## Introduction

Real estate is defined as the type of an assets class that is tangible in nature. This class covers a variety of assets such as buildings that include residential property, office buildings, retail as well as industrial buildings. The real estates also covers land that can be used for development purposes. For an investment asset to be considered to be a real estate, it must be indivisible as well as immovable.

The asset class should posses some unique characteristics that differentiate it from other assets classes. It should have a relatively high level of illiquidity and should not have a central market place. Real estate exists in different forms. The main forms include forms of equity such as free and clear, and leveraged. The forms also include mortgages and aggregation instruments (Sivitanides 2008). In real and clear equity form of real estate investment, the owner of the real estate acquires an indefinite ownership right of that specific asset. This means that he acquires the right to lease or to resell the asset he owns. This form of real estate is also called free simple real estates.

In the case of leveraged equity form of investment, a person acquires the rights to own the stated asset but on condition that all debt or mortgage is cleared. This requires the holder of the asset to transfer back the asset to the seller of that specific asset or another designated person, the equity in case he fails to pay for the debt or the mortgage (Wurtzebach ,Miles and Ethridge 1994). Aggregation on the other hand allows investors to have access to a variety of investment instruments which provide a diversification of investments in the real estate industry.

Various approaches can be used in valuation of real estates. The main methods used include cost approach which is made use of mainly in new structures. According to this method, the value of real estate is considered to be equal to the sum of the cost of construction and the purchase cost of the land. Sales comparison approach on the other hand uses the value other similar property would fetch in the market to fix the value of the real estate asset in question. Therefore this method makes use of benchmarks to come up with the value of a property. Closely related to this approach, is the hedonic price estimation method which identifies specific properties of an asset and then uses valuations of such properties to define the value of the real estate.

Another valuation method makes use of the income flow generated by the real estate over a period of time. In the income valuation approach, the value of the real estate is taken to be equal to the present value of the income received in perpetuity. In this case income is considered to constitute the net operating income calculated from gross income less other charges such as tax on property (Sivitanides 2008). Another valuation model is the discounted cash flow method.

The method considers factors that determine the value of the real estate and how an investor considers value from his view point. The method therefore, makes it possible for the inclusion of factors such as cost of borrowing, investor’s expectations and the tax position of the investor. Under this approach, the main methods that can be used include the net present value (NPV) and the internal rate of return (IRR).

## Property Identification

A real estate investor is confronted by a question on the right choice of investment to make between two rental buildings which promise high returns. The financing requirements for the investments differ with the first one requiring 75% mortgage finance while the other one requires 80% mortgage finance. His dilemma will be solved using NPV and IRR below.

## Discounted cash flow method

Discounted cash flow approach to real estate valuation uses assumptions on the benefits that can be accrued and the costs that can be incurred in the investment of a particular asset. In doing this, an appropriate discounting rate is required. The discounting rate is taken to be equal to the rate of return of the market or as the minimum rate of return that an investor would expect from a give investment. The rate is used to find the present value of a stream of incomes over a period of time. The method also makes use of free cash flows (Simons, Malmgren and Small 2008). The free cash flow is the net cash received from the business after taking into consideration all expense incurred in the generation of income and other expenses of capital in nature.

Capital costs may include the cost incurred to repair real estate, maintain or improve leaseholds. The free cash flows to equity on the other hand are the value that is determined from the deduction of interests from the cash flows. This form of cash flow is normally discounted using the cost of equity discount rate. In this case, the value of equity of a business can be estimated (Kahr and Thomsett 2005). The gross present value finds the sum of the discounted cash inflows and outflows of the real estate discounted at a given rate over the period in which the investor holds the real estate property, by making use of the discounted cash flow models. The value of this method is considered to be an indication of the value of the asset in the market.

Internal rate of return on the other hand refers to that rate which can be used to equate the value of an investment to the net present value of cash flows generated by an investment. In other words, IRR is the rate that can be used to make the net present value to equal a zero. The market value in the investment valuation on the other hand is taken to be equal to the amount of money that a willing buyer would exchange for the property with the willing seller on the valuation date (Arsenault, Hamilton, Leeds and Marcil 2005). Net present value on the other hand calculates the value of cash flows received in future in terms of their present value equivalent.

Therefore, from components of discounted cash flow models, the model consists of periodic cash flows generated from a particular real estate investment. It is therefore, these cash flows that are discounted to determine the present value of an investment. It should be noted that in using discounted cash flow model in valuation of real estate, all cash flow must refer to the same length of time. The income used in this model should also be related to the future instead of the present cash flows. The rate used to discount cash flows must also be in correspondence to the period through which a given income was generated.

## Net Present Value (NPV)

Net present value is calculated by discounting cash flows over a period of time using an appropriate discounting rate. From the present value of cash inflows, present value of cash outflow is deducted in order to determine the viability of an investment. Net present value of an investment is calculated as follows:

NPV=C_{0} + C_{1}/(1+k) + C_{2}/(1+k)^{2} + C_{3}/(1+k)^{3} +….+ C_{n}/(1+k)^{n} Where C refers to cash flows within a period of investment, k is the rate used to discount this cash flows with n representing the last investment period. C_{0} represents cash outlays. C_{n} on the other hand represents cash inflows received at the end of the investment period.

It includes terminal value received at the end of the investment period. An investor is faced with a dilemma between choosing two investment opportunities in the real estate industry. In the first case, he considers purchasing a building for rental purposes. The building will cost $450,000. The investor intends to fund 75% of the cost of the building using a mortgage in which he will be expected to make $19,000 in payment annually of which $15,000 covers interests and therefore, tax deductible. His forecast is that the house will fetch about $500,000 net after a period of three years. He hopes that the annual operating income will be $30,000. The tax savings made on depreciations is expected to be $6,000 annually. The marginal tax rate is 30%

In the first two years, his cash flow after tax will be the same. The net income after tax (NIAT) will be as follows:

NIAT= (NI- Interest – Depreciation)(1-taxation rate)

=($30,000- $15,000 -$6,000)(1-0.07) =$8,370

The cash flows after tax will be equal to the following:

C= (NIAT + Depreciation – principal paid on mortgage)

=$8,370 + $6,000 – $4,000 =$18,370

$500,000 that is expected from the sale of the building in the third year is added to the after tax cash flow. From this, the value of mortgage to be paid is deducted. In this case, the mortgage amount to be deducted is its initial value less the principle amount that has already been paid, which is equivalent to ($337,500 – $12,000). That is $325,500. This will give him an after tax cash flow shown below:

$18,370 + $500,000 – $325,500= $192,870.

The capital invested to buy the building is 25% of the cost of the building. Assuming a required rate of return (k) to be 10%, net present value will be given as follows:

NPV= C_{1}/(1+k) + C_{2}/(1+k)^{2} + C_{3}/(1+k)^{3} –C_{0}

=$18,370/(1+0.1) + $18,370/(1+0.1)^{2} +$192,870/(1+0.1)^{3} – $112,500

=$18,370/(1.10) +$18,370/(1.10)^{2} +$192,870/(1.10)^{3} – $112,500

=$ 299,145 – $112,500=$186,645

In the second scenario, the investor can invest in the property worth $300,000 where he will be required to finance 80% through a mortgage which requires payment of $18,000 annually. $14,000 of this will cover interest rate for the mortgage annually for the three years life of the mortgage. The price of the property at end off the holding period is expected to be $350,000 in net while operating income will be equal to $25,000. He also expects a depreciation amount of $4,500 and a marginal tax of 30%. To find out the viability of this investment, determination of NPV should be done.

NIAT=($25,000- $14,000 -$4,500)(1-0.07) =$6,045

The cash flows after tax will be equal to the following:

C= (NIAT + Depreciation – principal paid on mortgage)

=$6,045+ $4,500 – $4,000 =$6,545

$350,000 that is expected from the sale of the building in the third year is added to the after tax cash flow. From this, the value of mortgage to be paid is deducted. In this case, the mortgage amount to be deducted is its initial value less the principle amount that has already been paid. This will give him an after tax cash flow shown below

Outstanding mortgage= $240,000-$12,000=$228,000

C_{3}= $6,545+ $350,000 – $228,000= $128,545.

Calculate its NPV assuming a 12% expected rate of return.

NPV= C_{1}/(1+k) + C_{2}/(1+k)^{2} + C_{3}/(1+k)^{3} –C_{0}

=$6,545/(1+0.12) + $6,545/(1+0.12)^{2} +$128,545/(1+0.12)^{3} – $60,000

$6,545/(1.12) +$6,545/(1.12)^{2} +$128,545/(1.12)^{3} – $60,000 =$ 42,557

Since NPV in the two scenarios are positive, it is advisable for the investor to consider them and to determine the most profitable investment.

## Internal rate of return (IRR)

In case of real estate investment for commercial purposes, the levered internal rate of return is most appropriate for the valuation of the asset in which case the intention of the investor is to raise part of the investment capital using mortgage. The analysis of the levered internal rate of return consists of the payment of mortgage used to repay the mortgage loan (Wang and Wolverton 2002). Therefore, the mortgage rate forecast latest in the market is of great importance for the analysis of the investment intended for commercial purposes. Internal rate of return will take into consideration revenue, cost, interest on loan for the life of the loan and the loan balance repayment when the property is finally sold.

It also takes into consideration all tax deductible entitled to the investor. To approximate the resell value of the asset at the end of the investment period, internal rate of return uses exit cap rate. This is applied on the NOI of the last period of investment. The formulae used to determine this value is given below:

- Residual value=NOI/ECR (exit cap rate)

Reasonable assumptions on the calculation of levered internal rate of return are required for successful investment in real estate industry. The need to make predictions of the internal rate of return complicates the matter in cases where an investor considers using this method for the investment purposes. Using information on the investment above, internal rate of return of the investor can be calculated using financial calculators. For the calculation of the internal rate of return for the above investor, please refer to the attached Microsoft Excel worksheet. Although this method can be used by the investor to calculate the value of the real estate, it suffers from some limitations.

The model assumes the assumption on the reinvestment. Accordingly for this model to be effective in the calculation of the value of real estate, all positive returns generated by a business must be reinvested (Schmitz and Brett 2001). Due to this assumption, it becomes hard to determine with precision the possible value of a given asset. The assumption becomes unrealistic is some cases which in some cases lead to failure to take investment. Leveraged internal rate of return also leads to multiple results on calculation. This may lead to a problem to the investor since it may be hard to identify the right internal rate of return.

The problem with this internal rate of return can be solved by using the modified form of internal rate of return. This modified form of internal rate of return takes into account that not all returns are reinvested at the same rate. Some of these investments are made at a higher rate than others. Therefore the allowance given by this method can be used to include different rates to an investment valuation. In this model, the following steps are followed.

The first step involves identification of all negative cash flow that a property generates. These cash flows are discounted at a rate that would be used to pay interest payment annually. The next step involves determination of cash flows that would be generated in the future. The expected future cash flows are grown at a rate that would equal to the required rate of return for the investment. This rate is referred to as the re-investment rate. Once this has been done, the last step involves calculation of the modified internal rate of return (MIRR) which takes into account the fact that not all returns are invested at the same rate.

## Impact of leverage and risk in investment

The rate of return expected by an investor under some circumstances can be affected by the use of leverage to finance investments. This happens when the value of the property in question appreciates on its purchase. Also in cases where the property has been purchased below the market value for such property, the rate of return soon experiences a high growth when the same property is sold at the prevailing market price after its purchase (Wurtzebach ,Miles and Ethridge 1994).

The increase in this rate of return is considered to result from the behavior of cost of mortgage finance. This is referred by Wutzebach and Miles as mortgage constant. This constant is considered to apply only on the fixed interest source of debt. This constant is the representation of periodic payments made by the investor towards the repayment of the loan facility in form of interest on loan and principle repayment.

The mortgage constant is calculated as shown below:

= rate of interest /{1-[1/(1+ Rate of Interest)^{t}]}

Rate of interest is used as the rate at which mortgage is repaid while t represents the life of the loan. From this therefore, the mortgage rate for the first investment option is given as:

=3.3 %/{1-[1/(1.033)^{3}]}= 2.99%

In order to determine the ability of the leverage to boost generation of return by the investment, we find out the unleveraged returns from the investment by dividing net operating income with the price of purchase of the investment.

In our case this will be given as $30,000/450,000= 6.7%. This rate of return is more than the mortgage constant calculated above. This implies that the investor stands a better chance of making enhanced income by seeking a mortgage to finance part of his investment. However some assumptions must hold for this to be true. One of the assumptions is on the net operating income which is considered to be constant over the holding period of investment. In general therefore, the amount of excess return that an investor gets as a result of using mortgage increases with the increases in the amount of leverage as long as the mortgage constant is less than the unlevered rate of return.

Therefore, with a better consideration on various factors that affects the value of investment, an investor can gain considerable returns by using mortgage to finance investments. However, in the case where the mortgage constant is more than the unleveraged rate of returns, the return on the investment supported by the mortgage will be depressed (Hooke 2010). This therefore, means that the investor will be making low returns that are below the cost of debt.

As a result of this, the investor may be forced to look for ways to finance the principle and the interest rate for the loan. The reason for this may be due to low industrial activities that may lead to low returns. On the other hand, risk can also affect analysis of investment. Risk affects the rate of return required by the mortgage holder. The higher the risk, the higher is the rate of return that will be required by the mortgage holder. This is because they demand to be fully compensated for the extra risk taken by them. With this fact in place therefore, the value of the investment will go down.

## Conclusion

Given the scenarios facing the real estate investor, different factors should be considered before he can decide on which investment to take. One of the most important factors to consider is the risk exposure of each of these investments. Assuming similar exposure to risk, the real estate investor should take the first case since it promises a higher NPV than the second case. This investment has an NPV equal to $186,645 which means that it has the ability to contribute higher returns towards his wealth. He should also use mortgage to finance the investment since by doing this he will be able to enjoy enhanced returns from leverage.

## Reference List

Arsenault M., Hamilton J., Leeds B. and Marcil, G. 2005. *How to Build a Real Estate Empire: Wisdom from the Best in the Business. *Foundations of Wealth Publishing Company,Ohio.

Hooke J., C. 2010*. Security Analysis and Business Valuation on Wall Street: A Comprehensive Guide to Today’s Valuation Methods. *John Wiley & Sons*, *New York.

Kahr, J., and Thomsett M., C. 2005. *Real Estate Market Valuation and Analysis* John Wiley & Sons, New York.

Schmitz, A., and Brett D., L. 2001. *Real Estate Market Analysis: A Case Study Approach. *Urban Land Institute. Stamford.

Simons, R.,A., Malmgren, R. and Small, G. 2008.* Indigenous Peoples and Real Estate Valuation. *Springer, New York.

Sivitanides, P. 2008. *Real Estate Investing for Double-Digit Returns* CreateSpace, New York.

Wang, K, and Wolverton, M., L. 2002. *Real Estate Valuation Theory* Springer, New York.

Wurtzebach ,C., H., Miles M., E. and Ethridge, S., C. 1994. *Modern Real Estate* Wiley, New York.