if your local market just doesn’t seem workable, there’s no excuse to dump your dreams of financial freedom through real estate. Your first deal can be a remote-control investment.

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 #book Emerging Real Estate Markets: How to Find and Profit from Up-and-Coming Areas,

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 #buying #process 3. Determine What Types of Multi-Family Properties You’ll Buy Please don’t think that when I say determine, I mean you’re deciding on something permanently. Instead, I mean that you have to pick a provisional target. You can easily change it later to adjust for what information is coming in. But the only way to invest is to have a plan, and all good plans have goals.

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 What you’re determining in Step 3 is the subcategory of apartment deal you’ll first go after. It will make your marketing easier, because the more you’re searching for something specific, the more it jumps out at you when you find it.

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 #Play #Value I have another name for subcategory of apartment deal: It’s Value Play.

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 #property #types High vacancies or Low rents How can I tell if an apartment has those other problems? Work it so the landlords tell you which type of property they have.

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 Pick based on your general understanding of the size of building and area you’ve chosen

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 #buying #process 4. Put Your Team in Place The next step is to put together a team of people that will success- fully get you over the goal line to complete your deals. Successful businesspeople surround themselves with specialists who have more knowledge than they do—at least for that specialty. Real estate is a relationship business. These are the key relationships you will be establishing: r Real estate brokers (as many as you can get working for you) r Property management company r Bankers and other lenders r Attorney r Appraiser r Property inspector r Insurance agent

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 The first people you should put on your team are brokers. They are the people most likely to bring you deals.

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 5. Market to Get Your Deal Nothing happens until you have a potential deal.

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 There are a great many investors who are in reality spectators. They love the world of real estate investing, and can soak up knowledge on a par with the very best sponges. But they remain spectators because they never do the marketing to bring in a potential deal. This is the most critical—and most-often missing—step in your real estate investing path.

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 The primary users of financial statements are equity investors and creditors.
• Equity investors are primarily interested in the company's long-term earning power, growth, and ability to pay dividends.

• Short-term creditors (e.g., banks and trade creditors) are more interested in the company's immediate liquidity, because they seek an early payback of their investment.

• Long-term creditors (e.g., corporate bond owners such as insurance companies and pension funds) are primarily concerned with the company's long-term asset position and earning power.

1. The Roles of Financial Reporting and Financial Statement Analysis
to take these financial statements and other information to evaluate the company's past, current, and prospective financial position and performance for the purpose of making rational investment, credit, and similar decisions. <span>The primary users of financial statements are equity investors and creditors. Equity investors are primarily interested in the company's long-term earning power, growth, and ability to pay dividends. Short-term creditors (e.g., banks and trade creditors) are more interested in the company's immediate liquidity, because they seek an early payback of their investment. Long-term creditors (e.g., corporate bond owners such as insurance companies and pension funds) are primarily concerned with the company's long-term asset position and earning power. <span><body><html>

#### Annotation 1757094219020

 #reading-megafono These four financial statements, augmented by footnotes and supplementary data, are interrelated. In addition, there are other sources of financial information, such as management discussion and analysis, auditor's reports, etc.

Subject 2. Major Financial Statements
Income statement (statement of earnings) Balance sheet (statement of financial position) Cash flow statement Statement of changes in owners' or stockholders' equity <span>These four financial statements, augmented by footnotes and supplementary data, are interrelated. In addition, there are other sources of financial information, such as management discussion and analysis, auditor's reports, etc. Income Statement The income statement summarizes revenues earned and expenses incurred, and thus measures the success of business operations for a given period

#### Annotation 1757095791884

 #reading-megafono The income statement summarizes revenues earned and expenses incurred, and thus measures the success of business operations for a given period of time. It explains some but not all of the changes in the assets, liabilities, and equity of the company between two consecutive balance sheet dates.

Subject 2. Major Financial Statements
ts, augmented by footnotes and supplementary data, are interrelated. In addition, there are other sources of financial information, such as management discussion and analysis, auditor's reports, etc. Income Statement <span>The income statement summarizes revenues earned and expenses incurred, and thus measures the success of business operations for a given period of time. It explains some but not all of the changes in the assets, liabilities, and equity of the company between two consecutive balance sheet dates. The income statement lists income and expenses as they are directly related to the company's recurring income. The format of the income statement is not specified by U.S. G

#### Annotation 1757097364748

 #reading-megafono The goal of income statement analysis is to derive an effective measure of future earnings and cash flows.

Subject 2. Major Financial Statements
ts income and expenses as they are directly related to the company's recurring income. The format of the income statement is not specified by U.S. GAAP and actual format varies across companies. The following is a generic sample: <span>The goal of income statement analysis is to derive an effective measure of future earnings and cash flows. Analysts need data with predictive ability, hence income from continuing (recurring) operations is considered to be the best indicator of future earnings. As operating expenses do not i

#### Annotation 1757098937612

 #reading-megafono Analysts need data with predictive ability, hence income from continuing (recurring) operations is considered to be the best indicator of future earnings. As operating expenses do not include financing costs such as interest expenses, operating income (EBIT) is independent of the company's capital structure.

Subject 2. Major Financial Statements
come statement is not specified by U.S. GAAP and actual format varies across companies. The following is a generic sample: The goal of income statement analysis is to derive an effective measure of future earnings and cash flows. <span>Analysts need data with predictive ability, hence income from continuing (recurring) operations is considered to be the best indicator of future earnings. As operating expenses do not include financing costs such as interest expenses, operating income (EBIT) is independent of the company's capital structure. In the typical income statement this means segregating the results of normal, recurring operations from the effects of nonrecurring or extraordinary items to improve the fo

#### Annotation 1757100510476

 #reading-megafono The net income figure is used to prepare the statement of retained earnings.

Subject 2. Major Financial Statements
recurring income is persistent. If an item in the unusual or infrequent component of income from continuing operations is deemed not to be persistent, then recurring (pre-tax) income from continuing operations should be adjusted. <span>The net income figure is used to prepare the statement of retained earnings. Balance Sheet A balance sheet provides a "snapshot" of a company's financial condition. Think of the balance sheet as a photo of the business at a sp

#### Annotation 1757102345484

 #reading-megafono Statement of Changes in Owners' Equity This statement reports the amounts and sources of changes in equity from capital transactions with owners. It reports ownership interests in order of preference upon liquidation and dividends. For example, the first item listed gets paid off first after creditors in the event of liquidation.

Subject 2. Major Financial Statements
tion can be used to evaluate the effects of major investment and financing decisions. The details of income statements, balance sheets and cash flow statements will be covered in Study Session 8. <span>Statement of Changes in Owners' Equity This statement reports the amounts and sources of changes in equity from capital transactions with owners. It reports ownership interests in order of preference upon liquidation and dividends. For example, the first item listed gets paid off first after creditors in the event of liquidation. <span><body><html>

#### Annotation 1757104704780

 #reading-megafono What is the purpose of the analysis? Evaluating an equity or debt investment? Or issuing a credit rating? The context needs to be defined clearly too: Who is the intended audience? What is the nature and content of the final report? What is the time frame? What is the budget? Gather a company's financial data from financial statements and other sources described in Subject c (other financial information sources). Also gather information on the economy and industry to understand the environment in which the company operates. Compute ratios or growth rates, prepare common-size financial statements, create charts, perform statistical analyses, make adjustments to financial statements, etc. Periodic review is required to determine if the original conclusions and recommendations are still valid.

Subject 5. Financial Statement Analysis Framework
ut to support a conclusion (e.g., a buy decision). Develop and communicate conclusions and recommendations. Communicate the conclusion or recommendation in an appropriate format. Follow up. <span>What is the purpose of the analysis? Evaluating an equity or debt investment? Or issuing a credit rating? The context needs to be defined clearly too: Who is the intended audience? What is the nature and content of the final report? What is the time frame? What is the budget? Gather a company's financial data from financial statements and other sources described in Subject c (other financial information sources). Also gather information on the economy and industry to understand the environment in which the company operates. Compute ratios or growth rates, prepare common-size financial statements, create charts, perform statistical analyses, make adjustments to financial statements, etc. Periodic review is required to determine if the original conclusions and recommendations are still valid. <span><body><html>

#### Annotation 1757106277644

 The auditor (an independent certified public accountant) is responsible for seeing that the financial statements issued comply with generally accepted accounting principles. In contrast, the company's management is responsible for the preparation of the financial statements. The auditor must agree that management's choice of accounting principles is appropriate and that any estimates are reasonable. The auditor also examines the company's accounting and internal control systems, confirms assets and liabilities, and generally tries to be sure that there are no material errors in the financial statements. Though hired by the management, the auditor is supposed to be independent and to serve the stockholders and the other users of the financial statements.

Subject 4. Auditor's Reports
The auditor (an independent certified public accountant) is responsible for seeing that the financial statements issued comply with generally accepted accounting principles. In contrast, the company's management is responsible for the preparation of the financial statements. The auditor must agree that management's choice of accounting principles is appropriate and that any estimates are reasonable. The auditor also examines the company's accounting and internal control systems, confirms assets and liabilities, and generally tries to be sure that there are no material errors in the financial statements. Though hired by the management, the auditor is supposed to be independent and to serve the stockholders and the other users of the financial statements. An auditor's report (also called the auditor's opinion) is issued as part of a company's audited financial report. It tells the end-user the following: &

#### Annotation 1757107850508

 An auditor's report (also called the auditor's opinion) is issued as part of a company's audited financial report. It tells the end-user the following:
• Whether the financial statements are presented in accordance with generally accepted accounting principles.

• It identifies those circumstances in which such principles have not been consistently observed in the current period in relation to the preceding period.

• Informative disclosures in the financial statements are to be regarded as reasonably adequate unless otherwise stated in the report.

Subject 4. Auditor's Reports
to be sure that there are no material errors in the financial statements. Though hired by the management, the auditor is supposed to be independent and to serve the stockholders and the other users of the financial statements. <span>An auditor's report (also called the auditor's opinion) is issued as part of a company's audited financial report. It tells the end-user the following: Whether the financial statements are presented in accordance with generally accepted accounting principles. It identifies those circumstances in which such principles have not been consistently observed in the current period in relation to the preceding period. Informative disclosures in the financial statements are to be regarded as reasonably adequate unless otherwise stated in the report. An auditor's report is considered an essential tool when reporting financial information to end-users, particularly in business. Since many third-party users prefer

#### Annotation 1757109423372

 #reading-megafono An auditor's report is considered an essential tool when reporting financial information to end-users, particularly in business. Since many third-party users prefer or even require financial information to be certified by an independent external auditor, many auditees rely on auditor reports to certify their information in order to attract investors, obtain loans, and improve public appearance. Some have even stated that financial information without an auditor's report is "essentially worthless" for investing purposes.

Subject 4. Auditor's Reports
ntly observed in the current period in relation to the preceding period. Informative disclosures in the financial statements are to be regarded as reasonably adequate unless otherwise stated in the report. <span>An auditor's report is considered an essential tool when reporting financial information to end-users, particularly in business. Since many third-party users prefer or even require financial information to be certified by an independent external auditor, many auditees rely on auditor reports to certify their information in order to attract investors, obtain loans, and improve public appearance. Some have even stated that financial information without an auditor's report is "essentially worthless" for investing purposes. The Types of Audit Reports There are four common types of auditor's reports, each one representing a different situation encountered during the auditor's work.

#### Annotation 1757110996236

 #reading-megafono An unqualified opinion report is issued by an auditor when the financial statements presented are free of material misstatements and are in accordance with GAAP, which, in other words, means that the company's financial condition, position, and operations are fairly presented in the financial statements. It is the best type of report an auditee may receive from an external auditor. It is regarded by many as the equivalent of a "clean bill of health" to a patient, which has led many to call it the "clean opinion."

Subject 4. Auditor's Reports
s. The Types of Audit Reports There are four common types of auditor's reports, each one representing a different situation encountered during the auditor's work. The four reports are as follows: <span>An unqualified opinion report is issued by an auditor when the financial statements presented are free of material misstatements and are in accordance with GAAP, which, in other words, means that the company's financial condition, position, and operations are fairly presented in the financial statements. It is the best type of report an auditee may receive from an external auditor. It is regarded by many as the equivalent of a "clean bill of health" to a patient, which has led many to call it the "clean opinion." A qualified opinion report is issued when the auditor encountered one or two situations that did not comply with generally accepted accounting principles; however, the r

#### Annotation 1757112569100

 #reading-megafono A qualified opinion report is issued when the auditor encountered one or two situations that did not comply with generally accepted accounting principles; however, the rest of the financial statements are fairly presented. This type of opinion is very similar to an unqualified or "clean opinion," but the report states that the financial statements are fairly presented with a certain exception which is otherwise misstated.

Subject 4. Auditor's Reports
the best type of report an auditee may receive from an external auditor. It is regarded by many as the equivalent of a "clean bill of health" to a patient, which has led many to call it the "clean opinion." <span>A qualified opinion report is issued when the auditor encountered one or two situations that did not comply with generally accepted accounting principles; however, the rest of the financial statements are fairly presented. This type of opinion is very similar to an unqualified or "clean opinion," but the report states that the financial statements are fairly presented with a certain exception which is otherwise misstated. An adverse opinion is issued when the auditor determines that the financial statements of an auditee are materially misstated and generally do not comply with GAAP. It i

#### Annotation 1757114141964

 #reading-megafono An adverse opinion is issued when the auditor determines that the financial statements of an auditee are materially misstated and generally do not comply with GAAP. It is considered the opposite of an unqualified or clean opinion, essentially stating that the information contained to assess the auditee's financial position and results of operations is materially incorrect, unreliable, and inaccurate.

Subject 4. Auditor's Reports
ly presented. This type of opinion is very similar to an unqualified or "clean opinion," but the report states that the financial statements are fairly presented with a certain exception which is otherwise misstated. <span>An adverse opinion is issued when the auditor determines that the financial statements of an auditee are materially misstated and generally do not comply with GAAP. It is considered the opposite of an unqualified or clean opinion, essentially stating that the information contained to assess the auditee's financial position and results of operations is materially incorrect, unreliable, and inaccurate. A disclaimer of opinion, commonly referred to simply as a disclaimer, is issued when the auditor could not form, and consequently refuses to present, an opinion on the f

#### Annotation 1757115976972

 #reading-megafono A disclaimer of opinion, commonly referred to simply as a disclaimer, is issued when the auditor could not form, and consequently refuses to present, an opinion on the financial statements. This type of report is issued when the auditor tried to audit a company but could not complete the work due to various reasons and does not issue an opinion.

Subject 4. Auditor's Reports
ered the opposite of an unqualified or clean opinion, essentially stating that the information contained to assess the auditee's financial position and results of operations is materially incorrect, unreliable, and inaccurate. <span>A disclaimer of opinion, commonly referred to simply as a disclaimer, is issued when the auditor could not form, and consequently refuses to present, an opinion on the financial statements. This type of report is issued when the auditor tried to audit a company but could not complete the work due to various reasons and does not issue an opinion. Auditor's Report on Internal Controls Following the enactment of the Sarbanes-Oxley Act of 2002, the Public Company Accounting Oversight B

#### Annotation 1757117549836

 #reading-megafono Auditor's Report on Internal Controls Following the enactment of the Sarbanes-Oxley Act of 2002, the Public Company Accounting Oversight Board (PCAOB) was established in order to monitor, regulate, inspect, and discipline audit and public accounting firms of public companies. The PCAOB Auditing Standards No. 2 now requires auditors of public companies to include an additional disclosure in the opinion report regarding the auditee's internal controls, and to opine about the company's and auditor's assessment of the company's internal controls over financial reporting. These new requirements are commonly referred to as the COSO Opinion.

Subject 4. Auditor's Reports
s to present, an opinion on the financial statements. This type of report is issued when the auditor tried to audit a company but could not complete the work due to various reasons and does not issue an opinion. <span>Auditor's Report on Internal Controls Following the enactment of the Sarbanes-Oxley Act of 2002, the Public Company Accounting Oversight Board (PCAOB) was established in order to monitor, regulate, inspect, and discipline audit and public accounting firms of public companies. The PCAOB Auditing Standards No. 2 now requires auditors of public companies to include an additional disclosure in the opinion report regarding the auditee's internal controls, and to opine about the company's and auditor's assessment of the company's internal controls over financial reporting. These new requirements are commonly referred to as the COSO Opinion. <span><body><html>

#### Annotation 1757119384844

 #reading-megafono Financial footnotes are an integral part of financial statements. They provide information about the accounting methods, assumptions and estimates used by management to develop the data reported in the financial statements. They provide additional disclosure in such areas as fixed assets, inventory methods, income taxes, pensions, debt, contingencies such as lawsuits, sales to related parties, etc. They are designed to allow users to improve assessments of the amounts, timing, and uncertainty of the estimates reported in the financial statements.

Subject 3. Other Financial Information Sources
Financial Notes and Supplementary Schedules Financial footnotes are an integral part of financial statements. They provide information about the accounting methods, assumptions and estimates used by management to develop the data reported in the financial statements. They provide additional disclosure in such areas as fixed assets, inventory methods, income taxes, pensions, debt, contingencies such as lawsuits, sales to related parties, etc. They are designed to allow users to improve assessments of the amounts, timing, and uncertainty of the estimates reported in the financial statements. Supplementary Schedules: In some cases additional information about the assets and liabilities of a company is provided as supplementary data outside the financial statemen

#### Annotation 1757120957708

 #reading-megafono Supplementary Schedules: In some cases additional information about the assets and liabilities of a company is provided as supplementary data outside the financial statements. Examples include oil and gas reserves reported by oil and gas companies, the impact of changing prices, sales revenue, operating income, and other information for major business segments. Some of the supplementary data is unaudited.

Subject 3. Other Financial Information Sources
pensions, debt, contingencies such as lawsuits, sales to related parties, etc. They are designed to allow users to improve assessments of the amounts, timing, and uncertainty of the estimates reported in the financial statements. <span>Supplementary Schedules: In some cases additional information about the assets and liabilities of a company is provided as supplementary data outside the financial statements. Examples include oil and gas reserves reported by oil and gas companies, the impact of changing prices, sales revenue, operating income, and other information for major business segments. Some of the supplementary data is unaudited. Management Discussion and Analysis (MD&A) This requires management to discuss specific issues on the financial statements, and to assess the company's curr

#### Annotation 1757122530572

 #reading-megafono Management Discussion and Analysis (MD&A) This requires management to discuss specific issues on the financial statements, and to assess the company's current financial condition, liquidity, and its planned capital expenditure for the next year. An analyst should look for specific concise disclosure as well as consistency with footnote disclosure. Note that the MD&A section is not audited and is for public companies only.

Subject 3. Other Financial Information Sources
mples include oil and gas reserves reported by oil and gas companies, the impact of changing prices, sales revenue, operating income, and other information for major business segments. Some of the supplementary data is unaudited. <span>Management Discussion and Analysis (MD&A) This requires management to discuss specific issues on the financial statements, and to assess the company's current financial condition, liquidity, and its planned capital expenditure for the next year. An analyst should look for specific concise disclosure as well as consistency with footnote disclosure. Note that the MD&A section is not audited and is for public companies only. Auditor's Reports See next subject for details. Other Sources of Information Interim reports. Publicly held companies must fi

#### Annotation 1757124103436

 #reading-megafono Interim reports. Publicly held companies must file form 10-Q (interim report) on a quarterly basis. It is far less detailed than annual financial statements, as it contains unaudited basic financial statements, unaudited footnotes to financial statements, and management discussion and analysis.

Subject 3. Other Financial Information Sources
disclosure. Note that the MD&A section is not audited and is for public companies only. Auditor's Reports See next subject for details. Other Sources of Information <span>Interim reports. Publicly held companies must file form 10-Q (interim report) on a quarterly basis. It is far less detailed than annual financial statements, as it contains unaudited basic financial statements, unaudited footnotes to financial statements, and management discussion and analysis. Proxy statements. An analyst should look for litigation, executive compensation, and related-party transactions, known as proxy statements. Proxy statements should be co

#### Annotation 1757137734924

 #reading-megafono Proxy statements. An analyst should look for litigation, executive compensation, and related-party transactions, known as proxy statements. Proxy statements should be considered an integral part of the financial report, and they may contain special compensation "perks" for officers and directors, as well as lawsuits and other contingent obligations facing the company.

Subject 3. Other Financial Information Sources
report) on a quarterly basis. It is far less detailed than annual financial statements, as it contains unaudited basic financial statements, unaudited footnotes to financial statements, and management discussion and analysis. <span>Proxy statements. An analyst should look for litigation, executive compensation, and related-party transactions, known as proxy statements. Proxy statements should be considered an integral part of the financial report, and they may contain special compensation "perks" for officers and directors, as well as lawsuits and other contingent obligations facing the company. Companies' websites, press releases, and conference calls. <span><body><html>

#### Annotation 1757167619340

 RPR offers residential and commercial agents, brokers, and appraisers with data sets ranging from tax and mortgage history, to listings, sales, valuations, demographics, psychographics, and school information, to name just a few.

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#### Annotation 1757169192204

 Research hundreds of datasets on over 160 million properties

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#### Annotation 1757170765068

 Calculate the ROI for home improvements

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#### Annotation 1757172337932

 Use the exclusive Realtor Valuation Model ® (RVM ® ) in pricing discussions

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#### Annotation 1757173910796

 Refine the value of a home when conducting a comps analysis

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#### Annotation 1757194882316

 Pull up RPR and get accurate comps, based on current data.

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#### Annotation 1757197503756

 information on schools, neighborhoods, and recent home purchases in the area.

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#### Annotation 1757199076620

 Pull up RPR and every single house in the area is displayed, whether it’s for sale or not, schools are in the area, including ratings and reviews.

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#### Annotation 1757204319500

 It Starts With Searching for the Right Property “RPR’s database has hundreds of datasets and filters to get to where you want to be

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#### Annotation 1757205892364

 support the data with solid evidence that can either affirm or deny the seller’s asking price. RPR has pricing tools in place that help us pinpoint value

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#### Annotation 1757209562380

 “If you’re paying people to fix things, it eats your equity,”

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#### Annotation 1757211659532

 Use RPR’s refine value tool to measure the market value of the seller’s improvements to the home,

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#### Annotation 1757215067404

 present the most credible pricing strategy and the most informative reports,

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#### Annotation 1757217426700

 Have RPR as an analytical and reporting tool, coupled with my knowledge of the neighborhood and market

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#### Annotation 1757220834572

 Go to RPR, search for the property, select the Refine Value Tool, and added the home’s improvements. Select comps and rate each against subject property based on enhanced awareness of the home and the area.

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#### Annotation 1757223193868

 RPR’s comparative analysis tool allows you to pick comps and then tweak the value of each against the subject property

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#### Annotation 1757227126028

 RPR Mini Property Report

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#### Annotation 1757228961036

 RPR’s RVM and how it supersedes all other models. “As the only REALTOR ® -owned, automated valuation product, the RVM goes beyond the traditional AVM by incorporating listing and sales data from the MLS into the equation. It is a very credible automated tool for determining value.”

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#### Annotation 1757231058188

 MINI-PROPERTY REPORT The Mini-Property Report highlights everything a potential client wants to know about the property without overwhelming them with data

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#### Annotation 1757232631052

 NEIGHBORHOOD REPORT The Neighborhood Report provides an in-depth portrait of the people who live in an area, in addition to key indicators such as job growth, unemployment, cost of living, commute times and climate. The report also includes median list and sales prices, listing and sales volumes, and per square foot pricing on sold homes.

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#### Annotation 1757234466060

 SCHOOL REPORT The School Report summarizes student population, testing outcomes, parental reviews, ratings, and contact information about a public or private school—essential information for buyers with school-aged children

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#### Annotation 1757236038924

 The farming strategy includes identifying potential neighborhoods and then sending a team of up to three agents to go, as Chesnoff says, “belly to belly” with homeowners. “Telephone solicitations are no longer effective,” claims Chesnoff. “And marketing pieces, such as postcards, can be valuable, but our greatest reward comes from establishing relationships in neighborhoods, by meeting people on their sidewalks and in their living rooms.”

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#### Annotation 1757239708940

 With RPR, access the home’s estimated value, property facts, and mortgage and tax information, as well as the owner’s contact info. And as the conversation between agents and the homeowner ensues, you can add notes to the property details page.

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#### Annotation 1757242854668

 “We’d like to let you know what your home might be worth based on recent sales in the area,” says Antoinette after a brief introduction. Deliver an RPR Market Activity Report to the homeowner, and asks, “Do you know anyone in the area who is thinking of moving or needing a place to rent? We can help.”

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#### Annotation 1757255699724

 Use the Best Business Report all the time. The Esri data goes much deeper than what you’d expect. It breaks populations into segments like household income, male/female, married/single/ divorced, etc., but the extra sections like how and where consumers in the area spend their money are invaluable. And the report itself is really impressive. Graphs that show which business types are over-and-under represented

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#### Annotation 1757258321164

 I can run the Best Business Report and show him there’s an abundance of similar shops in the area. But I won’t leave it at that. I might advise my client to open a Dunkin Donuts, or a bakery that serves cakes as well as yogurt smoothies or frozen yogurt—something that gives him a competitive edge.

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#### Annotation 1757259894028

 RPR intentionally leaves off the page numbers so that we can further customize the report by pulling out pages that aren’t helpful to particular circumstances. Every single report can be tailored to that client’s needs and interests, including adding your own pages.”

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#### Annotation 1757262777612

 RPR maps are easy to use, intuitive, and have many, many layers of data. Seeing things visually provides greater insights that you don’t get from merely looking at the numbers.

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#### Annotation 1757264612620

 RPR’s maps identify nearby Points of Interest (POIs). There are hundreds of them in many different categories—manufacturing, government offices, banks, retail, hospitals, restaurants … the list goes on. And hovering over an icon reveals data about that company like sales volume, the number of employees, square footage, and year opened.

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#### Annotation 1757266971916

 create heat maps that show breakdowns of household income, age, married/divorced, etc., and depending on where you’re from, the flood zone maps can be really important.

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#### Annotation 1757268544780

 RPR maps to identify all the churches in an area and then encouraged my client, a pizza shop owner, to send flyers with coupons to all of those churches. Another time I conducted a map search of all available properties within specific ZIPs for a client who was licensed to conduct business in those areas only.”

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#### Annotation 1757270117644

 Crossover between commercial and residential What he likes “I work with a lot of international buyers and sellers. Most are looking for a business location first and possibly a residential property down the line. With RPR, I can easily jump between the two, finding the perfect site for their business and helping to identify areas they might be interested in for a home purchase.

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#### Annotation 1757273001228

 #commercial #training Video Learning Getting Started with RPR Commercial Navigate through the Commercial application of RPR. Your one-stop-shop for comprehensive market data, allowing REALTORS ® specializing in commercial properties to save time and money. This basic course is a complete step by step library of video tutorials that will introduce you to all the commercial features RPR has to offer. Learn more at: blog.narrpr.com/ video-learning/rpr-commercial- fundamentals

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#### Annotation 1757276409100

 RPR reports can show him how a location is more than adequate; but marketing strategy needed direction.

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#### Annotation 1757308128524

 I don’t consider myself in the real estate business! I’m in the marketing business.

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#### Annotation 1757309701388

 You will find good deals through effective marketing. You’ll find lenders willing to do no-money-down deals through marketing. And you will employ other marketing techniques to sell your deals at a handsome profit to other people.

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#### Annotation 1757311536396

 It doesn’t matter how much skill you have; it doesn’t matter how much knowledge you’ve accumulated: If your phone is not ringing and the mailbox is empty, you’re not going anywhere

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#### Annotation 1757313109260

 Have a whole bunch of marketing tools to apply to any market at any time.

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#### Annotation 1757316779276

 Create a pipeline of deals presenting themselves through the phone, e-mail, and post office. Once you’ve turned on that pipeline, never turn it off ! It’s your goose that’s laying your golden deals. Deal flow is the engine that drives your business.

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#### Annotation 1757319138572

 Analyze the Deals Once you start getting leads coming in to your business from all of your marketing, it’s time to separate the good deals from the bad. The majority of what you’ll see in the beginning will be worthless deals. No big deal. It’s just the nature of the beast.