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1 DISLAIMER: This publication is intended for EDUATIONAL purposes only. The information contained herein is subject to change with no notice, and while a great deal of care has been taken to provide accurate and current information, UB, their affiliates, authors, editors and staff (collectively, the "UB Group") makes no claims, representations, or warranties as to accuracy, completeness, usefulness or adequacy of any of the information contained herein. Under no circumstances shall the UB Group be liable for any losses or damages whatsoever, whether in contract, tort or otherwise, from the use of, or reliance on, the information contained herein. Further, the general principles and conclusions presented in this text are subject to local, provincial, and federal laws and regulations, court cases, and any revisions of the same. This publication is sold for educational purposes only and is not intended to provide, and does not constitute, legal, accounting, or other professional advice. Professional advice should be consulted regarding every specific circumstance before acting on the information presented in these materials. opyright: 2011 by the UB Real Estate Division, Sauder School of Business, The University of British olumbia. Printed in anada. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced, transcribed, modified, distributed, republished, or used in any form or by any means graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution, or used in any information storage and retrieval system without the prior written permission of the publisher.

2 FUNDAMENTALS OF INVESTMENT ANALYSIS, PART II: MULTI-PERIOD ANALYSIS After studying this chapter, a student should be able to: Learning Objectives # explain the rules pertaining to the calculation of apital ost Allowance; # create an after-tax cash flow pro forma, including income tax calculations; # discuss the resale issue and calculate the beforetax and after-tax reversion; # describe the time value of money; # calculate Net Present Value and Internal Rate of Return; and # perform a NPV and IRR analysis on an investment. Introduction In the previous chapter we addressed the issue of measuring costs and benefits associated with real estate investments. In addition, a set of one period investment criteria was introduced and their strengths and weaknesses were presented. All of the work in the previous chapter ignored the details of income tax calculations as they relate to passive real estate investments, and operated on the assumption that single period analysis would be sufficient for investment decision making. The purpose of this chapter is to extend the work from the previous chapter to include: detailed after-tax calculations for real estate returns; and analysis beyond one year to account more formally for the time value of money. In this chapter we will introduce the use of discounted cash flow analysis as a means of selecting from competing investment alternatives. Two basic discounted models will be presented: the net present value model; and the internal rate of return model. These are the most commonly used time adjusted investment decision criteria. The material will be presented in the following order: First, a discussion, albeit in a simplified manner, of the income tax calculations for real estate investments. This discussion will be limited to passive investments in fully developed real estate ventures. The more complete development opportunities or more complex forms of ownership will not be covered. You are encouraged to review the chapter on income tax. Second, the concept of the time value of money and the use of present value models will be developed and illustrated. Finally, extended versions of the investment decision criteria will be introduced. 19.1

3 hapter 19 The objective of this chapter is not to convert real estate licensees into tax lawyers or accountants, but rather to ensure that they have sufficient familiarity to discuss real estate investments and return measures with potential clients who are accustomed to using some of the complex investment decision approaches. After-Tax alculations apital ost Allowance Tax Rules The first step towards a better understanding of the income tax calculations is to explore how taxes are calculated for the annual income derived from rental properties. Three broad income tax principles need to be addressed. Business expenses may be deducted in the calculation of taxable income provided they are incurred with the expectation of making a profit. In general terms, the operating expenses associated with a rental property may be deducted in determining taxable income. In the case of prepaid expenses, they should be allocated over the period for which they properly apply (e.g., a three year insurance premium should be expensed over the three years, not all in the year it is actually paid). Interest expenses, but not principal payments, may be deducted in calculating taxable income providing the debt is used for business or investment purposes. Two points should be noted. First, you may deduct interest expense when the expense is incurred even if the interest is not paid (e.g., on an interest accruing loan). Second, prepaid interest expense generally cannot all be claimed in the year it is paid. Prepaid interest, like other prepaid expenses, is to be allocated over the period to which it rightfully applies. apital expenditures cannot be deducted in calculating taxable income. Instead, providing the capital expenditure is not for land, capital cost allowance (A) is claimed as an annual (non-cash) expense in calculating taxable income. The calculation of A is subject to three general In the year you acquire the capital asset, only half the normal A may be Unless specifically permitted under some specific provision of the Income Tax Act, A cannot be used to create a negative taxable A is not claimed for the year in which the asset is sold. After-Tax ash Flows Illustration 1: Swift Apartments omplex For purposes of illustration consider the purchase of the Swift Apartments omplex (from hapter 18, Illustration 1), costing $585,000. Your accountant has advised you to allocate $450,000 of the purchase price to the building and $135,000 to the land component. She also advises you that this structure qualifies for a 4% A rate. According to your own best estimate, the full year net operating income is estimated to be $71,640. The acquisition is financed using $235,000 equity and a $350,000 mortgage bearing interest at 14% per annum compounded semi-annually. The loan calls for monthly payments of $4, over a 25 year amortization. All rents and operating expenses are assumed to be paid in cash when incurred. There are no prepaid or accrued items. You wish to now estimate the annual before- and after-tax income and before- and after-tax cash flows. In general terms, you will do the calculations as follows: 19.2

4 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis Net Operating Income! Interest expense! A Building = Taxable Income Tax rate = Income Tax Payable and Net Operating Income! Interest expense! Principal payments = Before-tax cash flow! Income tax payable = After-tax cash flow Since you have already learned about the estimation of net operating income (in the previous chapter), the next step in this process is to calculate the annual permitted A. The A calculations can then be incorporated into the income tax calculation and the final step in the process is to determine after-tax cash flows. A Year One: Building ost of Building $ 450,000 A Rate 0.04 = Annual A $18,000 First year rule 0.5 = Maximum Permitted A $ 9,000 (Year One) The investor may claim a maximum of $9,000 A in the first year providing this does not make the taxable income negative. In the case of the Swift Apartments omplex, the taxable income before A is: Net Operating Income $ 71,640! Interest on the debt 47,521 = Taxable income before A $ 24,119! A permitted $ 9,000 = Taxable Income $ 15,119 In this case the investor can claim the full A available, since the taxable income is not made negative. Note that if the taxable income before A was only $5,600, only $5,600 A could be claimed, leaving taxable income at zero. A Year Two: Building Returning to our illustration, we note that the full $9,000 A can be used in the first year. Therefore, the A in the second year is: Original ost $ 450,000! A taken to date 9,000 = Undepreciated apital ost $ 441,000 A rate 0.04 = Maximum A Available $ 17,

5 hapter 19 As the cycle continues, the full after-tax cash flow calculations for an assumed five year holding period is illustrated in Figures 1 to 4. These forecasts assume that rents will increase at 6% per year and expenses will increase at 5% per annum, growth rates which the investor must forecast. Figure 1 Five Year ash Flow Pro Forma Year 1 Year 2 Year 3 Year 4 Year 5 Gross Potential Income $112,000 $118,720 $125,843 $133,394 $141,397 Plus Other Income Less Bad Debt Allowance 1,120 1,187 1,258 1,334 1,414 Less Vacancy Allowance 2,240 2,374 2,517 2,668 2,828 = Effective Gross Income $108,640 $115,159 $122,068 $129,392 $137,155 Less Variable Expenses: Utilities 6,000 6,300 6,615 6,946 7,293 Repairs and Maintenance 4,000 4,200 4,410 4,631 4,863 Services 2,000 2,100 2,205 2,315 2,431 Administration and Payroll 2,400 2,520 2,646 2,778 2,917 Supplies 1,500 1,575 1,654 1,737 1,824 Decorating 2,500 2,625 2,756 2,894 3,039 Management 6,000 6,300 6,615 6,946 7,293 Miscellaneous Total Variable Expenses 25,200 26,460 27,783 29,173 30,632 Less Fixed Expenses: Real Estate Taxes 10,000 10,500 11,025 11,576 12,155 Insurance 1,500 1,575 1,654 1,737 1,824 Other Taxes and Fees Total Fixed Expenses 11,800 12,390 13,010 13,661 14,344 = Net Operating Income $ 71,640 $ 76,309 $ 81,275 $ 86,558 $ 92,179 Figure 2 apital ost Allowance alculations A Building: Year 1 Year 2 Year 3 Year 4 Year 5 Adjusted ost $450,000 $450,000 $450,000 $450,000 $450,000! Accumulated A 0 9,000 26,640 43,574 59,831 = Undep. apital ost 450, , , , ,169 Rate = Maximum A 18,000 17,640 16,934 16,257 0 A Taken 1 $ 9,000 $ 17,640 $ 16,934 $ 16, Year One A = half the maximum No A can be claimed in the year of disposition 19.4

6 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis Figure 3 Income Tax alculations Income Tax alculations Year 1 Year 2 Year 3 Year 4 Year 5 Net Operating Income $ 71,640 $ 76,309 $ 81,275 $ 86,558 $ 92,179! Interest 47,521 47,263 46,967 46,628 46,241! A Building 9,000 17,640 16,934 16,257 0 = Taxable Income 15,119 11,406 17,374 23,673 45,938 Tax Rate = Income Tax Payable $ 7,560 $ 5,703 $ 8,687 $ 11,837 $ 22,969 Figure 4 After-Tax ash Flows Year 1 Year 2 Year 3 Year 4 Year 5 Net Operating Income $ 71,640 $ 76,309 $ 81,275 $ 86,558 $ 92,179 *! Principal $ 1,782 $ 2,040 $ 2,336 $ 2,675 $ 3,062 *! Interest 47,521 47,263 46,967 46,628 46,241 = Before-Tax ash Flow $ 22,337 $ 27,006 $ 31,972 $ 37,255 $ 42,876! Income Tax 7,560 5,703 8,687 11,837 22,969 = After-Tax ash Flow $ 14,777 $ 21,303 $ 23,285 $ 25,418 $ 19,907 * Appendix 1 to this chapter shows the principal and interest calculations for each year of the holding period. Appendix 2 summarizes the calculations in Figures 1 to 4 on one Investment Analysis Worksheet. Average Single Period Return Measures It would be possible to stop at this point and use our single period investment decision criteria but substitute a simple five year average for the one year return measures. For example, we could calculate an average equity dividend rate for five years: Year BTF 1 $ 22, , , , ,876 $161, ,446 Average = = $32,

7 hapter 19 And we could calculate the five year average equity dividend rate: $32,289 EDR = = or 13.7% $235,000 Recall that the single period EDR was 9.50%. While this would be mathematically sound, such averaging ignores the time value of money and for that reason is not commonly used. Later in this chapter we will find ways to reduce these five years of numbers to a single return measure. Resale Value and Residual ash In any analysis of benefits and costs, it is also necessary to include a forecast of the value of the asset at the end of the investment horizon. In the previous chapter, we used a one year investment period and calculated single period returns with appreciation included. In this chapter we will use a five year horizon. Having decided upon the expected holding period (five years in this example), the analyst must forecast the expected sale price of the asset at the end of this holding period. From this forecasted sale price, the analyst must deduct those costs and expenditures occasioned by the sale to arrive at a before and after-tax cash position. ALERT! Holding Period: An immediate question arises: What holding period do we use in the analysis? The answer is to use a holding period (or investment horizon) that is consistent with market practice. This suggests an eight to twelve year period. In fact, we can save some calculations by using the shortest period which will present a typical pattern for future benefits (e.g., cash flows). As a practical matter, periods of either five or ten years are commonly used and, with modern personal computers, we can do the calculations quickly. We will use five years because it captures the typical pattern of cash flows. For our illustration we need to estimate the property value five years in the future. This is essentially a future time appraisal and the estimate of a sale price can be determined by estimating future incomes and capitalization rates or, as is more common, by taking the current value and projecting an annual growth rate for property values (i.e., 6% per annum compound growth). In our example we have forecasted that rents are increasing by 6% per annum. If we simultaneously decide that property values are increasing by 10% per annum, this would imply a significant increase in the gross rent multipliers used in the marketplace, an assumption which would require some explanation. Similarly, in our example we have forecasted that net operating income before reserves will increase from $71,640 to $92,179 over the five years, an increase of 6.505% per annum (remember that operating expenses are only increasing by 5% per annum in the example). Hence if the analyst forecasted that property values were increasing by 10% per annum, this would also imply an increase in the net rent multiplier and would call for some explanation. 19.6

8 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis Net Forecasted Sale Price For the purposes of this illustration, assume that property values are increasing at 6% per annum over the five year period. The property was originally purchased for $585,000 and held for five years, and disposed of at the end of the fifth year. Therefore the expected sale price at the end of five years is: Expected Sale Price = $585,000 (1.06) 5 = $782,862 = $783,000 alculation Press Display PV 585,000 6 I/YR 6 1 O P/YR 1 5 N 5 0 PMT 0 FV -782, On the assumption that the property is sold for $783,000 at the end of the fifth year, the investor pays sale costs (legal, commission), is required to pay the outstanding mortgage and pay the necessary income tax. If one assumes the investor pays a real estate commission of $24,575 (5% on the first $200,000 and 2.5% on the balance) and legal fees of $2,500, the net sale price can be found as follows: Gross Sale Price $ 783,000! Real Estate ommission 24,575! Legal Fees (losing) 2,500 = Net Sale Price (before tax) $ 755,925 Before-Tax Reversion The analyst deducts the outstanding balance on all mortgages after the five year holding period. If any prepayment penalties apply, they must also be deducted. In this example, the original mortgage was in the amount of $350,000 at 14% per annum compounded semi-annually. The amortization period was 25 years with monthly payments of $4, The outstanding balance after 5 years or 60 months would be: 14 O NOM% 14 j 2 2 O P/YR 2 O EFF% j 1 12 O P/YR 12 alculation Press Display omments O NOM% j

9 hapter PV 350,000 Mortgage Amount 300 N 300 Amortization Period 0 FV 0 PMT %/& PMT -4, , Monthly Payment 60 INPUT O AMORT PER Range of payments to be amortized = Principal 60th payment = -3, Interest 60th payment = 338, OSB 60 Assuming there are no prepayment penalties, the before-tax cash reversion would be: Gross Sale Price $ 783,000! ommission 24,575! Legal Fees 2,500 = Net Sale Price $ 755,925! Outstanding Balance on Debt 338,105 = Before-Tax ash Reversion $ 417,820 The original purchase price for this property was $585,000, involving a mortgage in the amount of $350,000 and initial equity of $235,000. The mortgage balance has declined by $11,895 ($350,000! OSB 60) and the equity (on a pre-tax basis) has increased from $235,000 to $417,820. Two factors have contributed to this growth in equity: net capital appreciation and principal repayment on the loan as illustrated in Figure 5. Figure 5 Before-Tax Reversion Analysis 19.8

10 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis Note from Figure 4 that the allocation of the mortgage payments between principal and interest changes over time. The larger allocation to principal accelerates the equity build-up via loan repayment and the interest component of the payment, which is tax deductible, is lower, hence income taxes increase (all other things being equal). After-Tax Reversion In the case of most real estate investments in which the asset includes a building, the investor may face two elements of tax at the time of disposition: a tax on the capital gain and a tax on the recapture of capital cost allowance. The concept of a tax on capital gains is generally well understood even if the details of the calculation are not. Some component of the capital gains (after closing costs) will be subject to taxation, generally either all of the net capital gains or one-half of the gains. It might be noted that in anada we do not have a separate capital gains tax; rather we tax some percent of the net gain as ordinary income. For purposes of illustration, we shall assume that our investor qualifies for capital gains treatment of this investment but that one-half of the capital gain is taxable. As well, we assume our investor has a marginal tax rate of 50%. The tax on capital gain in our example would be determined as follows: Net Sale Price $ 755,925! ost 585,000 = apital Gain $ 170,925 % Taxable.50 = Taxable apital Gain $ 85,463 Tax Rate.50 = Tax on apital Gain $ 42,732 The concept of a tax on the recovery of capital cost allowance requires some comment. During the holding period the investor is claiming capital cost allowance as a non-cash expense for purposes of calculating income tax payable. apital cost allowance is anada ustoms and Revenue Agency's perception of the decline in asset value. In the event the assets (building and fixtures in our example) do not in fact decrease in value by as much as the capital cost allowance claimed over the holding period, then recapture may be deemed to occur at the time the asset is sold. This recapture is subject to taxation. The tax on capital cost allowance recapture will depend upon the value placed upon the depreciable asset (building) upon resale. We will assume the market value of the building and fixtures has not declined (and has in fact increased), and therefore full recapture will occur. Recapture building (total A taken) $ 59,831 (total of all A taken) Total Recapture $ 59,831 Tax Rate.50 = Tax on Recapture $ 29,915 Given these two assumptions concerning the income tax occasioned by the sale, the after-tax reversion is calculated as follows: Gross Sale Price $ 783,000! Real Estate ommissions 24,575! Legal Fees 2,500 = Net Sale Price $ 755,925! Outstanding Debt 338,105 = Before-Tax Reversion $ 417,820! Tax on apital Gain 42,732! Tax on Recapture 29,915 = After-Tax Reversion $ 345,

11 hapter 19 This is illustrated in Figure 6. Figure 6 After-Tax Reversion Analysis Time Value of Money The problem an investor now faces is how to use the forecasted benefits over the investment horizon and make a meaningful decision. While it would be possible to treat money in Year 1 as equivalent to money in Years 2, 3, 4, or 5, we know investors care when they receive their cash following the "A bird in the hand is better than two in the bush" concept. It would be possible to take a simple average of the cash flows over the five year period but this would ignore the time value of money and assume that investors are indifferent as to when expenditures are made and net cash flows are received. In a world where interest can be earned on deposited (or invested) funds, investors prefer a dollar in the present to one received in the future. Thus, a modification of this actual cash flow yield analysis has been developed which has widespread acceptance by professional investors. This method is referred to as the discounted cash flow (DF) method and is the next topic of discussion

12 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis Timing of ash Flows The emphasis in this chapter is on the techniques commonly used to analyze equity investments. While no new analytical concepts are involved (you have used them all in the chapter on mortgage financing), the terminology and the application of the techniques to equity investment are somewhat different. One of the most significant differences is that equity analysis generally involves irregular cash flow patterns, rather than the regular cash flow involved in ordinary simple annuities. Further, in the case of real estate investment analysis, revenues and expenses which occur throughout each year are treated as though they all occur at the end of the year. Thus, the timing of payments within the year is generally ignored; only aggregate, annual figures are considered. There are several reasons for this. First, conventional practice in investment markets is to evaluate investment yields annually: the extra time and effort involved in monthly (or weekly) analysis do not (generally) provide any greater accuracy than that provided by annual analysis. This is particularly significant when the cash flow associated with an investment in a debt vehicle (such as ownership of a mortgage), is contrasted with that associated with an equity investment (such as ownership of an apartment building). The holder of the mortgage is guaranteed, as a term of the contract, that payments of an exact amount will be made on precise dates. On the other hand, the owner of the property estimates the timing and amount of revenue and expenses. These projected figures are subject to uncertainty; vacancy rates, hydro and power rates, taxes, rent levels, turnover, and maintenance and repair costs cannot reasonably be projected on a month-by-month basis. Given this variability, therefore, annual projections are the most practical. Further, using annual estimates reduces, by a factor of twelve, the amount of work involved in analysis without significantly reducing its accuracy (given the foregoing comments about the lack of precision in projection). Note also that the financial analysis involving mortgages deals with the elements of legally binding contracts (as represented by mortgage agreements.) Investment analysis, on the other hand, involves forecasting rather than drawing up financial contracts. Investment analysis is merely one of several components of the study and selection of investment strategies: exact technical precision is not required in this context. In summary, cash flows are assumed to occur at the end of each year simply to facilitate their analysis by means of present value techniques. It is also correct to assume that the projected annual cash flows occur at the beginning or middle of each year, but it is analytically easier to assume that they occur at the end. It is usually assumed that the cash flows, other than the initial investment, occur annually at year end and the discount rates to be applied involve annual compounding. As a matter of practice, the original investment is assumed to occur at time zero. Present Values of osts and Benefits In the application of the present value approach to the analysis of the irregular cash flows associated with equity investments, the investor's required discount rate (expected yield) is used to find the present value of the cash flows. Note that any measure of benefits can be used in determining the present value. Net after-tax cash flow is the most commonly used measure of future benefits but, in some instances, investors may elect to use gross or net rents, gross income, taxable income, or some other indicator of benefits. It is important to remember that the measure of benefits is the "expected future value". In most cases these amounts are not known with certainty but represent someone's best estimate of the future. The present value of the investment is the sum of the present values of net cash flow for each year in the investment. Once determined, the present value of the cash flow is compared to the cost of the investment to determine whether the project is a "good investment". As each cash flow receipt is generally different in size (irregular cash flows), each is discounted over the appropriate time period, and the present values of these individual cash flows are then summed to determine the present value of the total investment

13 hapter 19 Illustration 2: Swift Apartments omplex An investor is considering the purchase of the Swift Apartments omplex. Based on the information obtained from Figure 4, the investor expects the property to produce the following end of year after-tax cash flows as shown in Figure 7. Figure 7 Swift Apartments omplex Five Year After-Tax Net ash Flow Projection Year After-Tax ash Flow 1 $ 14, , , , ,907 + $345,173 If the investor wishes to earn a return of 9% per annum after tax on equity (compounded annually), what is the maximum amount of equity the investor should be prepared to pay for the real estate investment? Note that the after-tax cash flows are equity returns. The investor should be prepared to pay the present value of the future after-tax cash flows (at a 9% discount rate). On a timeline, the projection would look like the following: Time Diagram: alculation Press Display omments O ALL 9 I/YR 1 O P/YR 0 F j F j F j F j F j ,173 F j O NPV ,777 21,303 23,285 25, , , lear all memory registers Discount rate (after tax) No cash flow at time zero Year 1 Year 2 Year 3 Year 4 Year 5 Present Value of Investment 19.12

14 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis It is determined that an investor who requires a minimum return of 9% per annum on equity (compounded annually) should invest no more than $304,751. This maximum is the present value (at j 1 = 9%) of the expected future after-tax cash flows to the equity holder. (Note that $304,751 is the present value only if the discount rate is j = 9%. At any 1 other rate, a different present value would be determined. You may wish to confirm that at j = 7% the present value 1 would be $331,113 and at j = 12% the present value would be $270,060.) Given that the Swift Apartments omplex 1 has a $350,000 mortgage, this implies the investor should be prepared to bid up to $654,751. However, since the asking price is only $585,000 it appears to be a "good buy". Note that, to this point, no mention has been made of the cost of the equity investment. The cost of the investment is only relevant when compared to the present value of the expected cash flows from the investment. If the investor can acquire the investment property for an equity less than $304,751, the investor will earn more than j 1= 9%. For example, if this investment, valued by the investor at $304,751, was acquired for $235,000, the investor (expecting to earn at least 9% per annum, compounded annually) will earn a higher yield. The yield will be approximately 15.6% on equity of $235,000 (calculated by the technique presented in the next section). In general, investors should acquire an asset providing the present value of all future net cash flows, at the investor's discount rate, exceeds the costs of acquiring the asset subject to certain limitations. Note that this investment criteria cannot be directly used to compare investments unless they all happen to cost the same. Net Present Value A common variation, or extension, of present value analysis is the net present value. The net present value is the difference between the present value of all future cash flows and the cost of the investment. Net Present Value = Sum of the PV of the Net ash Flows! Investment ost Using the investment described in Illustration 2, the net present value is calculated as: Net Present Value = $304,751! $235,000 NPV = $69,751 Note that in the previous calculator steps, the first F entered (F ) was 0. When calculating the Present Value of future j 0 cash flows, the calculator requires that 0 be entered as the investment cost, and that the NPV key be used. When 0 is entered as the investment cost, the NPV is equal to the Present Value because: and NPV = Sum of PVs of Net ash Flows! Investment ost NPV = Sum of PVs of Net ash Flows! 0 PV = Sum of PVs of Net ash Flows so NPV = PV when Investment ost =

15 hapter 19 O ALL 0 lear all memory registers 9 I/YR 9 Discount rate (after-tax) 1 O P/YR 1 alculation Press Display omments %/& F j -235,000 Investment ost F j 14,777 Year F j 21,303 Year F j 23,285 Year F j 25,418 Year F j 365,080 Year 5 O NPV 69, NPV of investment As a general rule, if the net present value, at the investor's required rate of return, is greater than zero, then the investment is acceptable. The net present value is the amount by which investment value (at a specified required rate of return) exceeds the cost of acquiring the asset. Illustration 3 A local real estate investment group is considering the acquisition of a real estate investment. The forecasted net cash flows are as follows: Year Net ash Flow 1 $ 12, , , , ,000 ost $ 45,000 Problem: The investment group would like to earn at least 11% per annum, compounded yearly, on their investment. alculate the present value and the net present value. alculation Press Display omments O ALL 11 I/YR 1 O P/YR 0 F j Fj ,000 lear all memory registers Discount Rate (after-tax) Year F j 12,800 Year

16 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis F j F j F j O NPV 13,600 14,400 15,000 49, Year 3 Year 4 Year 5 PV of the Investment Solution: Present Value at 11% = $49, Net Present Value = $49,531.28! Investment ost Net Present Value = $49,531.28! $45,000 = $4, Profitability Index The net present value provides a useful investment rule (i.e., invest if the net present value is greater than zero) but it is only of limited use if you are comparing two or more investments which are of similar size. For example, if you have three investment options and you are to select one, which do you select? Alternative Net Present Value (at the required return) A $ 100 B $ 200 $ 300 The answer is not obvious since you do not know how much you gain per dollar invested. All three provide the required return plus some extra. If all three cost $90, then you select the project with the highest net present value, Alternative, since it provides the most "extra" (over and above the discount rate). What happens, however, if each has a different cost? Alternative Present Value! ost = Net Present Value A $ 180! $ 80 = $ 100 B $ 280! $ 80 = $ 200 $ 700! $ 400 = $ 300 Now which is best? All three provide the required rate of return (which is the discount rate). Projects A and B cost the same, but Project B gives a larger net present value and should be selected over A. But what about Project? The profitability index is introduced to resolve this problem. The profitability index (PI) is: Profitability Index = Present Value of Positive ash Flows Present Value of Negative ash Flows As net cash flows are positive in most cases in this course, the Present Value of Negative ash Flows would be the Acquisition ost of the investment

17 hapter 19 And for the three alternatives, the profitability index would be: $180 PI A = = $280 PI B = = $700 PI = = The selection rule is to select the investment with the highest profitability index (Project B) from the menu of alternatives. Note that Project gives the highest absolute net present value ($400) but Project B provides the most extra per dollar invested ($3.50 extra per dollar invested). In the case of the Swift Apartments omplex, the profitability index is: $304,751 Profitability Index = = $235,000 And if the choice is whether or not to invest in a particular project, we take any project with a profitability index of 1.0 or more and take the project with the highest profitability index from among those on the menu of alternatives. Internal Rate of Return Analysis The present value measures considered thus far provide an indication of whether or not an investment may satisfy an investor's minimum criteria with respect to cost and value. For example, it was determined that the investment was worth equity of $304,751 at j 1 = 9%. If the investor could acquire the investment with an equity of $235,000, each of the various investment criteria indicate that the investor would earn more than the required 9%; that is, the present value exceeds the cost, the NPV is greater than zero, and the profitability index is greater than 1.0. However, these measures do not provide a measure of the yield the investor expects to earn (unless it is purchased for exactly its present value). The discounted cash flow or present value measure which provides information regarding the yield on an investment, is called the internal rate of return. Internal rate of return (IRR) analysis determines the rate of discount that the investor expects to earn where a property is purchased at a specified price, and then compares this rate to the minimum yield required by the investor. In the application of IRR analysis, it is assumed that the investor will acquire the asset at its current acquisition cost (or some other specified acquisition cost), expecting to receive the estimated net after-tax cash flows. The objective of the analysis is to determine the rate of interest at which the present value of the net cash flows equals the amount invested; alternatively, one is seeking the discount rate (or the internal rate of return) at which the net present value of the investment is exactly equal to zero. Thus, the internal rate of return is defined as the rate of interest that will exactly equate the present value of the benefits to the initial acquisition cost (or the discount rate that would result in a net present value of zero). Problem: Using the information from the Swift Apartments omplex, calculate the internal rate of return on the investment (which has a cost or initial equity of $235,000 since we are using equity returns and provides the following estimated after-tax cash flows): 19.16

18 Year Net After-Tax ash Flow 1 $ 14, , , , ,907 + $345,173 O ALL 0 lear all memory registers 1 O P/YR %/& F j -235,000 Investment ost F j 14,777 Year F j 21,303 Year F j 23,285 Year F j 25,418 Year F j 365,080 Year 5 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis Previous analysis determined that the net present value of the investment was $69,751 when the future benefits were discounted at 9%. As one wishes to determine the discount rate at which the net present value equals zero, it is apparent that the interest rate must be higher to reduce the net present value of the cash flows to zero. alculation Press Display omments O IRR/YR IRR (takes a few seconds to calculate) The internal rate, using the information from Swift Apartments omplex is approximately 15.6%. For all practical purposes, given the number of assumptions that went into the projection of net cash flow figures into the future, it would be sufficient to say that the internal rate of return on this investment is approximately 16% per annum, compounded annually. The apparent precision that is implied by a statement that the IRR is 15.6% may be misleading, in that it may cause a false sense of accuracy given that the source of the net cash flows were forecasts for five years in the future. However, for calculations on assignments and examinations, exact answers may be required. In summary, the Swift Apartments omplex investment can be described as having: a present value of $304,751 (at 9%); a net present value of $69,751 (at 9%); a profitability index of (at 9%); and an internal rate of return of 15.6%. The advantage of the internal rate of return measure is that the result of the analysis (15.6%) is in a form with which investors are familiar in the context of the analysis of investments. For instance, an investor may accept an investment if the internal rate of return is equal to or exceeds his or her minimum required rate. In the illustration under consideration, the investment is acceptable since the internal rate of return (15.6%) exceeds the investor's required rate of 9%

19 hapter 19 omparison of the Present Value and Internal Rate of Return Approaches Each of the measures discussed indicates to an investor whether an investment exceeds certain minimum requirements. If an investment has a net present value greater than zero, a profitability index greater than 1.0, or an internal rate of return greater than the required internal yield rate, that investment will be attractive according to that particular technical criterion. If an investor only wishes to know if an investment exceeds a certain minimum level according to these criteria and does not want to compare investments or to choose between alternative investments, these measures will be of some use. These multi-period investment decision criteria can then be summarized as shown in Figure 8. Figure 8 Summary: Multi-Period riteria Rule hoose One Investment From a Menu Decide to Invest Net Present Select project with highest NPV Select if NPV is equal to or Value (Only good if all alternatives greater than 0 have the same cost) Profitability Select project with highest Select if PI is equal to or Index profitability index greater than 1.0 Internal Select project with highest IRR Select if IRR is equal to or Rate of Return greater than required yield In most investment decisions, the IRR decision rule and the PI decision rule will point to the same choice from the menu of alternatives. Similarly the IRR, NPV, and PI rules will generally point to the same decision whether or not to invest. On occasion, these investment decision rules misbehave: one rule says select Alternative A and the other rule says select Alternative B. For example: Project IRR PI A 20% 1.5 B 18% 1.8 The IRR rule says select "A" and the profitability index says select "B". This does not occur often but when it does, it generally arises because of the implicit assumptions regarding the re-investment of cash flows during the investment period. Such problems are beyond the scope of this chapter, but students should be aware that the issue can arise. Risk Analysis and onclusions We began the previous chapter by outlining several key issues in the investment process. These included: the need to forecast and quantify costs and benefits; the need to develop and employ some decision criteria; and the need to account for risk in our investment decision making

20 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis The first two issues have been addressed. The chapter outlined alternative measures of costs and benefits and different investment criteria as follows. Alternative ways to measure costs and benefits include the following: Initial ost After-Tax Income Initial Equity After-Tax ash Flow Gross Rent Resale Price Net Rents (Net Operating Income) Before-Tax ash Residual Before-Tax Income After-Tax ash Residual Before-Tax ash Flow The weight of popular opinion is to use cash flows, either before or after tax, before or after financing, rather than measures of income. The investment criteria are: Single Gross Rent Multiplier Net Rent Multiplier Return on Investment Equity Dividend Rate ash on ash Return ( on Return on Equity Net Present Value Profitability Index Internal Rate of Return (IRR) The last item risk has not been addressed. Unfortunately, we know considerably less about how to measure and estimate risk. However, we do have some ideas on how to incorporate risk into our analysis. In general, we apply the various investment decision criteria to help us select investments from a menu of alternative investments having similar risk (e.g., compare various apartment buildings, not apartment buildings and raw land). However, if we compare investments with different risk, then the practice is to adjust the discount rate or required rate of return to reflect differing risks. For example, we may use a 9% discount rate for the Swift Apartments omplex but a 10% discount rate when analyzing a hotel investment. This is referred to as a risk-adjusted discount rate. Just how much we adjust the rate for different risk classes is less clear since we do not have a good yardstick for measuring risk

21 hapter 19 APPENDIX 1 Principal and Interest alculations for Swift Apartments omplex PRESS DISPLAY OMMENTS O ALL 14 O NOM% 2 O P/YR O EFF% 12 O P/YR O NOM% PV = N 0 FV , j 2 j 1 j 12 Mortgage Amount Amortization Period PMT -4, Monthly Payment %/& PMT -4, Re-enter rounded Payment 1 INPUT 12 O AMORT PER 1-12 Year 1 = -1, Principal = -47, Interest = 348, OSB INPUT 24 O AMORT PER Year 2 = -2, Principal = -47, Interest = 346, OSB INPUT 36 O AMORT PER Year 3 = -2, Principal = -46, Interest = 343, OSB INPUT 48 O AMORT PER Year 4 = -2, Principal = -46, Interest = 341, OSB INPUT 60 O AMORT PER Year 5 = -3, Principal = -46, Interest = 338, OSB

22 Fundamentals of Investment Analysis, Part II: Multi-Period Analysis APPENDIX 2 Investment Analysis Worksheet (This is provided for study purposes only) Net Operating Income alculation: Year Year Year Year Year 6 GROSS POTENTIAL RENTAL INOME 7 + Other Income 8 - Bad Debt (ollection Loss) Allowance 9 - Vacancy Allowance 10 = EFFETIVE GROSS INOME 11 - Variable Expenses 12 - Fixed Expenses 13 NET OPERATING INOME Mortgage alculations: 14 ANNUAL MORTGAGE PAYMENT 15 Principal Portion 16 Interest Portion 17 OUTSTANDING BALANE at Year End A alculation: 18 Adjusted Building ost to Date 19 - Accumulated A 20 = Undepreciated apital ost 21 Allowable A Rate 22 = Maximum A Allowable 23 A TAKEN Income Tax alculation: 24 Net Operating Income Interest Portion of Mortgage Payment A Taken = Taxable Income 28 Tax Rate 29 = TAX PAYABLE ON ASH FLOWS 19.21

23 hapter 19 Reversion ash Flow alculation: 30 Gross Sale Price 31 - Legal Fees 32 - ommission 33 = NET SALE PRIE 34 - ost of Land & Building 35 = apital Gain 36 Percentage of apital Gain which is Taxable 37 = Taxable apital Gain 38 Income Tax Rate 39 = INOME TAX PAYABLE ON APITAL GAIN Lower of: Adjusted ost OR Net Sale Price of Building 41 - Undepreciated apital ost = Taxable Recapture of apital ost 43 Tax Rate 44 = INOME TAX PAYABLE ON REAPTURE 45 NET SALE PRIE Outstanding Balance = Before Tax ash Reversion 48 - Income Tax Payable on apital Gain Income Tax Payable on Recapture = AFTER TAX REVERSION SUMMARY Year Year Year Year Year 51 Net Operating Income Annual Mortgage Payments = BEFORE TAX ASH FLOWS (BTF) 54 - Tax Payable on ash Flows = AFTER TAX ASH FLOWS (ATF) 56 + After Tax Reversion = TOTAL AFTER TAX ASH FLOWS INTERNAL RATE OF RETURN = NET PRESENT VALUE AT % = 19.22