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CHAPTER 1 THE NATURE OF REAL ESTATE AND REAL ESTATE MARKETS Study Questions 1 D U 4 The term real estate can be used in three fundamental ways List these three alternative uses or definitions Solution Real estate is most commonly defined as land and any improvements made to or on the land including fixed structures and infrastructure components The term is also used to describe the bundle of rights associated with the ownership and use of the physical characteristics of space and location Finally real estate may be described as the business activities related to the development construction acquisition operation and disposition of real property assets The US represents about 6 percent of the earth s land service or approximately 23 billion acres Who actually owns this land What is the distribution of this land among the various uses eg developed land federal land forest land Solution Developed land consisting of residential industrial commercial and institutional land represents approximately 6 percent of the total land in the US Federal lands and water areas occupy about 23 percent of the land crop land and CRP land represent about 21 percent and pasture land comprises about 6 percent of the land Finally the remaining land is divided between range land and forest land with each representing 21 percent of all US land Describe the value of US real estate by comparing it to the values of other asset classes eg stocks bonds Solution As of September 2005 real estate including owner occupied housing but excluding real estate held by non real estate corporations was the single largest asset class in the US valued at approximately 234 trillion Publicly traded corporate equities equated to about 172 trillion of the US market The value of mortgage debt is approximately 111 trillion This is larger than the existing stock of both corporate and foreign bonds and the outstanding value of US Treasury Securities How much of the wealth of a typical US household is tied up in real estate How does this compare to the role that assets and investments play in the portfolios of US households Solution Real estate is the single largest asset in the typical US household s portfolio representing approximately 30 percent of household wealth in September of 2005 In comparison the total value of corporate stocks and mutual fund shares represents 16 percent of household assets Pension reserves excluding stocks represent 17 percent of household assets Deposits and money market funds represent 9 percent of household assets LI 9 Real estate assets and markets are unique when compared to other assets or markets Discuss the primary ways that real estate markets are different from the markets for other asset that trade in well developed public markets Solution Real estate is unlike other asset classes because it is heterogeneous and immobile Real estate assets have unique and distinctive characteristics such as age building design and location Real estate is also immobile therefore location is an important attribute Because real estate assets are heterogeneous and immobile real estate markets are localized Potential users of real property and competing real estate are typically located in the same area or region Additionally real estate markets are highly segmented because of their heterogeneous nature Therefore potential users of a specific type of real property generally do not seek to substitute one property category for another Finally most real estate transactions are privately negotiated and have relatively high transaction costs Identify and describe the interaction of the three economic sectors that affect real estate value Solution The three economic sectors that in uence real estate value are user markets capital markets and government In real estate user markets households and firms compete for physical location and space This competition determines who will obtain the use of a specific property and how much will be paid for the use of this property Capital markets provide the financial resources necessary for the development and acquisition of real estate assets Real estate competes for resources against other investment opportunities in the capital market based on investor required rates of returns and risk considerations Capital markets are segregated into two categories equity interests and debt interests Government in uences the interaction between the user markets and capital markets through tax policy regulations provisions of services and infrastructure subsidies and other means CHAPTER 14 THE EFFECTS OF TIME AND RISK ON VALUE Study Questions 1 Dr Bob Jackson owns a parcel of land that a local farmer has offered to rent for the next 10 years The farmer has offered to pay 20000 today or an annuity of 3200 at the end of each of the next 10 years Which payment method should Dr Jackson accept if his required rate of return is 10 percent Solution Dr Jackson should choose the payment method that maximizes his net present value If he chooses the lump sum payment the net present value is simply the 20000 he will receive today If he chooses the annuity plan the net present value will be only 1966261 N210 110 PV PMT3200 FV0 Therefore Dr Jackson should choose the lump sum payment of 20000 2 You are able to buy an investment today for 1000 that gives you the right to receive 438 in each of the next three years What is the internal rate of return on this investment Solution This is simply a yield calculation problem Like any time value of money problem we are given four inputs and are asked to solve for the fifth In this case we must solve for the interest rate as follows N3 17 PV 1000 PMT438 FV0 Solving this setup tells us the above loan yields a 15 percent return 3 Calculate the present value of the income stream given below assuming a discount rate of 8 percent What happens to value if the discount rate increases to 20 percent ear Solution This problem is solved by entering the annual income stream and discount rate into the cash ow registers of any standard financial calculator and solving for the net present value Assuming an 8 discount rate the income stream is valued at 1170516 Alternatively if the discount rate is 20 the value of the income stream will be 923225 4 Calculate the IRR and NPV for the following two investment opportunities Assume a 16 percent discount rate for the NPV calculations Solution To solve this problem simply enter each set of cash ows into the cash ow registers of your financial calculator and ask it to find the IRR For Project 1 the internal rate of return is 1616 while for Project 2 the internal rate of return is 2123 The NPV for Project 1 is 3629 and the NPV for Project 2 is 93321 If these projects were independent each IRR should be individually compared to the required rate of return to determine whether the investment should be made However if the projects are mutually exclusive and are of equivalent risk Project 2 is preferred to Project 1 Addtionally the higher NPV of Project 2 clearly makes this alternative the most attractive investment option because the investor s net worth will increase by 93321 5 How much would you pay for an investment that provides 1000 at the end of the first year if your required rate of return is 10 percent Now compute how much you would pay at 8 percent and 12 percent rates of return Solution At 10 an investor would be willing to pay 90909 N1 110 PV PMT0 FV1000 At 8 an investor would be willing to pay 92593 N1 I8 PV PMT0 FV1000 At 12 an investor would be willing to pay 89286 N1 112 PV PMT0 FV1000 Chapter 15 Mortgage Calculations and Decisions Study Questions 1 D U Calculate the original loan size of a fixed payment mortgage if the monthly payment is 114678 the annual interest is 80 and the original loan term is 15 years Solution Rounding to the nearest whole dollar the original size of the loan is 120000 This problem is solved using the following keystrokes on a financial calculator N180I8l12 PVPMT114678 FV0 For a loan of 100000 at 7 percent interest for 30 years find the balance at the end of 4 years and 15 years Solution The loans balance at the end of 4 years and 15 years is 9547455 and 7401887 respectively as solved below First the loan payment must be calculated The loan payment is 66530 as solved below N360125833IPV 100000PMTFV0 The balance at the end of four years is 9547455 which is calculated by entering the following data into a financial calculator N312 125833 PV 7 PMT 66530 FV 0 The balance at the end of 15 years is 7401887 which is calculated by entering the following data into a financial calculator N180125833IPVIPMT66530FV0 On an adjustable rate mortgage do borrowers always prefer smaller tighter rate caps that limit the amount the contract interest rate can increase in any given year or over the life of the loan Solution Borrower preference is dependent at least in part on their expectations of future interest rates Borrowers choosing ARMS with price caps are charged a higher initial interest rate a higher margin more upfront costs or a combination of the three The borrower must consider these factors For example borrowers may prefer larger caps if they believe interest rates will not increase substantially In this scenario the loan interest rate will be lower because the borrower not the lender bears the risk of interest rates increasing 4 LI Consider a 75000 mortgage loan with an annual interest rate of 8 The loan term is 7 years but monthly payments will be based on a 30 year amortization schedule What is the monthly payment What will be the balloon payment at the end of the loan term Solution The monthly payment is 55032 and the balloon payment is 6935807 The payment is calculated using the following calculator keystrokes N360I667PV 75000PMTFV0 The balloon payment at the end of year seven is 6935807 as calculated with the following calculator keystrokes N276I667IPVIPMT55032IFV0 A mortgage banker is originating a level payment mortgage with the following terms Annual interest rate 9 percent Loan term 15 years Payment frequency monthly Loan amount 160000 Total up front financing costs including discount points 4000 Discount points to lender 2000 a Calculate the annual percentage rate APR for Truth in Lending purposes b Calculate the lender s yield with no prepayment c Calculate the lender s yield with prepayment is five years d Calculate the effective borrowing costs with prepayment in five years Solution The first step is to solve for the payment which is 162283 with the following calculator keystrokes N180175IPV 160000PMTIFV0 a The APR is approximately 943 percent as solved below N 180 I 7 PV 156000 PMT 162283 FV 0 b The lender s yield to maturity is 922 percent N 180 I 7 PV 158000 PMT 162283 FV 0 0 l 00 c In order to calculate the lender s yield the loan balance remaining at the end of year five must first be calculated N120I75IPVIPMT162283IFV0I The remaining balance is 12810867 With this information the lender s yield is 934 percent as calculated below N 60 I 7 PV 158000 PMT 162283 FV 12810867 d The effective borrowing cost with prepayment in five years is 969 percent N 60 I 7 PV 156000 PMT 162283 FV 12810867 Give some examples of up front financing costs associated with residential mortgages What rule can one apply to determine if a settlement closing cost should be included in the calculation of the effective borrowing costs Solution Examples of upfront costs include discount points loan origination fee loan application and documentation preparation fees appraisal fees credit check fees title insurance mortgage insurance charges to transfer the deed and record the mortgage pest inspection survey costs and attorney s fees The effective borrowing cost calculation should not include expenses that would be incurred if no mortgage financing were obtained Therefore only upfront costs associated with obtaining the mortgage funds should be included A homeowner is attempting to decide between a 15 year mortgage loan at 55 percent and a 30 year loan at 590 percent What would you advise What would you advise if the borrower also has a large amount of credit card debt outstanding at a rate of 15 percent Solution If the borrower does not have a significant amount of debt at a rate well above the rates on the loan then the difference in mortgage rates should be viewed as a maturity premium difference and the borrower can consider the loans as equivalent on a purely financial basis If the borrower owes significant amounts of high interest consumer debt then the longer term loan is preferable It will have a lower present value present cost discounted at the borrower s opportunity cost In other words if the opportunity costs of the household are substantially greater than the mortgage interest rate the household will be better off with the longer term mortgage Suppose a one year ARM loan has a margin of 275 an initial index of 300 percent a teaser rate for the first year of 400 percent and a cap of 100 percent If the index rate is 300 percent at the end of the first year what will be the interest rate on the loan in year two If there is more than one possible answer what does the outcome depend on 0 Solution If the periodic cap applies to the teaser rate the interest rate in year two will be constrained to 500 percent If the cap applies only to index plus margin the rate in year two would be 575 percent one year Treasury rate Loan amount Annual rate cap Life of loan cap Margin First year contract rate One year Treasury rate at end of year 1 One year Treasury rate at end of year 2 Loan term in years Assume the following for a one year rate adjustable rate mortgage loan that is tied to the 150000 2 5 275 550 525 550 30 Given these assumptions calculate the following a Initial monthly payment b Loan balance end of year 1 c Year 2 contract rate d Year 2 monthly payment e Loan balance end of year 2 f Year 3 contract rate g Year 3 payment Solution a The first year payment based on an interest rate of 55 percent is 85168 as calculated below N 360 I 4583 PV 150000 PMT 7 FV 0 b The loan balance at the end of year one is 147979 as shown below N348 124583 PVz PMT 85168 FV 0 c Assuming the annual cap applies to the teaser rate the interest rate in year two is 550 plus 200 or 750 percent d With a remaining term of 29 years interest rate of 75 percent and a balance of 14797941 the new payment in year 2 is 104432 calculated on a financial calculator with the following keystrokes N 348 I 6250 PV 147979 PMT 7 FV 0 e The loan balance at the end of year two is 146496 N 336 I 6250 PV 7 PMT 104432 FV 0 f The year three contract interest rate is index plus margin or 825 percent g The year three payment based on a balance of 146496 remaining term of 28 years and an interest rate of 825 percent is 1119 CHAPTER 18 Investment Decisions Ratios Study Questions Use the following information to answer questions 1 7 3 You are considering the purchase of an office building for 15 million today Your expectations include the following first year potential gross income of 340000 vacancy and collection losses equal to 15 percent of potential gross income operating expenses equal to 40 percent of effective gross income and capital expenditures equal 5 percent of EGI You expect to sell the property five years after it is purchased You estimate that the market value of the property will increase four percent a year after it is purchased and you expect to incur selling expenses equal to 6 percent of the estimated future selling price 1 What is estimated effective gross income EGI for the first year of operations Solution Item Amount Potential gross income PGI 340000 less VampC allowance at 15 of PGI 51000 Effective gross income EGI 289000 What is estimated net operating income N01 for the first year of operations Solution Item Amount Effective gross income EGl 289000 less Operating expenses OE 115600 less Capital expenditures CAPX 14450 Net operating income NOI 158950 What is the estimated going in cap rate R0 using N01 for the rst year of operations Solution The overall cap rate is 106 percent 158950 1500000 An investment opportunity having a market price of 1000000 is available You could obtain a 750000 25 year mortgage loan requiring equal monthly payments with interest at 70 percent The following operating results are expected during the first year Effective gross income 200000 Less operating expenses and CAPX 100000 Net operating income 100000 For the first year only determine the a Gross income multiplier Solution Market price Effective gross income 2 1000000 200000 2 50 b Operating expense ratio including CAPX Solution Operating expenses Effective gross income 2 100000 200000 2 050 or 50 percent c Monthly and annual payment Solution Monthly payment is 530084 Annual payment is 6361013 d Debt coverage ratio Solution NOI Annual debt service 2 100000 63610 157 e Overall capitalization rate Solution NOI Market price 2 100000 1000000 2 10 percent f Equity dividend rate Solution Before tax cash ow Equity 2 36390 250000 2 146 percent Note Equity investment 2 Acquisition price 7 loan amount 2 1000000 750000 You are considering the purchase of a quadruplex apartment Effective gross income EGI during the first year of operations is expected to be 33600 700 per month per unit First year operating expenses are expected to be 13440 at 40 percent of EGI Ignore capital expenditures The purchase price of the quadruplex is 200000 The acquisition Will be financed With 60000 in equity and a 140000 standard fixed rate mortgage The interest rate on the debt financing is eight percent and the loan term is 30 years Assume for simplicity that payments will be made annually and that there are no up front financing costs a What is the overall capitalization rate Solution N01 2 EGI 7 operating expenses 2 33600 7 13440 20160 NOI Market price 2 20160 200000 2 1008 percent b What is the effective gross income multiplier Solution Market price Effective gross income 2 200000 33600 595 c What is the equity dividend rate the before tax return on equity Solution Debt service 2 12436 as calculated below N30IYR8PV140000PMTFV0 Before tax cash ow 2 N01 Debt service 20160 12436 7724 Equity dividend rate Before tax cash ow equity invested 7724 60000 1287 percent d What is the debt coverage ratio Solution DCR NOI debt service 2 20160 12436 162 e Assume the lender requires a minimum debt coverage ratio of 12 What is the largest loan that you could obtain if you decide to borrow more than 140000 Solution Debt service must be such that the following relationship holds L 212 Debt Service But debt service is equal to the loan amount times the mortgage constant contract interest rate plus principal amortization Thus we can rewrite the above expression as NO 2 1 loan amount x mortgage constant Rearranging N01 1 2 10d amount 6 mortgage constant or NO 12 x mortgage constant loan amount For our problem 20160 12 x 00888 loan amount The mortgage constant is the stated interest rate plus the first year principal payment divided by the loan amount 1236140 000 0088 or 0888 20160 01066 loan amount 189130 2 loan amount Why do Class B properties generally sell at higher going in cap rates than Class A properties Solution Relative to class A properties class B properties are more risky andor are expected to produce smaller rental increases over time Both effects reduce the amount a rational investor is Willing to pay today per dollar of current income When valuesprices fall relative to current net rental income cap rates increase Why might a commercial real estate investor borrow to help finance an investment even if she could afford to pay 100 percent cash Solution Borrowing ie the use of other people s money iis also refereed to as the use of financial leverage If the overall return on the property exceeds the cost of debt the use of leverage can significantly increase the rate of return investors earn on their invested equity This expected magnification of return often induces investors to partially debt finance even if they have the accumulated wealth to pay all cash for the property CHAPTER 19 Investment Decisions NPV and IRR Study Questions 1 List three important ways in which DCF valuation models differ from direct capitalization models Solution Direct capitalization models require an estimate of stabilized income for one year DCF models require estimates of net cash flows over the entire expected holding period In addition the cash ow forecast must include the net cash ow expected to be produced by the sale of the property at the end of the expected holding period Finally the appraiser must select the appropriate yield required IRR at which to discount all future cash ows or to use as the hurdle rate in an IRR analysis Why might a commercial real estate investor borrow to help finance an investment even if she could afford to pay 100 percent cash Solution Borrowing ie the use of other people s money iis also refereed to as the use of financial leverage If the overall return on the property exceeds the co st of debt the use of leverage can significantly increase the rate of return investors earn on their invested equity This expected magnification of return often induces investors to partially debt finance even if they have the accumulated wealth to pay all cash for the property Other potential benefits of leverage include the ability to break through equity capital constraint in order to acquire more NPV projects the ability to apply the owneroperator s comparative advantage in acquisition and management to more projects and increased portfolio diversification Using the CE key of your financial calculator determine the IRR of the following series of annual cash ows CFO 31400 CF1 3292 CF2 3567 CF3 3850 CF4 4141 and CF5 50659 Solution IRR 1851 A retail shopping center is purchased for 21 million During the next four years the property appreciates at 4 percent per year At the time of purchase the property is financed with a 75 percent loan to value ratio for 30 years at 8 percent annual with monthly amortization At the end of year 4 the property is sold with 8 percent selling expenses What is the before tax equity reversion Solution Item Amount Loan amount 2 075 x 2100000 1575000 Monthly payments 1155679 Remaining mtg balance 1515450 Selling price 2100000 x 1044 less Selling expenses at 8 of SP Net selling price less Unpaid mtg balance Before tax equity reversion State in no more than one sentence the condition for favorable financial leverage in the calculation of NPV Solution Increasing the use of leverage Will increase the calculated NPV if the discount rate exceeds the effective cost of mortgage debt State in no more than one sentence the condition for favorable financial leverage in the calculation of the IRR Solution Increasing the use of leverage Will increase the calculated IRR if the unlevered IRR exceeds the effective cost of mortgage debt 2456703 196536 2260167 1515450 744717 An office building is purchased With the following projected cash ows NOI is expected to be 130000 in year 1 With 5 percent annual increases The purchase price of the property is 720000 100 equity financing is used to purchase the property The property is sold at the end of year 4 for 860000 With selling costs of 4 percent The required unlevered rate of return is 14 percent a Calculate the unlevered internal rate of return IRR b Calculate the unlevered net present value NPV Solution Net Present Purchase Operating Net Sale Total Cash Value at Year Price Income Proceeds Flow 14 0 720000 720000 720000 1 130000 130000 114035 2 136500 136500 105032 3 143325 143325 96740 4 150491 825600 976091 577924 a IRR 2188 percent b NPV 173732 CHAPTER 20 INCOME TAXATION AND VALUE Study Questions 1 D L 4 Why do investors generally care whether the IRS classifies cash expenditures as operating expenses rather than capital expenditures Solution Operating expenses are generally deductible for income tax purposes in the year they are paid Capital expenditures are added to the tax basis of a property treated like a separate building and expensed through annual depreciation deductions Tax benefits like other cash ow benefits have higher present values When they are received sooner rather than later How are the discount points associated With financing an income property handled for tax purposes Solution All up front financing costs are amortized over the life of the loan used to finance the purchase If the loan is prepaid before the end the loan term the remaining up front financing costs are fully deductible in the year in Which the loan obligation is extinguished What Will be the taxes due on sale Assume 6 selling costs 33 percent ordinary income tax rate a 15 percent capital gains tax rate and a 25 percent recapture rate Solution Annual depreciation deduction 750000 x 1275 2 2727273 Total depreciation over 5 years 5 x 2727273 2 136364 Sale Price 1270000 Less Selling Expenses 6 76200 Net Sale Proceeds 1193800 Less Adjusted Basis 1000000 136364 or five 863636 years of 2727273 in annual depreciation Taxable Gain 330164 Less Depreciation Recapture 136364 Capital Gain 193800 Capital Gain tax 15 29070 Add Depreciation Recapture tax 25 x 136364 34091 Taxes Due on Sale 63161 What will be the after tax equity reversion cash ow from the sale LI 0 Solution Net Sale Proceeds 1193800 Less Remaining loan balance 666648 Before Tax Equity Reversion 527152 Less Taxes Due on Sale 63161 After Tax Equity Reversion 463991 N25 112 PV 700000 and FV0 results in a yearly payment of 8924998 The remaining loan balance at the end of year 5 is 666648 N20 112 PV and PMT 8924998 Over the entire five year holding period how much were your taxes from rental operations reduced by the annual depreciation deductions Solution The amount of taxes saved from the annual tax depreciation is the total depreciation claimed of 136364 times 33 the ordinary income tax rate or 45000 What are the four classifications of real estate holdings for tax purposes Which classifications of property can be depreciated for tax purposes Solution The four classes of real estate holdings for tax purposes are 1 real estate held as a personal residence 2 real estate held for sale to others or dealer property 3 real estate held for use in a trade or business activity or trade or business property and 4 real estate held for investment or investment property Generally only property used in a trade or business or for the production of income such as rental real estate can be depreciated What is your annual depreciation deduction Solution The annual depreciation deduction is 3571429 adjusted basis of 100000028 years If you never sold the property what would be the present value of the annual tax savings from depreciation Solution The present value of the annual tax savings from depreciation is 9306568 N28 110 PMT3571429 x 028 and FV0 If you sold the property at the end of five years what would be the present value of the depreciation deductions net of all taxes due on sale Solution After tax value of annual depreciation deduction 3571429 X 028 10000 Present value of annual deduction 2 3790787 N25 IYR10 PV PMT10000 and FV0 Total depreciation over 5 years 5 x 3571429 2 17857145 Depreciation recapture tax at end of year 5 17857145 x 025 2 4464286 Present value of depreciation recapture tax 2 2771970 N25 IYR10 PV PMT0 and FV4464286 The NPV of the depreciation deductions over 5 year holding period is 10188 3790787 2771970 O Black Acres Apartment Inc needs to compute taxable income TI for the preceding year and wants your assistance The effective gross income EGI was 52000 operating expenses were 19000 2000 was put into a fund for future replacement of stoves and refrigerators debt service was 26662 of which 25126 was interest and the deprecation deduction was 17000 Compute the taxable income from operations Solution Effective Gross Income 52000 Less Operating Expenses 19000 Less Capital Expenditures 2000 Net Operating Income 31000 Add CAPX 2000 Less Interest on Debt Service 25126 Less Tax Deprecation 17000 Taxable Income Loss 9126 11 You are considering the purchase of a small apartment complex Calculate the mortgage payment the interest deduction the depreciation deduction and the amortized financing costs for the first year of operations b What will be your net equity investment at time zero c Estimate the after tax cash ow from the first year of operations E Solution a Annual mortgage payment 65575 N225 I8 PV 700000 and FV0 Interest Deduction in year 1 008 x 700000 2 56000 Depreciation 2727273 Depreciable Basis of 750000275 Amortization of financing costs 1000 2500025 The net equity investment at time zero is 325000 Down payment of 300000 plus upfront financing of 25000 c The after tax cash ow is calculated below 5 Tax Calculations Gross Potential Income 175000 Less Vacancy and Collection Losses 21000 Effective Gross Income 154000 Less Operating Expenses 36000 Less Capital Expenditures 2000 Net Operating Income 116000 Add Capital Expenditures 2000 Less Interest 56000 Less Depreciation 27273 Less Amortization of Financing Costs 1000 Taxable Income 33727 x 35 Tax Liability 11805 Cash Calculations Net Operating Income 116000 Less Debt Service 65575 Before Tax Cash Flow 50425 Less Tax Liability 11805 After tax Cash ow 38620 12 Compute the after tax cash ow from the sale of the following nonresidential property a Compute the annual depreciation expense b Compute the adjusted basis at the time of sale after two years c Compute the tax liability from sale d Compute the after tax cash ow equity reversion from sale Solution a Annual depreciation expense 980769 Depreciable Basis 085 x 450000 2 382500 Annual depreciation expense 2 382500 x 139 b Total depreciation over 2 year holding period 2 2 x 980769 2 19615 Adjusted basis at the time of sale 460385 450000 acquisition price plus 30000 in subsequent capital expenditures minus 19615 of depreciation c Computation of Tax Liability The book says the market value of the property increased to 472500 over the two year holding period and that selling costs at that time will be 6 percent of the sale price market value Assume instead that the market value has increased to 510000 and that selling expenses will be 3 percent Selling Price 510000 Less Selling Expenses 15300 Net Sale Proceeds 494700 Less Adjusted Basis 460385 Taxable Gain 34315 Les s Depreciation Recapture 19615 19 Capital Gain 14700 Capital Gain Tax 15 2205 Add Depreciation Recapture tax 25 4904 Total Taxes 7109 1 After tax cash ow Net Sale Proceeds 494700 Less Remaining Mortgage Balance 354276 Before Tax Equity Reversion 140424 Less Taxes Due on Sale 7109 After tax Equity Reversion 133315 20 CHAPTER 7 Valuation Using the Sale Comparison and Cost Approaches Study Questions 1 What is the theoretical basis for the direct sales comparison approach to the market valuation Solution The direct sales comparison approach to the market valuation relies on value judgments made by willing buyers and sellers Therefore this method uses market driven information The sales comparison approach involves comparing a subject property with recently sold comparable properties 2 What main difficulty would you foresee in attempting to estimate the value of a 30 year old property by means of the cost approach Solution The cost approach assumes that the market value of a new building is similar to that of constructing the building today Of the two methods available for estimating cost appraisers normally use the reproduction cost of a building for appraisal purposes A 30 year old building likely possesses many characteristics that render it obsolete Therefore calculating an accurate reproduction cost for an older building is difficult because outdated features such as room arrangement decorative features and materials are included in the reproduction costs Estimating these costs can be problematic because reproducing the cost of a 30 year old building requires significant effort and assumptions of accrued deprecation 3 The cost approach to market valuation does not work well in markets that are overbuilt Explain Solution In an overbuilt market the market value of an existing property is frequently less than the construction cost of the property The estimated value calculated using reproduction cost of the property is likely significantly different from the value obtained from the sales comparison approach and the income approach 4 What is meant by functional obsolescence Could a new building suffer from functional obsolescence Solution Functional obsolescence refers to a building s loss in value resulting from changes in tastes technical innovations or market standards Typically functional obsolescence is associated with a building s decline in utility through the passage of time but it is possible for a newer building to suffer from functional obsolescence For example costumer preferences and demands may change soon after a relatively new building is completed 5 Why is an estimate of the developer s fair market profit included in the costs estimate S olution In practice developers and contractors frequently include their profit in the calculated cost amount because a fair and reasonable profit amount is considered a cost of the project 21 6 Reproduction cost has been estimated as 350000 for a property with a 70 year economic life The current effective age of the property is 15 years The value of the land is estimated to be 55000 What is the estimated market value of the property using the cost approach assuming no external or functional obsolescence Solution Reproduction cost 350000 Less Depreciation 175000 350000 X 1570 Depreciable Cost of Building Improvements 275000 Add Estimated Value of Site 55000 Indicated Value by the Cost Approach 330000 7 What is an appraisal report Solution An appraisal report is the document prepared by the appraiser This report contains the appraiser s final estimate of value the data forming the foundation of this estimate and the calculations supporting the estimate 8 What is the difference between market value and investment value Solution Market value is the most probable selling price investment value is the value to a particular investor 9 Contrast self contained appraisal reports summary appraisal reports and restricted appraisal reports Solution A self contained appraisal report includes all the detail and information that were used by the appraiser to derive his or her estimate of market value or the other conclusions within the report A summary appraisal reports simply summarizes the conclusions of the appraisal The majority of the data and techniques used in the appraisal are kept in the appraiser s work file A restricted appraisal reports provides a minimal discussion of the appraisal with many references to the appraiser s work fileinternational documentation 10 You are appraising a single family residence located in the Huntington neighborhood at 4632 NW 56th Drive The property is being acquired by a mortgage applicant and you have been asked to appraise the property by the lender Seven potential comparable sales were initially identified However three of these seven were highly similar to the subject property in their transactional physical and locational characteristics You therefore decided to exclude the other four transactions from the comparable set 22 The elements of comparison you used to compare and adjust the sale prices of the comparable properties are listed in the market data grid below The property rights being conveyed in the acquisition of the subject property are fee simple absolute Conventional mortgage financing will be used by the purchaser and the acquisition appears to be an arm s length transition Thus no adjustments need to be made to the sale prices of the comparable properties for the type of property rights conveyed financing terms or conditions of sale However the buyer of comparable 2 was aware that she would have to replace one of the air conditioning units immediately after acquiring the property thus she was able to negotiate a 3000 price reduction from the seller Comparable 1 sold three months ago while comparables 2 and 3 sold six months ago Based on your knowledge of recent price appreciation in this market you have decided that comparable 2 would sell for 2 percent more if sold today and that comparables 2 and 3 would sell for 4 percent more if sold today The subject property is located in Huntington as is comparable 1 However comparables 2 and 3 are located in Kensington and Millhoper respectively Although Huntington is a high end neighborhood both Kensington and Millhoper are generally considered to be slightly more desirable In fact homes in these two neighborhoods generally sell for about a 3 percent price premium relative to similar homes in Huntington In these neighborhoods an incremental square foot of lot size or living area is worth about 20 per square foot and 80 per square foot respectively Each year of effective age reduces the value of properties in this market by about 3000 per year You experience suggests that each additional half bath is worth 500 each additional full bath 1000 Additional garage spaces wood decks and pools in these neighborhoods are worth 8000 1000 and 12000 respectively No significant non realty items were included in the comparable transactions and non realty items are not part of the acquisition of the subject property 23 Sales Comparison Approach Market Data Grid for 4632 NW 56th Drive Comp Comp Comp Elements of Com arison Subject Sale 1 Sale 2 Sale 3 Sale price of comparable 510000 525000 499000 Transactian characteristics Property rights conveyed Fee simple Same Same Same Financing terms Conventinal Same Same Same Conditions of sale Arm39s length Same Same Same Expenditures immed after purchase None 3000 None Market conditions Today 3 mos ago 6 mos ago 6 mos Ago add 2 total add 4 total add 4 total Property characteristics Location Huntington Huntington Kensington Millhoper Physical characteristic s Sitelot size 6662 sq ft 6700 sq ft 6800 sq ft 6600 sq ft Construction quality Typical Typical Typical Typical Condition Average Average Average Average Effective age 55 years 7 years 8 years 10 years Living area 3473 sq ft 3920 sq ft 3985 sq ft 3835 sq ft Number of baths 30 baths 35 baths 30 baths 20 baths Garage Spaces 2car 2car 2car 1 car Porch patio deck Cov porchwood deck Cov Porch Cov Porch Cov Porch Fence pool etc None None Pool Pool Economics characteristics NA NA NA NA Use Singlefamily Same Same Same Non realty components None None None None Based on the above discussion of the elements of comparison complete an adjustment grid for the three comparable properties What is the final adjusted price indication of the subject s value for comparable 1 2 and 3 24 Adjustment Grid for 2380 Appletree Court Comp Comp Comp Elements of Com arison Subject Sale 1 Sale 2 Sale 3 Sale price of comparable 510000 525000 499000 Transactian adjustments Adj for property rights conveyed Fee simple 0 0 0 Adjusted price 5 10000 525000 499000 Adjustment for financing terms Conventinal 0 0 0 Adjusted price 5 10000 525000 499000 Adjustment for conditions of sale Arm39s length 0 0 0 Adjusted price 5 10000 525000 499000 Adj for expend immed after purchase None 0 3000 0 Adjusted price 5 10000 528000 499000 Adjustment for market conditions Today 10200 21120 19960 Adjusted price 520200 549120 5 18960 Property Adjustments far Location Huntington 0 16474 15569 Physical characteristics Sitelot size 6662 sq ft 760 2760 1240 Effective age 55 years 4500 7500 13500 Living area 3473 sq ft 35760 40960 28960 Baths 30 baths 500 0 1000 Garage Spaces 2car 0 0 8000 Porch patio deck Cov porchwood deck 1000 1000 1000 Fence pool etc None 0 12000 12000 Total adj for physical characteristics 31520 47220 16220 Economics characteristics 0 0 0 Use Singlefamily 0 0 0 N on realty components None 0 0 0 Indication of subject value 488680 485426 487171 11 Assume the market value of the subject site is 120000 You estimate that the cost to replicate the improvements to the subject property would be 428000 today In addition you estimate that accrued depreciation on the subject is 60000 What is the indicated value of the subject by the cost approach Reproduction cost of improvements Less Accrued depreciation Depreciated value of improvements Plus Value of site Indicated value by cost approach 428000 60000 368000 120000 488000 25 CHAPTER 8 Valuation Using the Income Approach Study Questions 1 N Data for five comparable income properties that sold recently are shown below What is the indicated overall rate R0 Solution The indicated overall cap rate of 1005 percent is the simple average of the overall rates for the five comparable properties Why is the market value of real estate determined partly by the lender s requirements and partly by the requirements of equity investors Solution Real estate investments are frequently financed using a combination of equity and mortgage debt A real estate investment can be viewed as a joint investment made by both the lender and equity investor and therefore both parties required rates of return are relevant Consequently the investor s minimum required rate of return is heavily in uenced by the availability and terms of financing provided by lenders as well by evaluating the required returns on alternative investments of similar risk In general a levered investment has greater risk than an unlevered investment which increases the investor s required rate of return Assume a reserve for non recurring capital expenditures is to be included in the pro forma for the subject property Explain how an above line treatment of this expenditure would differ from a below line treatment S olution In an above line treatment the reserve for non recurring capital expenditures would be taken out in the calculation of net operating income ie above line In a below line treatment the reserve for non recurring capital expenditures would be subtracted from net operating income ie below line 26 4 Use the following property data Cash ow from operations Year 1 2 3 4 5 N01 150000 150000 150000 150000 150000 Debt Service 125 000 125 000 125 000 125000 125 000 Cash Flow at sale Sale Price 2000000 Cost of sale 125000 Mortgage balance 1500000 a Assuming the going in capitalization rate is 800 percent compute a value for the 5 property using direct capitalization Solution Value NOlllR 150000008 2 1875000 Assuming the required yieldreturn on unlevered cash ows is 10 percent and that the property will be held by a buyer for five years compute the value of the property based on discounting unlevered cash ows Solution Sale Price 2000000 Cost of saleselling expenses 125000 Net sale proceeds 1875000 Net Sale Total Present Value Year NOI Proceeds Cash Flow 10 1 150000 150000 136364 2 150000 150000 123967 3 150000 150000 112697 4 150000 150000 102452 5 150000 1875000 2025000 1257366 Total present value 1732845 Assuming the relevant required yieldreturn on levered cash ows is 15 percent and that the property Will be held by a buyer for five years What is the present value of the levered cash ows Solution 27 Year 1 2 3 4 5 NOI 150000 150000 150000 150000 150000 Debt Service 125 000 125 000 125 000 125 000 125 000 BTCF 25000 25000 25000 25 000 25 000 Sale Price 2000000 Cost of saleselling expenses 125000 Net sale proceeds 1875000 Mortgage balance 1500000 Before tax equity reversion 375000 Net Sale Total Present Value Year NOI Proceeds Cash Flow 15 1 25000 25000 21739 2 25000 25000 18904 3 25000 25000 16438 4 25000 25000 14294 5 25000 375000 400000 198871 Total present value 270245 5 Given the following owner s income and expense estimates for an apartment property formulate a reconstructed operating statement The building consists of 10 units that could rent for 550 per month each Owner s Income Statement Rental income last year 60600 Less Expenses Power 2200 Heat 1700 Janitor 4600 Water 3700 Maintenance 4800 Reserves for replacement 2800 Management 3000 Depreciation 5000 Mortgage payments 6300 34100 Net income 26500 Estimating vacancy and collection losses at 5 percent of potential gross income reconstruct the operating statement to obtain an estimate of N01 Remember there may be items in the owner s statement that should not be included in the reconstructed operating statement Using the N01 and a R0 of 110 percent calculate the property s indicated market value Round your answer to the nearest 500 28 Solution Reconstructed Operating Statement PGI 10 units X 550 x 12 66000 Less Vacancy Loss at 5 percent 3300 EGI 62700 Less Operating Expenses Power 2200 Heat 1700 Janitor 4600 Water 3700 Maintenance 4800 Reserves for replacement 2800 Management 3000 22800 Net Operating Income 39900 Note Mortgage payments and depreciation are not included in the calculation of the property s N 01 The indicated value of the property is 362727 39900 011 which rounds to 363 000 29 Settings on Calculator Set 5 decimal place For accurate answers End Mode Assume payments are made at the end of the period which is an ordinary annuity 1 PMT per year Can vary inputs by yourself SetupTroubleshooting HP Setup Set on END mode Shift BegEnd Set to 5 decimal places Shiftdisplay5 Set to 1 payment per year 1 Shift PY Tl Setup Set on END mode 2nd BGN 2nd SET Set to 5 decimal places 2nd Format 5 ENTER Set to 1 payment per year 2nd PY1 ENTER TVM Keys Example HP10 5 N 8 IN OPMT 1000 PV FV 146933 T BAII Plus 5 N 8 IN OPMT 1000 PV CPT FV 146933 CaShflow Keys Example Problem CFOO CF1100 Freq12 CF250 Freq12 CF3225 Freq12 At 8 388560 Note monthly compounding HP10 0 CF 100 OF 12 Shifth 50 CF 12 Shifth 225 OF 12 Shift Nj 812 IYR Shift NPV T BAII Plus CF 0 ENTER Down Arrow 100 ENTER Down Arrow 12 ENTER Down Arrow 5O ENTER Down Arrow 12 ENTER Down Arrow 225 ENTER Down Arrow 12 ENTER NPV 812 ENTER Down Arrow CPT Six Functions of a Dollar Future Value of a lump sum If you purchase a parcel of land today for 25000 and you expect it to appreciate 10 percent per year in value how much will your land be worth 10 years from now Given N10110 l 101 10 PV 25000 PMT0 Solve FV 6484356150 Present Value of a lump sum If your parents purchased an endowment policy of 10000 for you and the policy will mature in 12 years how much is it worth today discounted at 15 and compound quarterly Given N124 48 154 375 FV10000 PMT0 Solve PV 470832675 Capitalization rate amp mortgage constant PMT You want to purchase a house having a price of 80000 The real estate salesperson believes you could obtain an 80 monthly payment loan for 30 years at a 15 percent interest rate How much will your monthly payments be Given N 3012 360 1512 125 PV 8000008 64000 FV 0 Solve PMT 80924417 Future Value of an annuity If you deposit 50 per month in a savings and loan association at 10 percent interest how much will you have in your account at the end of the 12th year Given N 1212 144 1012 083333 PMT 5O PV 0 Solve FV 13821 85473 Sinking Fund Factor If you wish to accumulate 10000 in a bank account in eight years and the account will draw 15 compounded monthly you must deposit At the end of year 10 Is this askinq at the end of month 120 Given N 812 96 1512125 FV 10000 PV 0 Solve PMT 5445405 Present Value of annuity If someone pays you 200 semiannually for 15 years the value of the series of future payments discounted at 10 percent is how much Given N 152 30 102 5 PMT 200 FV O Solve PV 307449021 Another Cashflow Example CFO 100000 CF1 CF2 CF3 30000 50000 40000 8 9 NPV 239800843 IRR 926470 10 9 NPV 135236664 IRR 926470
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