Moscow Automobile and Highway Institute
(State Technical University)
DEPARTMENT OF ROAD TRANSPORT ECONOMICS
Discipline "Real Estate Economics"
“Fundamentals of investment and mortgage analysis”
Moscow 2009
direct, strong connection of the property with the land;
the property cannot be moved away from the land plot without significant damage to its purpose;
real estate belongs to the category of financial assets;
real estate transactions are carried out in the real estate market - a specific segment (sector) of the financial market;
real estate market - the sphere of capital investment (investment sphere), as well as the system of economic relationships between participants in the financial market regarding real estate transactions; the purchase and sale of real estate is associated with the movement of capital or value that generates income;
purchasing a property means investing capital in this property, which generates income for its owner during operation or rental, as well as after its resale at a higher price;
due to the specificity of real estate as a financial category and its high cost, the state places high demands on compliance with the legality of real estate transactions, therefore almost all transactions in the real estate market must undergo state registration;
the demand for real estate is not interchangeable, therefore, even when supply exceeds demand, it (demand) often remains unsatisfied;
The amount of demand for real estate is determined by geographical and historical factors, as well as the state of infrastructure in the area where the property is located.
It should be noted that the main element or attribute of real estate is land.
Due to the high dynamics of prices for all objects of the financial, as well as all other markets, as well as the lack of a more or less efficient information base on real estate objects, the real real estate market cannot exist without an assessment of its objects. Real estate appraisal refers, first of all, to the assessment of ownership rights to real estate and the real estate itself.
Almost all real estate purchase transactions are made using mortgage loans, or loans secured by real estate. In such conditions, the value of real estate is determined as the sum of the mortgage loan, the present value of income from the use of real estate and proceeds from the resale of real estate. In general, the assessment of the value of real estate encumbered or acquired with a mortgage loan is carried out using mortgage investment analysis. This paper will discuss issues related to mortgage lending and the basics of investment and mortgage analysis.
Mortgage - pledge of real estate as a way to secure obligations. The presence of a mortgage lending system is an integral part of any developed system of private law. The role of mortgages especially increases when the state of the economy is unsatisfactory. In this case, a well-thought-out and effective mortgage system, on the one hand, helps reduce inflation by drawing on temporarily free funds of citizens and enterprises, and on the other, helps solve social and economic problems.
Often the term “mortgage” refers to mortgage lending, but “mortgage” has an independent meaning - collateral of real estate as a way to secure obligations.
Real estate is an integral element of most economic processes. However, due to its characteristics, it refers to objects that are optimal for lending. The most important features include the following.
1. The cost of real estate as a unit of goods is very high and requires significant capital from the investor.
2. Real estate, first of all, is a plot of land on which some improvements are being built to ensure its profitability; the process of using income-generating real estate can only be carried out at the site of its original creation, since it cannot be transported.
3. The right to real estate as a commodity is subject to mandatory registration in the unified state register of rights to real estate in the manner established by federal law.
4. Real estate has a fairly large physical size; physical and economic aging of real estate occurs over a long period of time.
5. During the economic life of real estate, capital measures may be carried out that affect the amount of income, and, therefore, it can be stable, decrease and increase over time.
6. Investments in real estate depreciate to a lesser extent, since changes in the value of real estate usually compensate for inflationary processes.
The expediency of using borrowed funds when carrying out real estate transactions exists for both the borrower and the lender.
The advantages of raising borrowed funds to purchase real estate allows the investor (borrower):
1. Purchase a more expensive object compared to the equity capital that he has at the time of the transaction.
2. Diversify the real estate portfolio by investing the released own funds during lending in other properties.
3. Purchasing income-producing real estate in installments allows the owner to repay the debt to the creditor with interest from the income generated by the same property.
4. Increase the rate of return on equity capital by choosing optimal financing conditions.
Considering the positive aspects of an investor's use of borrowed funds, it is necessary to note the disadvantages.
1. The amount returned to the lender exceeds the loan received, since the investor must pay interest.
2. A mortgage loan is a borrowed source that requires timely and full repayment.
3. A change in the terms of the loan laid down in the initial loan agreement, a drop in the value of the net operating income of the property during the operation of the property can lead to negative financial leverage.
4. Violation of the loan repayment schedule gives the creditor the right to foreclose on the pledged property. In this case, the property is sold and the debt is paid off from the sale price. The balance of the proceeds from the sale of real estate due to the owner may be less than the amount of the repaid loan.
The lender makes a decision to provide borrowed funds on a long-term basis secured by real estate based on an analysis of the following factors:
1. The loaned object, due to its physical, economic and legal characteristics, can be controlled by the creditor throughout the entire period of debt repayment.
2. Mandatory state registration of rights to real estate, as well as transactions with it, including mortgages, serves as a legal guarantee of the fulfillment of contractual obligations by the borrower.
3. The long physical and economic life of the property is the basis for the return of not only the principal amount, but also the interest due.
4. A flexible system for drawing up a loan agreement and the possibility of including special conditions in it enable the lender to take into account changes in the market profitability of credit resources, the financial stability of the borrower, and influence the process of resale of the loaned property during the repayment period of the debt.
5. Registration of a “mortgage” for granted mortgage loans allows the mortgage bank to put mortgages into circulation and replenish its credit resources.
The considered features of real estate have led to the fact that in countries with developed market economies, real estate properties are purchased with the participation of a mortgage loan. A mortgage loan is a type of loan, which is characterized by: provision of funds for a long time, lending to a transaction for the acquisition of real estate, the purchased real estate serves as collateral.
Thus, a distinctive feature of a mortgage loan is the combination of the collateral object and the purchased object.
During the entire loan term, the borrower (mortgagor) and the lender (mortgagee) do not have full rights to the pledged property. While retaining the rights of ownership and use, they cannot dispose of the property. At the same time, the borrower must operate the property in such a way that the income received allows him to repay the principal debt, pay accrued interest, taxes, insurance premiums, carry out timely repairs to maintain the property in proper condition, and also receive income on the invested equity capital.
Currently, there are many mortgage lending schemes, which differ mainly in the terms of obtaining loans, interest payment schemes and amortization of the principal amount. The most common types of loans are:
with balloon payment;
self-cushioning;
with a variable interest rate;
Canadian roll-over;
final mortgage;
joint participation;
loan with discount points.
Loans with balloon payment provide for payment and interest on the principal amount at the end of the loan term. There are intermediate options, such as periodic interest payments and repayment of the debt amount at the end of the loan period. Balloon loans are most typical for investors who seek to minimize costs during the development of the project and at the end of this period fulfill debt obligations after the sale of their assets.
Self-amortizing loan provides for equal periodic payments, including interest payments that fall as the debt is amortized and growing payments for loan amortization. These loans are issued in amounts that are a fraction of the value of the property, largely depending on the lender's perception of the liquidity of the investment asset. A self-amortizing mortgage loan is most convenient when analyzing the structure of investments and the economic characteristics of income-producing real estate, therefore, in the future, when considering methods of mortgage investment analysis, we will use a loan of this particular type.
Loan with variable interest rate usually used when investors and lenders seek to take into account the rapidly changing price situation in the capital and resource markets. In this case, the interest rate can change either directly or through a change in the size of payments or amortization periods.
Canadian roll-over - a form of variable-rate loan in which the interest rate adjusts at predetermined time intervals (usually several years).
Final Mortgage given by a third party or by the holder of a first mortgage, creating a junior mortgage. The owner of the final lien assumes the obligations on the balance of the first loan, requiring higher interest payments on the final loan amount, which includes the balance of the old and own loan. Thus, the new lender uses financial leverage for its own loan.
Joint participation - in this case, the lender participates in the distribution of profits from income and (or) increase in the value of assets in addition to interest payments, providing a loan at a more preferential interest rate.
Loan with discount points means that the borrower actually receives an amount less than that specified in the loan agreement. However, interest and amortization payments must be paid on the entire debt amount. The investor agrees to a discount on the loan amount in exchange for a low interest rate, while the lender, by providing a loan at a discount, increases the final return relative to the actual loan. The discount on the agreed amount is measured in discount points. One discount point is equal to one percent of the contractual debt amount.
In practice, several other types of mortgage loans are used, but they are all modifications of the above.
Analysis of mortgage obligations as an integral part of an investment project creates the necessary basis for determining cash flows, the current value of assets and equity. The appraiser needs to know the current interests and preferences of owners and creditors, as well as the current conditions on the capital market, in order to competently adjust the nominal value of borrowed obligations as an integral part of the current value of the property.
In Russia, mortgages have been used relatively recently (Federal Law of the Russian Federation “On Mortgages (Pledge of Real Estate)” No. 102-FZ was adopted on July 16, 1998). However, we can already say that the institution of mortgage lending in Russia (before the global financial crisis) was developing quite quickly . Below are some provisions of the Federal Law “On Mortgage (Pledge of Real Estate)”, which it is advisable for a practicing real estate appraiser to focus on.
The basis for the emergence of a mortgage. The basis for a mortgage may be a law or an agreement. Under the agreement, the pledgor (including those who are not the debtor) voluntarily pledges any real estate belonging to him, thereby guaranteeing satisfaction of the creditor's claims in the event of failure to fulfill the obligation secured by the pledge. The contract is the main form of mortgage. In some cases, a mortgage may arise on the basis of legal provisions.
An obligation secured by a mortgage. A mortgage may be established to secure an obligation under a credit agreement, a loan agreement or another obligation, including an obligation based on purchase and sale, lease, contract, other agreement, damage, unless otherwise provided by federal law.
Property that can be the subject of a mortgage. Under a mortgage agreement, the real estate specified in paragraph 1 of Article 130 of the Civil Code of the Russian Federation, the rights to which are registered in the manner established for state registration of rights to real estate and transactions with it, may be pledged, including:
1) land plots, with the exception of land plots specified in Article 63 of this Federal Law;
2) enterprises, as well as buildings, structures and other real estate used in business activities;
3) residential buildings, apartments and parts of residential buildings and apartments, consisting of one or more isolated rooms;
4) dachas, garden houses, garages and other buildings for consumer purposes;
5) aircraft and sea vessels, inland navigation vessels and space objects.
Right of pledge property that belongs to the pledgor on the right of ownership or on the right of economic management may be encumbered.
In the mortgage agreement the subject of the mortgage, its valuation, the essence, size and period of fulfillment of the obligation secured by the mortgage must be indicated. The subject of the mortgage is determined in the agreement by indicating its name, location and a description sufficient to identify this subject. The valuation of the subject of the mortgage is determined in accordance with the legislation of the Russian Federation by agreement between the mortgagor and the mortgagee and is indicated in the mortgage agreement in monetary terms. The obligation secured by a mortgage must be named in the mortgage agreement, indicating its amount, the basis for its occurrence and the deadline for fulfillment. In cases where this obligation is based on any agreement, the parties to this agreement, the date and place of its conclusion must be indicated.
Mortgage is subject to state registration by judicial authorities in the unified state register of rights to real estate and transactions with it. The mortgage agreement is considered concluded and comes into force from the moment of its state registration.
Alienation of mortgaged property. Property pledged under a mortgage agreement may be alienated by the mortgagor to another person by sale, donation, exchange, making it as a contribution to the property of a business partnership or company or a share contribution to the property of a production cooperative or in any other way only with the consent of the mortgagee, unless otherwise provided for in the mortgage agreement. In the case of the issuance of a mortgage, alienation of the pledged property is permitted if the mortgagor’s right to do so is provided for in the mortgage, subject to the conditions established therein.
The mortgagor has the right to bequeath the pledged property. The terms of the mortgage agreement or other agreement limiting this right of the mortgagor are void.
Subsequent mortgage. It is possible to conclude another mortgage obligation (subsequent mortgage) in relation to property already intended under the mortgage agreement to secure a previous obligation (previous mortgage), unless this is prohibited by the previous mortgage. A subsequent mortgage is not allowed if the previous one is certified by a mortgage.Satisfaction of the mortgagee's claims under the prior mortgage has priority over satisfaction of the mortgagee's claims under the subsequent mortgage. The priority of mortgagees is established on the basis of data from the Unified State Register of Rights to Real Estate and transactions with it on the moment the mortgage arose.
Rights under a mortgage agreement , if it is not certified by a mortgage, may be sold by the mortgagee to another person, unless this is prohibited by the agreement. The person to whom the rights under the mortgage agreement are transferred also receives the rights under the main obligation secured by the mortgage.
Mortgage may be transferred to another person with the transfer of rights under the obligation secured by a mortgage, and also pledged to another person in accordance with the obligation under the loan agreement between this person and the mortgagee. When transferring rights to a mortgage, a transaction is made in simple written form. When transferring rights to a mortgage, the person transferring the right makes a note on the mortgage about the new owner, unless otherwise provided by Federal Law. The transfer of rights to a mortgage to another person means the transfer thereby to that person of all the rights certified by it in the aggregate.
Judicial procedure for foreclosure on mortgaged property. Foreclosure on the claims of the mortgagee is applied to the property pledged under the mortgage agreement by a court decision, with the exception of cases where, in accordance with Article 55 of the Federal Law, it is allowed to satisfy such claims without going to court.
The court decision to foreclose on the mortgaged property must indicate the initial sale price of the property for its sale at public auction.
Mortgage of land plots. The subject of collateral under a mortgage agreement may be land plots that are in municipal ownership and land plots for which state ownership is not demarcated, if such land plots are intended for housing construction or for integrated development for the purpose of housing construction and are transferred to secure the repayment of the loan, provided by a credit institution for the development of these land plots through the construction of engineering infrastructure facilities.
Decisions on the mortgage of municipally owned land plots are made by local government bodies. Decisions on the mortgage of land plots, state ownership of which is not delimited and which are specified in paragraph 1 of Art. 130 of the Civil Code of the Russian Federation, are adopted by state authorities of the constituent entities of the Russian Federation or local government bodies vested with the authority to dispose of the specified land plots in accordance with the legislation of the Russian Federation.
Mortgage of individual and multi-apartment residential buildings and apartments is allowed if they are privately owned, and not allowed if these objects are in state or municipal ownership
The variety of forms of relationship between the borrower and the lender leads to the existence of different financing conditions. Financing conditions usually include the method of debt repayment, interest payment, the procedure for changing interest rates, loan terms, and the possibility of including additional clauses in the loan agreement that affect the risk of the parties to the loan agreement.
Special conditions require the inclusion in the loan agreement of clauses relating to the rights of the lender and borrower to early repayment of the loan, the presence of justifying obligations, the possibility of selling the object before the expiration of the loan term, and the definition of the principle of subordination. The presence or absence of these conditions, as well as their specific content, influence the results of assessing the market value of real estate.
1. Justifying circumstance. The presence of this clause in the loan agreement means that if the borrower violates the terms of the loan agreement, the bank can count on repayment of the debt only at the expense of the pledged property. Other property owned by the borrower cannot be used for these purposes. If this clause is missing, the borrower must respond with all property belonging to him.
2. The right to early debt collection. In accordance with this condition, the borrower receives the right to repay the debt before the loan expires. The presence of such a right is important if the investor does not exclude the possibility of resale of the property before the debt is repaid. Western practice provides for the borrower to pay fines to the bank in such cases. The penalty level decreases as the debt's final repayment date approaches. In some cases, loans are “locked” for a certain period of time, prohibiting early repayment.
3. The creditor’s right to early repayment of the debt. The presence of such a right provides for early repayment of the balance of the debt (“balloon” payment) regardless of whether the borrower violated the terms of the loan agreement. The possible date of early repayment is set at the time of concluding the loan agreement. When it occurs, the creditor can expect to receive the balance of the debt or to review such positions as the interest rate and the remaining maturity of the debt. Having such a right is beneficial to the bank.
4. The right to sell real estate along with debt. This right allows the borrower to sell the property before repaying the loan, and the balance of the debt will be repaid by the new owner, the lender remains the same. The presence of such a right increases the risk of the lender, so the bank reserves the right to give permission to sell real estate to a specific buyer or the right to increase the interest rate. It should be noted that in this case the seller is solely responsible if the new owner receives an exculpatory circumstance.
5. The principle of subordination. This clause suggests the possibility of changing the priority of a mortgage loan. If an investor purchases real estate with a mortgage loan and intends to subsequently use it as part of an investment project that will be financed with borrowed funds, then he must negotiate in advance the possibility of reducing the priority of the first loan. The absence of this clause will complicate obtaining a new loan secured by the same property.
The specific terms of the financing must be taken into account by the appraiser, who compares them with the so-called typical financing. Typical financing refers to the amount of credit that can be extended to an investor and the interest rate that is set.
The classical theory of valuation distinguishes between the concepts of “price” and “cost” of a real estate property. Value reflects the hypothetical amount of money for which the valued object can be exchanged, taking into account specific conditions. The value is determined by the potential profitability of the property. The cost depends on the amount of income generated by the property, as well as on possible changes in its value during the period of ownership. Net operating income depends on:
physical parameters of the object;
market rent rates;
demand for this property;
management quality;
operating costs.
All of these factors relate to the scope of use of the object being assessed. Since debt service costs are classified as financing costs, their size, presence or absence does not affect the amount of net operating income.
Price is the amount of money that will be paid for the property during the actual transaction. The price is often determined as a result of negotiations between the seller and the buyer.
An investor will be willing to pay a higher price for the property being purchased if he obtains a loan at a rate below market, or has positive financial leverage due to an increase in the loan term, or the seller pays discount points on the mortgage loan obtained by the buyer. The appraiser, by comparing specific financing terms with typical financing, especially if the loan is not provided by a third party but directly by the seller, may evaluate them as favorable. This factor can be taken into account in the price as a corresponding premium to the cost.
Thus, financing conditions do not change the value of the property, but do influence its price. Mortgage investment analysis represents a set of calculations and analytical activities that allow for the assessment of real estate taking into account specific financing conditions.
Mortgage investment analysis consists of determining the value of property as the sum of the costs of equity and borrowed capital. In this case, the investor’s opinion is taken into account that he is not paying for the cost of real estate, but for the cost of capital. A loan is seen as a means of increasing the invested funds necessary to complete the transaction. The cost of equity capital is calculated by discounting the cash flows coming to the investor's equity capital from regular income and from reversion, the cost of borrowed capital is calculated by discounting debt service payments.
The current value of the property is determined depending on discount rates and cash flow characteristics. That is, the current value depends on the duration of the project, the ratio of equity and debt capital, the economic characteristics of the property and the corresponding discount rates.
Methods of mortgage investment analysis
The analysis uses two methods (two techniques): the traditional method and the Ellwood technique. The traditional method explicitly reflects the logic of investment and mortgage analysis. Ellwood's method, reflecting the same logic, uses ratios of profitability ratios and proportional ratios of investment components.
Traditional method. This method takes into account that the investor and lender expect to receive a return on their investment and return it. These interests must be ensured by the total income for the entire amount of investment and the sale of assets at the end of the investment project. The amount of investment required is determined as the sum of the present value of the cash flow consisting of the investor's equity and the current debt balance.
The present value of an investor's cash flow consists of the present value of periodic cash receipts, the increase in the value of equity assets resulting from loan amortization. The value of the current debt balance is equal to the present value of loan service payments for the remaining term, discounted at the interest rate.
Cost calculation in traditional technology is carried out in three stages.
Stage 1. Determining the present value of regular income streams:
– a report on income and expenses is compiled for the forecast period, while the amounts for debt servicing are calculated based on the characteristics of the loan - the interest rate, the full amortization period and repayment terms, the size of the loan and the frequency of payments to repay the loan;
– cash flows of own funds are determined;
– the rate of return on invested capital is calculated;
– based on the calculated rate of return on equity, the current value of regular cash flows before tax is determined.
Stage 2. Determining the present value of the reversion proceeds minus the outstanding loan balance:
– income from reversion is determined;
– the remaining debt at the end of the period of ownership of the object is deducted from the income from reversion;
– based on the rate of return on equity capital calculated at stage 1, the current value of this cash flow is determined.
Stage 3. Determining the value of property by summing up the current values of the analyzed cash flows.
Mathematically, determining the value of an asset can be represented as a formula
where NOI is the net operating income of the nth year of the project;
DS is the amount of debt service in the nth year of the project;
TG – reversion amount excluding sales costs;
UM – unpaid loan balance at the end of the project termP;
i – return on equity;
M – The original loan amount or the current principal balance.
This formula can be used as an equation in the following cases:
– if the amount of reversion of property is difficult to predict, but it is possible to determine trends in its change in relation to the initial value, then in calculations you can use the amount of reversion expressed as a fraction of the initial value;
– if the problem statement does not define the amount of the loan, but only the share of the loan.
Let's consider the main criteria for the effectiveness of investment projects.
Net present value – a criterion that measures the excess of benefits from a project over costs, taking into account the current value of money
,
where NPV is the net present value of the investment project; Co – initial investment; WITH i – cash flow of period t; i, – discount rate for period t.
A positive NPV value means that the cash flows from the project exceed the costs of its implementation.
Steps to apply the net present value rule:
– forecasting cash flows from the project over the entire expected tenure, including income from resale at the end of this period;
– determining the opportunity cost of capital in the financial market;
– determining the present value of the cash flows from the project by discounting at a rate corresponding to the opportunity cost of capital and subtracting the amount of the initial investment;
– selecting a project with the maximum NPV value from several options.
The higher the NPV, the more income the investor receives from investing capital.
Let's consider the basic rules for making investment decisions.
1) The project should be invested if the NPV value is positive. The considered efficiency criterion (NPV) allows us to take into account changes in the value of money over time, depending only on the projected cash flow and the opportunity cost of capital. The net present values of several investment projects are expressed in today's money, which allows them to be correctly compared and added up.
2) The discount rate used in calculating NPV is determined by the opportunity cost of capital, i.e. the profitability of the project is taken into account when investing money with equal risk. In practice, the profitability of a project may be higher than that of a project with alternative risk. Therefore, a project should be invested if the rate of return is higher than the opportunity cost of capital.
The considered rules for making investment decisions may conflict if there are cash flows in more than two periods.
Payback period – the time required for the total cash flows from a project to equal the amount of the initial investment. This investment performance meter is used by investors who want to know when a full return on their invested capital will occur.
Disadvantage: payments following the payback period are not taken into account.
Ellwood technique . It is used in investment and mortgage analysis and gives the same results as the traditional technique, since it is based on the same set of initial data and ideas about the relationship between the interests of equity and borrowed capital during the development period of the investment project. The great thing about Ellwood’s technique is that it allows you to analyze property relative to its price based on the return ratios of equity indicators in the investment structure, changes in the value of total capital, and quite clearly shows the mechanism of changes in equity capital over the investment period.
General view of the formula Ellwood:
R o =/(l + Δ n a),
where R 0 - general capitalization ratio;
C - Ellwood mortgage ratio;
Δ - fractional change in property value;
(sff,Y e) - compensation fund factor at the rate of return on equity capital;
Δn - share change in income for the forecast period;
A - stabilization coefficient.
Ellwood Mortgage Ratio:
С = Y e + p(sff, Y e ) -R m,
where p - share of the current loan balance amortized over the forecast period,
Expression 1/(1 + Δ n A ) in the equation is a stabilizing factor and is used when income is not constant, but changes regularly. Usually the law of income change is specified (for example, linear, exponential, according to the accumulation fund factor), in accordance with which the stabilization coefficient is determined A according to pre-calculated tables. The value is determined by dividing the income for the year preceding the valuation date by the capitalization rate, taking into account the stabilization of income. In the future, we will consider Ellwood’s technique only for permanent income.
Let's write Ellwood's expression without taking into account changes in the value of real estate and with constant income:
R = Y e - t.
This expression is called the basic capitalization ratio, which is equal to the rate of final return on equity capital adjusted for financing conditions and depreciation.
Let's consider the structure of the overall capitalization ratio in the Ellwood formula without taking into account changes in property values, for which we use the investment group technique for return rates. This technique weighs the rates of return on equity and debt in their respective shares of total invested capital:
Y 0 =mY m +(1-m)Y e .
In order for this expression to become equivalent to the base coefficient r, Two more factors need to be taken into account. The first is that the investor must periodically deduct from his income to amortize the loan, reducing his equity. Therefore, it is necessary to adjust the Y value 0 in the previous expression by adding the periodic payment shares of the entire capital at an interest equal to the interest rate on the loan. The expression for this adjustment is the gearing ratioT, multiplied by the compensation fund factor at the interest rate (sff,Y m). Quantity (sff,)Y m ) is equal to the difference between the mortgage constant and the interest rate, i.e. R m -Y m . Thus, taking into account this amendment:
Y 0 = mY m + (1 -m)Y e + m(R m -Y m ).
The second adjustment term must take into account the fact that the investor's equity as a result of reversion will increase by the amount of the portion of the loan amortized over the holding period. To determine this adjustment, you need to multiply the depreciated amount as a share of the total original capital by the replacement fund factor at the rate of final return on equity (realization into equity occurs at the end of the holding period). Therefore, the second correction term has the form: mp(sff,Y m), and with a minus sign, since this amendment increases the cost.
Thus:
Y 0 = mY m +(1-m)Y e +m(R m -Y m )-mp(sff,Y e ),
and after combining similar terms and replacing Y 0 to r (we do not take into account changes in property value):
r = Y 0 -m.
Thus, we obtain the basic capitalization ratio of the Ellwood expression. Progressing from the investment group technique through the necessary adjustments to Ellwood's expression shows that this expression indeed reflects all the elements of the transformation of equity and borrowed funds combined in the invested capital, in particular financial leverage, amortization of the mortgage loan and the increase in equity as a result of amortization of the loan.
A.V. Tatarova. Real estate valuation and property management Training manual. Taganrog: TRTU Publishing House, 2003
S.V. Grinenko Economics of real estate.Lecture notes. Taganrog: Publishing house TRTU, 2004.
A.V. Ponukalin MORTGAGE AND INVESTMENT ANALYSIS. Methodological instructions for performing practical exercises. Publishing house of Penza State University PENZA 2004
FEDERAL LAW ON MORTGAGE (REAL ESTATE PLEDGE)(as amended by Federal Laws dated November 9, 2001 No. 143-FZ, dated February 11, 2002 No. 18-FZ, dated December 24, 2002 No. 179-FZ, dated February 5, 2004 No. 1-FZ, dated June 29, 2004 No. 58-FZ, dated 02.11.2004 No. 127-FZ, dated 30.12.2004 No. 214-FZ, dated 30.12.2004 No. 216-FZ, dated 04.12.2006 No. 201-FZ, dated 18.12.2006 No. 232-FZ, dated 26.06.2007 No. 118-FZ, dated 04.12.2007 No. 324-FZ, dated 13.05.2008 No. 66-FZ, dated 22.12.2008 No. 264-FZ, dated 30.12.2008 No. 306-FZ).
MINISTRY OF EDUCATION AND SCIENCE OF THE RF
INTERNATIONAL ACADEMY OF EVALUATION AND CONSULTING
Course work
Discipline: “Real Estate Valuation”
Mortgage investment analysis and types of loans
Moscow 2008
Introduction
Chapter 1. The concept of mortgage investment analysis. Approaches to its implementation
1.1. Traditional approach
1.2. Mortgage investment analysis based on income capitalization
Chapter 2. Methods for determining the overall capitalization ratio within the framework of mortgage investment analysis
2.1. Ellwood Mortgage and Investment Technique
2.2 Investment group method
2.3. Direct capitalization method
Chapter 3. An example of the use of mortgage investment analysis in real estate valuation. Credit and its types
3.1. Credit and its types
3.2. An example of the use of mortgage investment analysis in real estate valuation
Conclusion
Literature
Introduction
The word “real estate” was formed in Russian from three words: “immovable”, “property” (“estate”), “property”. Thus, the Russian word “real estate” contains the following features: immobility, belonging to someone, belonging by right of ownership. The concept of “real estate” is inseparable from another concept – “property”.
Property – a set of property, i.e. subject to monetary valuation, legal relations in which this person (individual or legal) is located.
Property owned by any individual or legal entity is divided by content into:
· asset: a set of things owned by a person by right of ownership or by virtue of another property right; a set of rights to the actions of others (for example, debt property);
· passive: a set of things that belong to other persons, but are temporarily in the possession of a given person; the totality of obligations incumbent on a given person.
Historically, since the times of Roman law, property has been divided into movable and immovable.
According to Art. 130 of the Civil Code of the Russian Federation, “immovable things (real estate, real estate) include land plots, subsoil plots, isolated water bodies and everything that is firmly connected to the land, that is, objects whose movement without disproportionate damage to their purpose is impossible, including forests, perennial plantings, buildings, structures.
Immovable property also includes aircraft and sea vessels, inland navigation vessels, and space objects subject to state registration. The law may classify other property as immovable property.”
According to the Town Planning Code of the Russian Federation, real estate objects are objects in respect of which town planning activities are carried out. Urban planning activities are activities for the development of territories, including cities and other settlements, carried out in the form of territorial planning, urban zoning, territory planning, architectural and construction design, construction, major repairs, reconstruction of capital construction projects.
In addition, the enterprise as a whole is recognized as real estate as a property complex used to carry out business activities.
In foreign literature, there is a division between the concepts of “real estate” and “real property”. Moreover, the first constitutes the material, physically tangible essence of the concept of real estate, and the second denotes the legal essence of this concept as a set (package) of property rights of all entities related to this thing.
Improvements are things that are made by human hands and require the investment of labor and the expenditure of resources. At the same time, it is accepted that the improvement itself cannot be considered as a real estate object separately from the land plot, since it remains immovable and fulfills its purpose only if and while it is firmly attached to the land.
The legal essence consists of: the right of ownership, the right of economic management, the right of operational management, the right of lifelong inheritable possession, the right of permanent use, mortgage, easements, as well as other rights in cases provided for by the Civil Code of the Russian Federation and other laws.
Encumbrances (restrictions) - the presence of conditions, prohibitions established by law or by authorized bodies in the manner prescribed by law that constrain the right holder in the exercise of ownership or other real rights to a specific real estate object (easement, mortgage, trust management, lease, seizure of property and others).
The structure of the concept of “real estate”
· direct, strong connection of the property with the land; the property cannot be moved away from the land plot without significant damage to its purpose;
· real estate belongs to the category of financial assets;
· real estate transactions are carried out on the real estate market - a specific segment (sector) of the financial market;
· real estate market - the sphere of capital investment (investment sphere), as well as the system of economic relationships between participants in the financial market regarding real estate transactions;
· purchase and sale of real estate is associated with the movement of capital or value that generates income;
· purchasing a property means investing capital in this property, which brings income to its owner during its operation or rental, as well as after its resale at a higher price (unfortunately, in an unstable economy, speculative real estate transactions have the greatest share, bringing income to the owner precisely on the difference in the price of acquisition and sale of the asset);
· due to the specificity of real estate as a financial category and its high cost, the state places high demands on compliance with the legality of real estate transactions, therefore almost all transactions in the real estate market must undergo state registration;
· demand for real estate is not interchangeable, therefore, even when supply exceeds demand, it (demand) often remains unsatisfied;
· the amount of demand for real estate is determined by geographical and historical factors, as well as the state of infrastructure in the area where the property is located.
It should be noted that the main element or attribute of real estate is land. Due to the high dynamics of prices for all objects of the financial, as well as all other markets, as well as the lack of a more or less efficient information base on real estate objects, the real real estate market cannot exist without an assessment of its objects.
Under real estate valuation refers, first of all, to the assessment of property rights to real estate and the real estate itself. Here it is necessary to separate two concepts - price and value of the property
1. The market price of a real estate object is the contract price, the price of a specific purchase and sale transaction of a real estate object. The price of a property reflects an already accomplished fact, a transaction.
2. The value of a property has different forms or manifestations. Let's focus on the most relevant - the market value of the property.
The market value of a property is the most likely price that can be obtained from the sale of property on the market at the moment.
The market value of a property may be greater than, less than, or equal to its market price. In addition, a distinction is made between the cost of replacing a property, the cost of reproducing a property, the investment value or investment potential of the property, etc.
Almost all real estate purchase transactions are made using mortgage loans, or loans secured by real estate. In such conditions, the value of real estate is determined as the sum of the mortgage loan, the present value of income from the use of real estate and proceeds from the resale of real estate.
In general, the assessment of the value of real estate encumbered or acquired with a mortgage loan is carried out using mortgage investment analysis.
The mortgage investment analysis technique is a technique for estimating the value of income-generating property (real estate), based on adding the principal amount of the mortgage debt with the discounted present value of future cash receipts and proceeds from the resale of the asset.
Chapter 1. The concept of mortgage investment analysis. Approaches to its implementation
1.1 Traditional approach
Mortgage-equity models determine the true value of property based on the ratio of equity and debt capital. Mortgage-equity analysis, or capital structure analysis, is an analytical tool that can in many cases facilitate the valuation process. It has been theoretically proven that debt capital plays a major role in determining the value of real estate.
Almost all real estate investment transactions are made using mortgage loans. By using mortgage lending, investors gain financial leverage, which allows them to increase current returns, benefit more from property appreciation, provide greater asset diversification, and increase deductions for interest and depreciation for tax purposes. Mortgage lenders receive a reasonably guaranteed amount of income securing the loan. They have the right of first claim to the borrower's operating income and its assets in the event of a breach of debt obligations. Mortgage investment analysis is a residual technique. Equity investors pay the balance of the initial costs.
They receive the remainder of the net operating income and resale price after all payments to creditors have been made, both during the current use and after the property is resold.
The period of realization of ownership of real estate can be divided into three stages, at each of which capital investors receive residual income:
1. acquisition of an asset - the investor makes a mandatory cash payment, the amount of which is equal to the remaining price after subtracting from it the mortgage loan, which turns into debt;
2. use of property - investors receive residual net income from the use of property after deducting mandatory debt service payments;
3. liquidation - when the property is resold, the owner of the capital receives money from the sale price after repaying the balance of the mortgage loan.
There are two approaches to conducting mortgage investment analysis:
1. Traditional - the premise of the traditional model of mortgage investment analysis is that the total value of the property is equal to the sum of the present value of the equity interest and the present value of the debt capital interest. The value of equity interest is determined by discounting the cash flow before taxes, while the rate of return on equity capital, defined as the market average, is used as the discount rate.
2. Mortgage investment analysis models based on capitalization of income from the use of property. The most common approach to mortgage investment analysis of this group is to determine the overall capitalization ratio using the Ellwood formula. In addition, the investment group method and the direct capitalization method are used.
Traditional mortgage investment analysis technique is a method of estimating the value of property that is based on the determination of the total amount of the repurchase capital, including mortgage loans and equity investments. Under this technique, the value of a property is calculated by adding the present value of cash receipts and resale proceeds expected by the investor to the principal amount of the mortgage. Thus, both the entire projected net operating income and the amount of proceeds from the resale of the property are estimated.
The traditional technique requires estimates of the projected cash flows to be received by the investor, as well as the proceeds from resale. These two elements give the estimated current value of equity. The original loan balance (whether it is a new loan or a vested debt) is then added to the equity value to determine the market appraised value. If the new loan is provided on current market conditions and the final return on equity meets current market requirements, the result will be the estimated market value of the property. This technique does not take into account tax implications.
The principle underlying the traditional technique is that the assessed returns accrue to both investors and creditors.
The combined present value of the income of creditors and investors constitutes the maximum amount of redemption capital; accordingly it is the price that must be paid for the property. This technique improves on the equity cash flow valuation method because it takes into account resale proceeds. The latter includes the amount of increase (or decrease) in the value of the property and the depreciation of the mortgage received by the investor upon resale.
The returns received by both mortgage lenders and investors should include both return on investment and return on investment.
As for a mortgage, the current income on it represents debt service. Self-amortizing mortgages provide for the simultaneous payment of interest (income on the principal amount of the loan) and amortization (repayment of the principal amount of the mortgage) over a specified period. The principal balance at any point in time is equal to the present value of all payments remaining before the loan is fully amortized, discounted at the nominal interest rate of the mortgage. Mortgages are often paid off before the full amortization period has expired. In this case, the balance of the mortgage is paid in a one-time cash payment, thereby eliminating the debt. The par value of a debt obligation is equal to the sum of the present value of periodic cash payments and the present value of a lump sum cash payment when repaying the loan, discounted at the nominal interest rate of the mortgage.
The present value of an equity investment is equal to the sum of the income stream and the proceeds from liquidation (resale), discounted at the rate of return on equity. Under certain mortgage terms, the equity price is justified by the cash flows as well as the resale proceeds that investors expect to receive. Therefore, the current value of equity is equal to the sum of the present value of cash receipts and the present value of proceeds from resale, discounted at the rate of final return on equity, taking into account the associated risks. Thus, the amount and timing of benefits received by investors are taken into account.
The value of property or its price is calculated using formula (1):
Price = Cost of Equity + Mortgage Loan , (1)
The cost of equity is defined as the sum of two elements: cash receipts and resale proceeds. Both elements are discounted at the appropriate rate of return and their present values are calculated using present value factors.
If projected cash receipts are expected to be uniform, then their annual amount is multiplied by the annuity factor. Reversion or resale proceeds are valued using the current unit value factor since the proceeds are received as a lump sum.
The formula for calculating the cost of equity capital (investment in equity capital), taking into account the above - formula (2) - has the following form:
Cost of equity = PWAF * (CF) + PWF * (PS) , (2)
where PWAF is the factor of the current value of the annuity at the rate of return on equity,
CF - cash receipts,
PS - proceeds from resale.
To estimate the value of the property, the current mortgage balance must be added to the equity value. All income is assessed in this way. The remaining balance on the mortgage is equal to the present value of the required debt service payments, discounted at the nominal interest rate of the mortgage. Thus, the general formula for estimating property value (3) is as follows:
V = PWAF * (CF) + PWF * (PS) + MP , (3)
where V is the value of the property (initial),
PWAF - factor of the current value of the annuity at the rate of return on equity capital,
CF - cash receipts,
PWF is the factor of the current value of reversion at the rate of return on equity capital,
PS - proceeds from resale,
MP is the current principal balance of the mortgage.
If we accept that
CF = NOI - DS , (4)
where NOI is net current operating income,
DS - debt service (annual), and
PS = RP - OS , (5)
where RP is the resale price of the property,
OS - the balance of the mortgage debt upon resale;
then formula 3 will take the form:
V = PWAF * ( NOI - D.S. ) + PWF * ( R.P. - OS ) + MP , (3*)
The use of traditional technology involves a three-stage calculation for a certain forecast period. The forecast period is the period during which the owner expects to hold the property being valued.
Table 1. Stages of traditional mortgage investment analysis techniques
The monthly mortgage repayment payment is calculated based on formula (6) for calculating the unit depreciation contribution (self-amortizing mortgage):
where DSm is monthly debt service,
I - initial mortgage loan amount,
i is the annual interest rate on the loan,
t is the term (years) for which the mortgage loan was granted.
The annuity factor (formula 7) reflects the current value of a unit annuity at a given discount rate:
where Y is the rate of return on equity capital,
The current value factor of reversion (Formula 8) reflects the current cost of a unit for a period at a given discount rate:
The balance of the mortgage debt with equal payments is determined as the present cost of debt service payments over the remaining amortization period (formula 9):
The resale price of a property is calculated taking into account the increase or decrease in the value of the property per year (d):
RP = P * (1 + d) T , (10)
where RP is the resale price of the property;
P is the initial cost of the property;
d - increase (decrease) in property value over the year;
T is the period of ownership of the property.
So, the traditional technique of mortgage investment analysis is an assessment method within the framework of the income approach. When conducting a mortgage investment analysis, either the principal amount of the mortgage loan or the mortgage debt ratio must be known. The analysis should include an estimated resale price or percentage change in value over the forecast period.
This technique can be used if the investor assumes an existing debt or if a new loan is attracted. It can be modified to take into account more than one mortgage and changes in cash flow. If the price is known, the technique can be used to estimate the rate of return on equity.
The traditional technique of mortgage investment analysis is a flexible method that can take into account any situation. However, due to the assumptions made, objectively obtained estimates are approximate.
1.2 Mortgage investment analysis based on income capitalization
The capitalization method converts annual income into property value by dividing the annual income by the appropriate rate of return or multiplying it by the appropriate income ratio.
Determination of property value based on the general capitalization ratio is carried out according to formula (11):
Where V- property value;
NOI- net operating income;
k- general capitalization ratio.
To determine the overall capitalization ratio within the framework of mortgage investment analysis, the following is used:
· Ellwood Mortgage and Investment Technology;
· Investment group method;
· Direct capitalization method.
Chapter 2. Methods for determining the overall capitalization ratio within the framework of mortgage investment analysis
2.1 Ellwood's mortgage and investment technique
The main appeal of the Ellwood technique is that it offers a concise mortgage-investment formula given a known mortgage debt ratio and an estimated percentage change in property value over the forecast period. The traditional technique is more applicable when the dollar amount of the loan and the resale price are given. The Ellwood technique is easier to use when the coefficients are known.
Ellwood's formula (12) for determining the capitalization ratio is as follows:
Where k- the general rate of return for capitalizing net operating income into value for a given expected change in value over the forecast period;
m is the mortgage debt ratio (the share of the loan in the total value of the property);
C - Ellwood mortgage ratio;
d - change in property value over the forecast period:
Dep - reduction in cost, increases the capitalization ratio;
App - increase in value, reduces capitalization ratio;
(SFF;Y) - compensation fund factor at the rate of return on equity capital for the forecast period;
Δ - change in income;
J - income stabilization coefficient. The J-ratio is always positive, so if there is a positive change in income, the overall capitalization ratio will be adjusted downward. With constant income, the denominator of the general formula will be equal to 1, then the overall capitalization ratio will be equal to: R = Y - m * C - d * (SFF;Y).
The Ellwood Mortgage Ratio is calculated using the formula:
C = Y + P * (SFF;Y) - f , (13)
where C is the Ellwood mortgage ratio;
Y - rate of return on equity capital;
P - part of the current loan balance that will be paid during the forecast period;
(SFF;Y) - compensation fund factor at the rate of return on equity for the forecast period;
f is the annual mortgage constant, calculated based on annual payments and the current (not original) debt balance.
The part of the current loan balance that will be paid for the forecast period - the loan repayment percentage is defined as the ratio of the compensation fund coefficient for the entire loan term to the compensation fund coefficient for the calculation period (14):
where P is the loan repayment percentage;
i - interest rate on the loan;
t is the full amortization period of the loan;
T is the period of ownership of the property.
The compensation fund factor is calculated using formula (15):
where Y is the rate of return on equity;
T is the period of ownership of the property.
The annual mortgage constant can be calculated as an annuity
on a basis, as a contribution to the depreciation of the unit (16):
where f is the annual mortgage constant;
i is the interest rate on the loan per year;
t is the full amortization period of the loan.
The Ellwood technique can be used both when new financing is being obtained and when the buyer is taking on existing debt.
The Ellwood technique requires the same assumptions as the traditional mortgage investment technique and is defined in the same way by those assumptions. The latter include certain financing terms, resale price or estimated change in value, and a forecast period.
In the Ellwood technique, the most important is the C-factor. It is the result of a synthesis of other variables. Users of this method of mortgage investment analysis must pay great attention to the choice of assumptions, since the estimate of value is entirely determined by the latter.
2.2 Investment group method
The overall capitalization ratio can be calculated using the investment group method. In general terms, the investment group method takes into account how much of the buyout capital comes from the mortgage loan and how much from home equity. It weights the shares in the buyout capital by the interest rate and the required rate of final return on equity, respectively.
In the total capitalization ratio obtained by the investment group method, it is necessary to enter two amendments so that it becomes equivalent to the overall Ellwood capitalization ratio (before appreciation or depreciation in property values). Both adjustments relate to loan amortization.
Amendment 1 is to recognize that mortgage amortization payments must be made from net annual operating income. This adjustment reduces the current income attributable to the equity investor, so it is added to the rate obtained by the net investment group method. Payments for amortization of the principal amount of the loan are equal to the excess of the mortgage constant over the interest rate. The exact amount is calculated by multiplying the excess (mortgage constant minus the mortgage interest rate) by the mortgage debt ratio.
Amendment 2 necessary to account for the future date when the equity investor will benefit from the amortization of the mortgage debt. When a property is flipped, equity investors receive the resale price minus transaction costs and the outstanding debt balance. Thus, the reduction in mortgage debt is realized upon resale as a gain in equity. Since this benefit will be received by the investor at a later date, its effective annual rate should be calculated using the recovery fund factor, then this rate is subtracted from the factor obtained by the net investment group method. The effective benefit to home equity investors depends on the mortgage debt ratio and the amount of mortgage payable over the forecast period. The calculation of the effective annual rate of return on equity is carried out using the replacement fund factor at the rate of return on equity.
Property value assessment using the investment group method is carried out according to the following scheme:
Table 2. Investment group technique
2.3 Direct capitalization method
This method was developed and used by specialists of the Russian Society of Appraisers (ROO).
To describe the method, we will use the arguments used by ROO evaluators:
X - property value;
q - net operating income;
p t- payment for t th year to repay a single loan;
k - capitalization rate;
Y - discount rate;
i - annual interest rate on the loan;
d is the annual increase in property value;
n is the expected period of ownership of the property;
m - mortgage debt ratio
Then the property value (X)(17):
Capitalization coefficient (rate) ( k) is calculated using formula (18):
To simplify calculations for finding, we will use the Inwood coefficient or annuity coefficient. p t- payment for t th year to repay a single loan, and represents an annuity - a stream of equal payments over n periods. Then p t there is a mortgage constant (20).
where f is the mortgage constant [formula (16)].
Chapter 3. An example of the use of mortgage investment analysis in real estate valuation. Credit and its types
3.1 Credit and its types
Credit is a category of exchange. When selling their product, when purchasing raw materials, equipment, real estate, and other goods necessary to continue their activities, commodity producers experience a significant need for additional means of payment. As an important payment instrument, credit is used to meet the diverse needs of the borrower. These needs arise not only in exchange, where the gap in payment turnover is most pronounced, but also in other stages of reproduction. Economic organizations producing a product spend the loans received to purchase means of production and meet the needs for payroll settlements with employees and with budgetary organizations.
The population receives credit to meet their consumer needs. Acting as a category of exchange, credit is used to meet the needs of production, distribution and consumption of the gross product. Loans are divided into types and depending on their industry focus. When a loan serves the needs of industrial enterprises, it is an industrial loan. There is also agricultural and trade credit.
The sectoral focus of credit is often embodied in government statistics of a number of countries (loans to industry, trade, agriculture, etc. are separately highlighted). Loans and individual commercial banks are divided by industry. The classification of loans is also determined by the objects of lending. The object expresses what is opposed to credit. Most often, credit is used to purchase various goods (in industry - raw materials, basic and auxiliary materials, fuel, packaging, etc., in trade - goods of a varied assortment, among the population - durable goods) and here the credit is opposed by various inventory items values. In some cases, a loan is issued to cover various production costs.
For example, in agriculture, credit is mostly directed towards costs of crop and livestock production, in industry - towards seasonal costs (repairs, preparation for the new season of production of agricultural products, etc.).
The loan object may or may not have a tangible form. The borrower does not necessarily take out a loan to accumulate the inventory he needs. Credit will therefore not necessarily be resisted by specific types of materials. A loan is quite often taken out due to a gap in the payment turnover, when an enterprise temporarily lacks available funds, but has obligations for various types of current payments.
These may be needs related to the need to pay wages to the personnel of the enterprise, various taxes to the federal or local budgets, property insurance premiums, etc. In this case, the loan covers the lack of funds or the gap in payment turnover.
The type of loan is a more detailed description of it based on organizational and economic characteristics, used to classify loans. There are no uniform world standards for their classification. Each country has its own characteristics.
In Russia, loans are classified depending on:
· stages of reproduction serviced by credit;
· industry focus;
· lending objects;
· its security;
· urgency of lending;
· fees, etc.
The classification of a loan by type also depends on its security. Typically, security is distinguished by nature, degree (completeness) and forms.
Based on the nature of the collateral, loans are divided into those that have direct and indirect collateral. Direct collateral contains, for example, loans issued for a specific material object, for the purchase of specific types of inventory items. Indirect collateral may include, for example, loans issued to cover a gap in the payment turnover. Although the loan is issued to cover the borrower’s payment obligations, there may be no direct payment for inventory items that would directly oppose the loan, but indirect material support appears in the form of inventory items created from one’s own monetary sources.
According to the degree of security, loans can be distinguished with full (sufficient), incomplete (insufficient) security and without security. Full collateral is available if the amount of collateral is equal to or greater than the amount of the loan provided. Incomplete collateral occurs when its value is less than the loan amount. The loan may not have collateral. This type of loan is called a blank loan. Most often, it is provided if the bank has sufficient confidence in the borrower and the bank is confident in the return of funds provided to the borrower for temporary use.
Securing a loan can be considered not only from the standpoint of opposing it to a certain mass of values, liquid inventories, but also certain external guarantees. In addition to the usual pledge of inventory items and property owned by the borrower, the group of loan repayment security includes various types of guarantees, sureties of third parties, insurance, etc.
When classifying a loan, depending on the urgency of lending, short-term, medium-term and long-term loans are distinguished.
Short-term loans serve the current needs of the borrower related to the movement of working capital. Short-term loans are those loans whose repayment period, according to international standards, does not exceed one year. However, in practice their duration may not be the same. This is determined by economic conditions and the degree of inflation. So, in Russia in the 90s. Due to significant inflationary processes, short-term loans often included loans with a term of up to three to six months.
Medium-term and long-term loans serve long-term needs caused by the need to modernize production and make capital expenditures to expand production.
There is no established standard term as a criterion for classifying a loan as a medium-term or long-term loan. In the USA, for example, medium-term loans are those loans whose repayment period does not extend beyond eight years, in Germany - up to six years. There is also no uniformity in the length of the term for long-term loans.
In Russia, medium-term loans included loans with a repayment period of six to twelve months, and long-term loans included loans whose payment period extended beyond a year. Dividing loans according to their duration of operation in the borrower's household was justified, because in conditions of money depreciation, even their short-term stay in the borrower's household could lead to loss of capital safety. Strong inflation transformed the idea of lending terms and changed the criteria for the urgency of lending to borrowers.
Credit can be classified by type and depending on the fee for its use. There are paid and free, expensive and cheap loans. This division is based on the interest rate established for using the loan.
In a modern economy, credit functions as capital. This means that the lender transfers the loaned value not as a sum of money, but as a self-increasing value, which is returned to him incrementally in the form of loan interest. The borrower must use the funds received in such a way that with their help it is possible not only to ensure continuity of production, but also to create new value sufficient to pay off the creditor - to return to him the originally advanced amount and pay the loan interest. That is why credit as a cost category is of a paid nature.
However, in both ancient and modern history, free credit exists in very limited amounts. Most often in modern economics it is used when lending to insiders (bank employees), with personal (friendly) forms of credit, etc.
With a trade loan (in the form of bills), the deferment of payment is also not accompanied by the collection of interest. At the same time, although the loan fee does not manifest itself directly here, the interest is indirectly included in the price of the product for which payment was deferred.
Within the framework of payment for a loan, the concept of an expensive, cheap loan is used.
The concept of an expensive loan is associated with the collection of an interest rate that is higher than its market level. As a rule, this rate is set for loans that have an increased risk of non-repayment of the loan (due to the low credit rating of the borrower, questionable collateral, etc.). Other loans (with a higher interest rate) are also used as a kind of sanction for late repayment of the loan, as well as violations that contradict the loan agreement with the client.
Most often, the lender differentiates the amount of payment depending on the term of the loan, the quality of the collateral, and the solvency of the borrower. Payments vary according to the economic cycle - boom, depression or economic crisis.
Expensive and cheap loans are relative concepts. For example, for Western practice, interest rates of Russian banks in the conditions of the economic crisis and inflation of mid-1990 may seem astronomical in terms of their size. However, taking into account the monthly and annual inflation rates, they will no longer be the same, since the depreciation of money in 1996 - 1997. reached from 1 to 2% monthly.
In global banking practice, other criteria for classifying loans are used. In particular, loans can be divided into loans issued in national and foreign currency to legal entities and individuals, etc.
3.2 An example of the use of mortgage investment analysis in real estate valuation
Initial data:
− Potential gross income - CU 100,000
− Losses during collection of payments - 20%
− Other income - CU 0
− Operating expenses - 15%
− The initial principal amount of the mortgage is CU400,000.
− Full depreciation period - 25 years
− Interest rate - 12%
− Discount rate - 15%
− Estimated year of sale of the property - 20
− Annual increase in value - 0%
− The initial cost of the property is CU500,000.
Amendment 1
Amendment 2
Based on the calculation results, it is necessary to analyze the results obtained and draw conclusions.
Conclusion
Mortgage and investment analysis in valuation is a set of methods and methods for assessing the value of real estate purchased with the help of a loan secured by this real estate (mortgage). In countries with developed market economies, over 90% of investment real estate transactions are carried out using mortgage loans. Investors who use loans have the opportunity to increase the return on their own funds by attracting borrowed funds. In addition, the effect from the increase in property value increases, greater diversification of assets and additional tax savings are ensured. Lenders receive a reasonably guaranteed amount of income as well as strong collateral for their loan.
They have the first priority right to the borrower’s income and assets in the event of non-payment of debt.
Mortgage investment analysis assumes that investors:
· firstly, they pay the initial costs on a residual basis;
· secondly, income is also received on a residual basis after all payments to creditors have already been made, both in the course of current activities and after the sale of the property.
In this case, the period of realization of ownership of real estate can be divided into three stages:
· acquisition
· usage
· liquidation.
At each stage, capital owners receive residual income.
At the 1st stage, they make a mandatory cash payment, the amount of which is equal to the remaining price (the difference between the price and the amount of the mortgage loan transferred to them as a debt);
On the 2nd - they receive residual income from the use of property, after deducting mandatory debt service payments from it;
On the 3rd, they receive cash equal to the selling price. The value of an income-producing property can be estimated by adding the original mortgage debt amount and the investor's estimated equity value. The basis for determining the cost of capital is the present value of the expected future return: the residual cash flow from the use of the property and the residual resale price. The sum of the mortgage debt and the assessed equity value gives the likely market value of the property.
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The use of a mortgage loan as a source of financing for purchased real estate introduces some features into the use of income approach methods in real estate valuation for the following reasons:
The market value of the asset does not coincide with the amount of equity capital invested in it, because real estate was partially purchased with borrowed funds;
The current cost of the loan provided by the borrower depends on the specific financing terms.
The income capitalization method determines the value of the property being appraised by converting annual net operating income into value using a capitalization ratio that includes a rate of return on investment and a rate of return on capital. The peculiarity of this method when assessing credited objects is the method of calculating the capitalization ratio.
If the loan provides for the repayment of the principal debt at the time of resale of the property, then the capitalization ratio is calculated as the weighted average of the rate of return the investor wants to receive on the invested equity capital and the interest rate on the mortgage loan.
R e – investor’s rate of return (on equity capital);
R k – interest rate on the loan;
K m – mortgage debt ratio.
If an investor obtains a self-amortizing loan, then the capitalization rate is calculated using the mortgage constant (R m) instead of the loan interest rate (R k).
The mortgage constant reflects the lender's rate of return, taking into account the repayment of the debt evenly in annuity payments.
where R is the capitalization ratio;
R e – investor’s rate of return (on equity capital);
R m – mortgage constant;
K m – mortgage debt ratio.
Problem No. 20.
Condition: To purchase real estate that brings in 1870 thousand rubles annually. net operating income, you can get a self-amortizing mortgage loan for a period of 32 years at 14% with a mortgage debt ratio of 48%. Appraise the property if the investor’s required rate of return on equity is 12%. The loan repayment scheme provides for monthly payments.
Solution:
1. Capitalization rate
Rm=(iaof, interest accrued monthly, 20%, 21 years.)*12=0.2023
2. Cost of the loaned property
The discounted cash flow method determines the market value of real estate as the sum of discounted income that is expected from the property in the future. This method is usually called traditional mortgage investment analysis technique.
If the purchase of real estate involves mixed financing, then its cost will be the sum of the amount of the mortgage loan provided and the current value of equity. Equity represents the sum of the investor's discounted cash flows over the holding period and the discounted proceeds from the expected sale of the property at the end of the holding period.
The specifics of using the traditional scheme of the discounted cash flow method are manifested in the following:
The discount rate must correspond to the investor's required rate of return on equity;
As current income for the holding period, it is not net operating income that is used, but cash receipts on equity capital, which represent the balance after subtracting mandatory payments to the bank;
The proceeds from the proposed sale of the property at the end of the holding period are the difference between the sale price and the remaining mortgage debt at that date.
Task No.21.
Condition: Determine the market value of real estate, the net operating income of which will be the following values: in the 1st year - 160 thousand rubles, in the 2nd year - 300 thousand rubles, in the 3rd year - 500 thousand rubles, in the 4th year 1st – 800 thousand rubles, 5th – 1000 thousand rubles.
The sale price of the property at the end of the 5th year is expected to be 3,100 thousand rubles. The rate of return on the investor's equity is 15%. The investor receives a loan from the bank in the amount of 805 thousand rubles. for 30 years at 9%. The debt is repaid annually in equal installments with interest accrued on the balance of the debt.
Solution:
1. Drawing up a loan repayment schedule during the analyzed period and calculating debt servicing costs (Table 9). The analyzed period until the sale of the property is 5 years.
Table 9 – Calculation of debt service income
|
Index | ||||||
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Amount of loan to be repaid, thousand rubles. (925/17) | ||||||
|
Balance of debt at the end of the year, thousand rubles. | ||||||
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The amount of accrued interest on the balance of the previous period (rate 18%) | ||||||
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Debt servicing expenses, thousand rubles. | ||||||
2. Calculation of the amount of discounted cash receipts (Table 10). The currency present value factor (pvf) is applied.
Table 10 - Calculation of the amount of discounted cash receipts
|
Index | ||||||
|
Net operating income, thousand rubles. | ||||||
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Debt servicing expenses, thousand rubles. | ||||||
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Cash receipts, thousand rubles. | ||||||
|
Current value factor of a monetary unit | ||||||
|
Discounted cash receipts, thousand rubles. | ||||||
|
Amount of discounted income, thousand rubles | ||||||
3. Calculation of the current value of proceeds from the sale of real estate:
Sale price = 3100 thousand rubles.
Balance of debt at the end of the 5th year = 670.85 thousand rubles.
Sales proceeds = 3100-670.85 = 2429.15 thousand rubles.
Current value of sales proceeds = 805*0.64993 = 523.2 thousand rubles.
4. Assessment of the market value of the investor’s equity
V e = 1633+523.2 = 2156.2 thousand rubles.
5. Assessment of the market value of real estate
V = V m +V e = 805+2156.2= 2961.2 thousand rubles.
The use of traditional mortgage investment analysis techniques makes it possible to evaluate real estate both on the basis of cost indicators and without their participation, taking into account only the amount of net operating income.
The traditional technique of mortgage investment analysis is considered as follows:
where V is the value of real estate;
V m - mortgage loan;
NOI - net operating income;
DS - annual debt service costs;
pvaf - factor of the current value of the annuity;
FV B - sale price of the property at the end of the analyzed period;
V mn is the balance of the mortgage loan at the end of the analyzed period;
pvf - factor of the current value of a monetary unit;
R e - rate of return on equity;
n - analyzed period.
Problem No. 22.
Condition: Determine the value of real estate, net operating income which over the next 8 years will amount to 1,420 thousand rubles. At the end of the 8th year, the object is planned to be sold for 12,540 thousand rubles. The investor receives a mortgage loan in the amount of 8860 thousand rubles. for 30 years at 12% with monthly repayment. The investor's required rate of return on invested equity capital is 19%.
Solution:
1. Mortgage constant
Rm = (12%, 30 years) *12 = 0.010286*12=0.1234
2. Annual debt service costs
DS=V m *R m = 8860*0.1234 = 1093.3 thousand rubles.
3. The balance of the debt is finally in the 12th year
Monthly payment RMT = 8860 * 0.010286 = 91.1 thousand rubles;
The remaining loan period after the sale of the property is 30 - 8 = 22 years;
Balance of debt on the date of sale V mn = 91.1*92.76968=8451.3 thousand rubles.
4. Present value of cash receipts
PV 0 = (19%, 8 years) = (1420-1093.3)*4.48732 = 1466.0 thousand rubles.
5. Current value of proceeds from the sale of the object
РV BO = (12540-8451.3)*0.32690 = 1336.6 thousand rubles.
6. Market value of equity
V e = РV o + РV BO = 1466+1336.6= 2802.6 thousand rubles.
7. Property value
V=V m +V c = 8860 + 2802.6= 11662.6 thousand rubles.
Answer: the cost of real estate will be 11662.6 thousand rubles.
Valuation of real estate encumbered by a previously obtained mortgage loan:
where V mo is the balance of the debt as of the valuation date;
V mnk is the balance of the debt on the date of sale, taking into account the period separating the date of receipt of the loan from the date of valuation.
Problem No. 23
Condition: It is required to evaluate the property. The conditions of the previous problem 22 are used. The mortgage loan was received 3 years before the valuation date.
Solution:
1. The balance of the mortgage loan as of the valuation date
V mo = RMT * (pvaf, monthly, 12%, 27 years) = 91.1 * 96.02007 = 8747.2 thousand rubles.
2. Balance of debt as of the date of sale
Remaining loan term after the sale of the property = 30 – 3 – 8 = 19 years;
Balance of debt on the date of sale V mnk = RMT * (pvaf, monthly, 12%, 30 years) = 91.1 * 89.65509 = 8167.6 thousand rubles.
3. Current value of cash receipts (does not change)
РV 0 = (NOI-DS)*(pvaf annually) = (1420-1093.3)*4.48732 = 1466.0 thousand rubles.
4. Current value of proceeds from the sale of the object (including the remaining debt)
PV BO = (FV in -V m)*(pvf, annually, 12%, 15 years) = (12540-8167.6)*0.32690 = 1429.3 thousand rubles.
5. Market value of equity
V e = РV o + РV BO = 1466+1429.3=2895.3 thousand rubles.
6. Cost of real estate (taking into account the balance of debt on the date of valuation and date of sale)
V = V m +V e = 8747.2+2895.3=11642.5 thousand rubles.
The basis of investment and mortgage analysis is the idea of property value as a combination of the value of equity and borrowed funds. In accordance with this, the maximum reasonable price of property is determined as the sum of the current value of cash flows, including reversion proceeds, attributable to the investor's funds, and the amount of the loan or its current balance.
When investing and mortgage analysis, the investor’s opinion is taken into account that he is not paying for the cost of real estate, but the cost of equity, and the loan is considered as an additional means to complete the transaction and increase equity capital. The analysis uses two methods (two techniques): the traditional method and the Ellwood technique. The traditional method explicitly reflects the logic of investment and mortgage analysis. Ellwood's method, reflecting the same logic, uses ratios of profitability ratios and proportional ratios of investment components.
Traditional method. This method takes into account that the investor and lender expect to receive a return on their investment and return it. These interests must be ensured by the total income for the entire amount of investment and the sale of assets at the end of the investment project. The amount of investment required is determined as the sum of the present value of the cash flow, consisting of the investor's equity and the current debt balance.
The present value of an investor's cash flow consists of the present value of periodic cash receipts, the increase in the value of equity assets resulting from loan amortization. The value of the current debt balance is equal to the present value of loan service payments for the remaining term, discounted at the interest rate.
Cost calculation in traditional technology is carried out in three stages.
Stage I. For the accepted forecast period, a statement of income and expenses is drawn up and the cash flow before tax is determined, i.e., for equity capital. The stage ends with determining the current value of this flow in accordance with the forecast period and the final return on equity expected by the investor Y e .
Stage II. The proceeds from the resale of property are determined by subtracting from the resale price the costs of the transaction and the remaining debt at the end of the forecast period. The present value of the proceeds is assessed at the same rate.
Stage III. The current value of equity capital is determined by adding the results of the stages. The value of a property is estimated as the result of the sum of the equity value and the current debt balance.
Let's apply the traditional technique to a specific investment project and use it as a base to illustrate all subsequent considerations of the elements of investment and mortgage analysis.
1. Initial data for the project.
The property will generate $70,000 in annual income over a projected period of five years. At the end of this period, the property will be sold for $700,000 (less selling expenses). To purchase real estate, a self-amortizing mortgage loan in the amount of $300,000 is used, taken out for twenty years at 5% per annum with monthly payments. The investor requires a final return on equity of 20% (Table 8.1).
Let's determine the price of real estate using traditional techniques, using initial data and assumptions. First, let's determine what the possible maximum price for real estate purchased without borrowing funds (debt-free property) is. In this case, all net income and all resale price come entirely from the investor's equity (there are no interest payments or amortization of debt).
Table 8.1 Calculation of current value
Thus, an investment of $490,660 (rounded) without borrowing will provide the investor with a 20% final return. Although the current return is
70000/490660= 0,1427(14,27%),
it will increase to a final return of 20% due to an increase in the value of real estate over the forecast period.
2. Now we will determine the reasonable price of real estate purchased with a loan. To solve, we use traditional techniques in algebraic form.
The algebraic expression for cost is written in the same three-step logical sequence:
V = I + II + MR,
Where MR-- current principal balance;
(pvaf Y e ,n) -- factor of the current value of a unit annuity with a final return on equity capital Y e and term n;
NOI-- net operating income;
D.S.-- annual debt service;
(pvfY e ,n)--factor of the current value of the unit (reversion);
R.P.-- resale price of real estate (reversion);
OS-- balance of debt at the end of the term P.
We substitute the initial data and the values of the factors defined above into this expression. Values D.S. And OS are calculated based on known loan terms:
V = 2,99 (70 000 - 47 404,4) + 0,4 (700 000 - 282 252,4) + 300 000,
V = $534,660 (rounded).
The calculated reasonable price of $534,660 is higher than the price of the property purchased without borrowed funds. As mentioned earlier, the investor is primarily interested in the price and growth of equity capital. The investor is willing to pay a large amount with positive leverage, as is the case in this case (return on equity is higher than interest rates on the loan), for the opportunity to significantly increase the final return on equity and reduce own capital investments.
The algebraic form of the traditional technique is convenient when the amounts of current debt and (or) resale are determined as fractions (percentages) of the original price of the property. Let's write the general expression in algebraic form when, instead of the loan amount, the mortgage debt ratio is known T, A the cost is determined in shares D of the current price V.
V = (pvaf)(N0I-mVDS 1) + [(pvf)(l±Д)V-mVOS 1)] + mV,
Where D.S. 1 -- debt servicing for a single loan, or permanent mortgage;
OS 1 -- the unpaid portion of the loan by the end of the forecast period, or the remaining debt for a single loan;
D - the share of increase or decrease in the value of real estate.
3. Let us assume that instead of the loan amount, the mortgage debt ratio is given t = 60%, and instead of the resale price, an increase in value during the ownership period is given by 25%.
Substitute numerical values:
V=2.99(70000 -- 0.6V 0.158)+ 0.4 (1.25 V--0.6V 0.938) + 0.6 V,
V= 512,236.91=$512,237
4. Using traditional techniques, we will determine the price of real estate with an existing mortgage. Let us assume that the property in its current condition is encumbered with a mortgage to secure a mortgage taken out seven years ago in the amount of $300,000 for a term of twenty years with monthly payments of 15% per annum. The remaining conditions are from the basic example.
The current debt balance is
MR= $270,519.95 (from loan terms).
Balance of debt at the time of reversion:
OS= $166,052.17 (in 7+ 5 = 12 years).
Substitute the values:
V= 2,99 (70 000 - 47 404,4) + 0,4 (700 000 - 166 052,17) + 270 519,95,
V=$551,660
5. Determine the rate of final return on equity capital with known project parameters to the current real estate price. Such a task may arise, for example, when an appraiser tries to determine the requirements of investors in a particular market, relying on recently sold analogues with known investment parameters.
When using an algebraic form to solve this problem, one should determine the factors (pvaf) and (pvf) at different rates of return and substitute them into equality with the known current price SP until this equality turns into identity.
The problem is solved by the approximation method and much faster using a financial calculator, since the final return on equity capital with a known current value of equity capital is equal to the internal rate of return IRR for equity and related cash flow.
Let's use the data from the previous example.
Current equity value: 551660-270520 = $281,140
Return on equity: 70,000 - 47,404.4 = $22,595.6/year.
Sales proceeds: 700,000 - 166,052 = $533,948
Calculation result: Y e = IRR 20%.
Getting the value Y e , where the equity investment value of $281,140 matches the projected cash flow.
The traditional technique of mortgage investment analysis allows one to draw certain conclusions regarding the influence of the forecast period on the assessment results. An important factor limiting the holding period from an investor's point of view is the reduction over time of depreciation (assets) and interest deductions from profits for tax purposes. Besides , it is possible that more preferable investment options may emerge (external factors). On the other hand, the current value of the mortgage debt ratio is gradually decreasing, which leads to a drop in the effectiveness of financial leverage. Analysis using traditional techniques of options with different tenures shows the obvious influence of the forecast period on the value of the estimated value. Moreover, the dependence is such that with an increase in the predicted tenure, the value of the assessed value decreases in the absence of changes in value over the forecast periods.
Ellwood technique. It is used in investment and mortgage analysis and gives the same results as the traditional technique, since it is based on the same set of initial data and ideas about the relationship between the interests of equity and borrowed capital during the development period of the investment project. The great thing about Ellwood’s technique is that it allows you to analyze property relative to its price based on the return ratios of equity indicators in the investment structure, changes in the value of total capital, and quite clearly shows the mechanism of changes in equity capital over the investment period.
General view of the Ellwood formula:
R o =/(l + D n a),
where R 0 is the overall capitalization ratio;
C -- Ellwood mortgage ratio;
D - share change in property value;
(sff,Y e) -- compensation fund factor at the rate of return on equity;
D n -- share change in income for the forecast period;
A--stabilization coefficient.
Ellwood Mortgage Ratio:
С = Y e + p(sff, Y e )-R m ,
Where R-- share of the current loan balance amortized over the forecast period,
R m-- mortgage constant relative to the current debt balance.
Expression 1/(1 + D n A) in the equation is a stabilizing factor and is used when income is not constant, but changes regularly. Usually the law of income change is specified (for example, linear, exponential, according to the accumulation fund factor), in accordance with which the stabilization coefficient is determined A according to pre-calculated tables. The value is determined by dividing the income for the year preceding the valuation date by the capitalization rate, taking into account the stabilization of income. In the future, we will consider Ellwood’s technique only for permanent income.
Let's write Ellwood's expression without taking into account changes in the value of real estate and with constant income:
R = Y e - t.
This expression is called the basic capitalization ratio, which is equal to the rate of final return on equity capital adjusted for financing conditions and depreciation.
Let's consider the structure of the overall capitalization ratio in the Ellwood formula without taking into account changes in property values, for which we use the investment group technique for return rates. This technique weighs the rates of return on equity and debt in their respective shares of total invested capital:
Y 0 =mY m +(1-m)Y e .
In order for this expression to become equivalent to the base coefficient r , Two more factors need to be taken into account. The first is that the investor must periodically deduct from his income to amortize the loan, reducing his equity. Therefore, it is necessary to adjust the value of Y 0 in the previous expression by adding the periodically paid share of the total capital at an interest equal to the interest rate on the loan. The expression for this adjustment is the gearing ratio T, multiplied by the compensation fund factor at the interest rate (sff,Y m). The value (sff,)Y m) is equal to the difference between the mortgage constant and the interest rate, i.e. R m -Y m . Thus, taking into account this amendment:
Y 0 = mY m + (1 -m)Y e + m(R m -Y m).
The second adjustment term must take into account the fact that the investor's equity as a result of reversion will increase by the amount of the portion of the loan amortized over the holding period. To determine this adjustment, you need to multiply the depreciated amount as a share of the total original capital by the replacement fund factor at the rate of final return on equity (realization into equity occurs at the end of the holding period). Therefore, the second correction term has the form: mp(sff,Y m), and with a minus sign, since this amendment increases the cost.
Thus:
Y 0 = mY m +(1-m)Y e +m(R m -Y m)-mp(sff,Y e),
and after combining similar terms and replacing Y 0 with r (we do not take into account changes in property value):
r = Y 0 -m.
Thus, we obtain the basic capitalization ratio of the Ellwood expression. Progressing from the investment group technique through the necessary adjustments to Ellwood's expression shows that this expression indeed reflects all the elements of the transformation of equity and borrowed funds combined in the invested capital, in particular financial leverage, amortization of the mortgage loan and the increase in equity as a result of amortization of the loan.
1. Appraise a debt-free income property that, over a five-year tenure, generates a net annual income of $70,000. By the end of that period, the property's value will increase by 30%. The investor requires a 20% final return on equity.
In this case, the formula will look like this:
R = Y e + D(sff, Y e),
since m = 0 according to the conditions of the problem.
(sff,Y e 5 years) = 0.1344.
Let's substitute the values:
R = 0.2 -0.3 x 0.1344 = 0.1597;
V=NOI/R = 70,000/0.1597 = $438,360
2. The same property is purchased with a mortgage loan in the amount of 60% of the cost of the property for twenty years with a monthly payment of 15% per annum. Determine the value of real estate.
Ellwood's expression for the overall cap rate:
R 0 = Y e -m+ D(sff, Y e).
After substituting the values:
R 0 = 0.2-0.6(0.2+ 0.0594x0.1344-0.158)-0.3x0.1344 = 0.1297;
V = NOI /R o = 70,000/0.1297 = $539,707
The Ellwood technique can be used if debt and property appreciation are specified in monetary terms. In this case, the coefficients and share parameters are expressed through the cost V.
3. Real estate (previous example) is purchased with a loan of $300,000. The value of the property is expected to increase by $160,000 over five years. What is a reasonable maximum price for the property?
Let's write the Ellwood equation, substituting known and calculated values and expressing the corresponding parameters in terms of cost:
V=$532 -195
In the case of assessing real estate with an existing mortgage, it is necessary to take into account that the values r, R m And T in the Ellwood formula represent the portion of the debt repaid during the forecast period relative to the current balance, the mortgage constant calculated on the basis of the current loan balance, and the current mortgage debt ratio, respectively.
4. Determine the price of real estate with an existing mortgage on a mortgage loan issued seven years ago in the amount of 60% of the cost for twenty years at 15% per annum with monthly payments without taking into account changes in value.
R o = r = Y e - M .
Let's determine the current values of m, R m and p:
m = 0.5383; R m =0.1761; p = 0.1957.
r = 0.2 - 0.53883 (0.2 + 0.1957 x 0.1344-0.1761) = 0.173;
V = 70,000/0.173 = $404,680
The Ellwood equation expressed in terms of the debt coverage ratio. Financing projects associated with significant risks regarding the receipt of stable income may change the orientation of lenders regarding the criterion determining the amount of borrowed funds. The lender believes that in this situation it is more appropriate to determine the loan size not on a price basis, but on the basis of the ratio of the investor’s annual net income to annual payments on the loan obligation, i.e. the lender requires guarantees that the value of this ratio (naturally, greater than one) is not will be less than a certain minimum value determined by the lender. This ratio is called the debt coverage ratio: DCR = NOI/DS.
In this case, the mortgage debt ratio in the Ellwood equation should be expressed in terms of the debt coverage ratio DCR:
DCR = NOI/DS = RV/(R m Y m ,)=R/(R m m), or m = R/(DCRR m).
After substituting this expression instead m we obtain the Ellwood equation expressed in terms of the debt coverage ratio:
5. Evaluate an income property generating a net annual income of $70,000, tenure of 5 years. It is assumed that after this period the value of the property will increase by 30%. The property is purchased with a mortgage loan at 15% per annum, with monthly payments, a 20-year term and a debt coverage ratio of 1.3. The investor requires a 20% final return on equity.
We substitute the values and determine the overall capitalization ratio:
SP = 70,000/0.1283 = $545,800
The basis of investment and mortgage analysis is the idea of property value as a combination of the value of equity and borrowed funds. In accordance with this, the maximum reasonable price of the property is determined as the sum of the current value of cash flows, including the proceeds from reversion attributable to the investor's funds, and the amount of the loan or its current balance.
When investing and mortgage analysis, the investor’s opinion is taken into account that he is not paying for the cost of real estate, but the cost of equity, and the loan is considered as an additional means to complete the transaction and increase equity capital. The analysis uses two methods (two techniques): the traditional method and the Elwood technique. The traditional method explicitly reflects the logic of investment and mortgage analysis. Elwood's method, reflecting the same logic, uses ratios of profitability ratios and proportional ratios of investment components.
Traditional method. This method takes into account that the investor and lender expect to receive a return on their investment and return it. These interests must be ensured by the total income for the entire amount of investment and the sale of assets at the end of the investment project. The amount of investment required is determined as the sum of the present value of the cash flow consisting of the investor's equity and the current debt balance.
The present value of an investor's cash flow consists of the present value of periodic cash receipts, the increase in the value of equity assets resulting from loan amortization. The value of the current debt balance is equal to the present value of loan service payments for the remaining term, discounted at the interest rate.
Cost calculation in traditional technology is carried out in three stages.
StageI. For the accepted forecast period, a statement of income and expenses is drawn up and cash flow before tax is determined, i.e. on own capital. The stage ends with determining the current value of this flow in accordance with the forecast period and the final return on Ye's equity capital expected by the investor.
StageII. The proceeds from the resale of property are determined by subtracting from the resale price the costs of the transaction and the remaining debt at the end of the forecast period. The present value of the proceeds is assessed at the same rate.
StageIII. The current value of equity capital is determined by adding the results of the stages. The value of equity and current debt balance is assessed.
The traditional technique of mortgage investment analysis allows one to draw certain conclusions regarding the influence of the forecast period on the assessment results. An important factor limiting the holding period from an investor's point of view is the reduction over time of depreciation (assets) and interest deductions from pre-tax earnings. In addition, more preferable investment options may emerge (external factors). On the other hand, the current value of the current debt ratio gradually decreases, which leads to the effectiveness of financial leverage. Analysis using traditional techniques of options with different tenures shows the obvious influence of the forecast period on the value of the estimated value. Moreover, the dependence is such that with an increase in the predicted tenure, the value of the assessed value decreases, provided that the value decreases over the forecast periods.
Elwood technique. It is used in investment and mortgage analysis and gives the same results as the traditional technique, since it is based on the same set of initial data and ideas about the relationship between the interests of equity and borrowed capital during the development period of the investment project. The difference between Elwood’s technique is that it is based on the return ratios of equity indicators in the investment structure, changes in the value of total capital and quite clearly shows the mechanism of changes in equity capital over the investment period.
General view of the Elwood formula:
where R 0 is the overall capitalization ratio
WITH– Ellwood mortgage ratio
- share change in property value
(sff,Y e ) – compensation fund factor at the rate of return on equity capital
- share change in income for the forecast period
- stabilization coefficient
Elwood Mortgage Ratio:
C = Ye + p(sff, Ye) – Rm
Where p is the share of the current loan balance amortized over the forecast period
Rm – mortgage constant relative to the current debt balance.
Expression 
in the equation is a stabilizing factor and is used when income is not constant, but changes regularly. Usually the law of income change is specified (for example, linear, exponential, according to the accumulation fund factor), in accordance with which the stabilization coefficient is determined 
according to pre-calculated tables. The value is determined by dividing the income for the year preceding the valuation date by the capitalization rate, taking into account the stabilization of income. In the future, we will consider the Elwood technique only for permanent income.
Let's write Elwood's expression without taking into account changes in the value of real estate at constant income:
This expression is called the basic capitalization ratio, which is equal to the rate of final return on equity capital adjusted for financing conditions and depreciation.
Let's consider the structure of the overall capitalization ratio in Elwood form without taking into account changes in property values, for which we use the investment group technique for rates of return. This technique weighs the rates of return on equity and debt in their respective shares of total invested capital:
Yo = m*Ym + (1 – m)*Ye
In order for this expression to become equivalent to the basic coefficient r, two more factors must be taken into account. The first is that the investor must periodically deduct from his income to amortize the loan, reducing his equity. Therefore, it is necessary to adjust the value of Yo in the previous expression by adding the periodically paid share of the total capital at interest equal to the interest rate on the loan. The expression for this adjustment is the leverage ratio m multiplied by the recovery fund factor at the interest rate (sff, Ym). The value (sff, Ym) is equal to the difference between the mortgage constant and the interest rate, i.e. Rm – Ym. Thus, taking into account this amendment:
Yo = m*Ym + (1 – m)*Ye + m*(Rm – Ym)
The second adjustment term must take into account the fact that the investor's equity as a result of reversion increases by the amount of the portion of the loan amortized over the holding period. To determine this adjustment, you need to multiply the depreciated amount as a share of the total original capital by the replacement fund factor at the rate of final return on equity (realization into equity occurs at the end of the holding period). Consequently, the second correction term has the form: mp(sff, Ym), with a minus sign, since this amendment increases the cost.
Thus:
Yo = m*Ym + (1 – m)*Ye + m(Rm – Ym) – mp(sff, Ye)
And after combining similar terms and replacing Yo with r (we do not take into account the change in property value):
R = Ye – m*(Ye + (p(sff) – Rm))
Thus, we obtain the basic capitalization ratio of the Elwood expression. Progressing from the investment group technique through the necessary adjustments to Elwood's expression shows that this expression actually reflects all the elements of the transformation of equity and borrowed funds combined in the invested capital, in particular financial leverage, amortization of the mortgage loan and the increase in equity as a result of amortization of the loan.
The Elwood equation expressed in terms of the debt coverage ratio. Financing projects associated with significant risks regarding the receipt of stable income may change the orientation of lenders regarding the criterion determining the amount of borrowed funds. The lender believes that in this situation it is more appropriate to determine the loan size not on a price basis, but on the basis of the ratio of the investor’s annual net income to annual payments on the loan obligation, i.e. the creditor requires guarantees that the value of this ratio (naturally, greater than one) will not be less than a certain minimum value determined by the creditor. This ratio is called the debt coverage ratio:
In this case, the mortgage debt ratio in the Elwood equation should be expressed through the debt coverage ratio DCR:
DCR = NOI/DS = RV/(Rm*Vm) = R/(Rm*m), or
After substituting this expression for m, we obtain the Elwood equation, expressed in terms of the debt coverage ratio:
