Real Estate Chapter 8

CHAPTER 8 Valuation Using the Income Approach Test Problems 1. Which of the following expenses is not an operating expense? d. Mortgage payment. 2. An overall capitalization rate (Ro) is divided into which type of income or cash flow to obtain an indicated market value? a. Net operating income (NOI). 3. Which of the following types of properties probably would not be appropriate for income capitalization? e. Public school. 4. Reserves for replacement and other nonrecurring expenses are allowances that reflect: d. The annual depreciation of the short-lived components of the building and expenses that occur only occasionally. 5. An appraiser estimates that a property will produce NOI of $25,000, the Yo is 11 percent, and the growth rate is 2.0 percent. What is the total property value (unrounded)? a. $277,778. 6. If a comparable property sells for $1,200,000 and the effective gross income of the property is $12,000 per month, the effective gross income multiplier is b. 8.33 7. The final value estimate produced by one approach is called d. Indicated value. 8. The methodology of appraisal differs from that of investment analysis primarily regarding e. Point of view and types of data used. Use the following information to answer questions 9-10. You have just completed the appraisal of an office building and have concluded that the market value of the property is $2,500,000. You expect Potential Gross Income (PGI) in the first year of operations to be $450,000; vacancy and collection losses to be 9 percent of PGI; operating expenses to be 38 percent of Effective Gross Income (EGI), and capital expenditures to be 4 percent of EGI. 9. a. What is the implied going-in capitalization rate? 9.5 percent 10. b. What is the effective gross income multiplier (EGIM)? 6.11 Study Questions 1. Data for five comparable income properties that sold recently are shown below: Propert y A B C D E NOI Sale Overall Price Rate $ $ 566,600 0.1020 57,800 49,200 496,900 0.0990 63,000 630,000 0.1000 56,000 538,500 0.1040 58,500 600,000 0.0975 What is the indicated overall rate (RO)? Solution: The indicated overall cap rate of 10.05 percent is the simple average of the overall rates for the five comparable properties. 2. 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 influenced 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. 3. 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. Solution: In an above-line treatment, the reserve for non-recurring capital expenditures would be taken out in the calculation of net operating income (i.e., above line). In a below-line treatment, the reserve for non-recurring capital expenditures would be subtracted from net operating income (i.e., below line). 4. Use the following property data: Cash flow from operations: Year 1 NOI $150,000 Debt Service $125,000 2 $150,000 $125,000 3 $150,000 $125,000 4 $150,000 $125,000 5 $150,000 $125,000 Cash Flow at sale: Sale Price: Cost of sale: Mortgage balance: $2,000,000 $125,000 $1,500,000 a. Assuming the going-in capitalization rate is 8.00 percent, compute a value for the property using direct capitalization. Solution: Value = NOI1/R = $150,000/0.08 = $1,875,000 b. Assuming the required yield/return on unlevered cash flows 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 flows. Solution: Sale Price: Cost of sale/selling expenses: Net sale proceeds $2,000,000 $125,000 $1,875,000 c. Assuming the relevant required yield/return on levered cash flows 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 flows? Solution: Year 1 NOI $150,000 Debt Service $125,000 BTCF $25,000 2 $150,000 $125,000 $25,000 Sale Price: - Cost of sale/selling expenses: Net sale proceeds - Mortgage balance Before-tax equity reversion 3 $150,000 $125,000 $25,000 4 $150,000 $125,000 $25,000 5 $150,000 $125,000 $25,000 $2,000,000 $125,000 $1,875,000 $1,500,000 $375,000 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) $60,600 Less: Expenses Power $2,200 Heat 1,700 Janitor 4,600 Water 3,700 Maintenance 4,800 Reserves for replacement 2,800 Management 3,000 Depreciation 5,000 Mortgage payments 6,300 34,100 Net income $26,500 Estimating vacancy and collection losses at 5 percent of potential gross income, reconstruct the operating statement to obtain an estimate of NOI. Remember, there may be items in the owner’s statement that should not be included in the reconstructed operating statement. Using the NOI and a Ro of 11.0 percent, calculate the property’s indicated market value. Round your answer to the nearest $500. Solution: Reconstructed Operating Statement PGI: (10 units x $550 x 12) $66,000 Less: Vacancy Loss (at 5 percent) (3,300) EGI: 62,700 Less: Operating Expenses Power $2,20 0 Heat 1,700 Janitor 4,600 Water 3,700 Maintenance 4,800 Reserves for replacement 2,800 Management 3,000 22,800 Net Operating Income $39,900 Note: Mortgage payments and depreciation are not included in the calculation of the property’s NOI. The indicated value of the property is $362,727 ($39,900 / 0.11), which rounds to $363,000. 6. You have been asked to estimate the market value of an apartment complex that is producing annual net operating income of $44,500. Four highly similar and competitive apartment properties within two blocks of the subject property have sold in the past three months. All four offer essentially the same amenities and services as the subject. All were open-market transactions with similar terms of sale. All were financed with 30-year fixed-rate mortgages using 70 percent debt and 30 percent equity. The sale prices and estimated first-year net operating incomes were as follows: Comparable 1: Comparable 2: Comparable 3: Comparable 4: Sale price $500,000; NOI $55,000 Sale price $420,000; NOI $50,400 Sale price $475,000; NOI $53,400 Sale price $600,000; NOI $69,000 What is the indicated value of the subject property using direct capitalization? Solution: The abstracted going-in capitalization rates from the four properties are listed below: Comparable 1: Comparable 2: Comparable 3: Comparable 4: Simple Ave. 0.110 0.120 0.112 0.115 0.114 The simple average of the four comparable cap rates is 0.114. Thus, the indicated value of the subject property is $390, 351, ($44,500 / 0.114), which rounds to $390,000. 7. You are estimating the value of a small office building. Suppose the estimated NOI for the first year of operations is $100,000. a. If you expect that NOI will remain constant at $100,000 over the next 50 years and that the office building will have no value at the end of 50 years, what is the present value of the building assuming a 12.2% discount rate? If you pay this amount, what is the indicated initial cap rate? Solution: The present value, using a financial calculator, is $817,078. N = 50 I = 12.2 PV = ? PMT = 100,000 FV = 0 The initial (going-in) cap rate is $100,000/$817,078 = 12.24% b. If you expect that NOI will remain constant at $100,000 forever, what is the value of the building assuming a 12.2% discount rate? If you pay this amount, what is the indicated initial cap rate? Solution: The value of the building with NOI remaining constant at $100,000 is calculated using the formula for a perpetuity, which is $100,000/0.122, or $819,672. If you pay $819,672 for the property, the initial (going-in) cap rate is 12.2% ($100,000 / $819,672). c. If you expect the initial $100,000 NOI will grow forever at a 3% annual rate, what is the value of the building assuming a 12.2% discount rate? If you pay this amount, what is the indicated initial cap rate? Solution: The capitalization rate consists of a required IRR on equity and a growth rate. Applying the general constant-growth formula and assuming that the growth rate is 3%, the indicated capitalization rate is equal to 9.2% (12.2% - 3.0%.). Therefore, using a cap rate of 9.2%, the indicated value of the building is $100,000/0.092, or $1,086,957. 8. Describe the conditions under which the use of gross income multipliers to value the subject property is appropriate. Solution: The use of gross income multipliers is predicated on two primary assumptions. First, it is assumed that the operating expense percentage of the subject property and the comparable properties are equal. Second, this approach assumes that the subject property and comparable properties are collecting market rents. In practice, gross income multipliers are most appropriate for valuing apartment buildings. 9. In what situations or for which types of properties might discounted cash flow analysis be preferred to direct capitalization? Solution: Direct capitalization is dependent on information obtained from sales of properties that are deemed to be comparable to the subject property. Identifying comparable properties is particularly difficult with commercial real estate investments. Discounted cash flow analysis is useful for valuing income-producing properties because the unique expected cash flows for a particular property are evaluated using the appropriate required internal rate of return. DCF is especially useful when valuing multitenant office buildings and shopping centers were lease terms can vary widely across even otherwise similar properties. 10. Distinguish between levered and unlevered cash flows. In what sense does the equity investor have a residual claim on the property’s cash flow stream if mortgage financing is employed? Solution: The use of mortgage debt to finance the acquisition of a real estate investment property is referred to as leverage. Levered cash flows measure a property’s income stream after deducting debt service payments. The amount of cash flow available for distribution to an equity investor is reduced by the amount paid to the lender. Therefore, the equity investor has a residual claim, known as the before-tax cash flow, which is simply NOI less debt service. 11. What is the difference between a fee simple estate and a leased fee estate? Solution: A fee simple estate is the highest form of property ownership. It is complete ownership of a property without regard to leases. A leased fee estate is ownership of a property subject to leases on the property. When acquiring existing commercial real estate, investors are most often acquiring a leased fee estate because they are acquiring the property subject to the existing leases. 12. What is the difference between contract rent and market rent? Why is this distinction more important for investors purchasing existing office buildings than for investors purchasing existing apartment complexes? Solution: Contract rent refers to the actual rent paid under existing lease contracts executed between owners and tenants. Market rent refers to the potential rental income a property could receive on the open market as of the effective date of an appraisal. The distinction is particularly important for investors in office buildings because commercial leases tend to be for multiple years, unlike apartment leases. Existing leases at below market rates will be included in the calculation of potential gross income, which will depress the appraised value of the property relative to the appraised value assuming market rental rates. 13. Estimate the market value of the following small office building. The property has 10,500 square feet of leasable space that was leased to a single tenant on January 1, four years ago. Terms of the lease call for rent payments of $9,525 per month for the first five years, and rent payments of $11,325 per month for the next five years. The tenant must pay all operating expenses. During the remaining term of the lease, there will be no vacancy and collection losses; however, upon termination of the lease it is expected that the property will be vacant for three months. When the property is released under short-term leases, with tenants paying all operating expenses, a vacancy and collection loss allowance of 8 percent per year is anticipated. The current market rental for properties of this type under triple net leases is $11 per square foot, and this rate has been increasing at a rate of 3 percent per year. The market discount rate for similar properties is about 11 percent, the "going-in" cap rate is about 9 percent, and terminal cap rates are typically 1 percentage point above going-in cap rates. Prepare a spreadsheet showing the rental income, expense reimbursements, NOIs, and the net proceeds from the sale of the property at the end of an 8-year holding period. Then use the information provided to estimate the market value of the property. Solution: The fifth year of the 10-year lease is the first year of analysis. The problem calls for an 8-year analysis--one for the last year of the 1st 5-year period, five for the second 5-year period, one to allow the vacancy and collection loss to achieve a normal level, and one at the normal level for calculating the property's value (sale price) at that time. Assume vacancy and collections losses in year 7 are 25 percent, which reflects 100 percent vacancy for three months and no vacancy for 9 months. Assume the “normal” vacancy rate of 8 percent will apply in year 8 of the analysis and beyond. Yr. 1 Yr. 2 Contract Rent 114,300 135,900 Market Rent 115,500 118,965 Less: VC Effective Gross Inc. 0 114,300 0 135,900 Less: Operating Exps Net Operating Inc. 0 114,300 0 135,900 Yr. 3 135,90 0 122,53 4 0 135,90 0 0 135,90 0 Yr. 4 135,90 0 126,21 0 0 135,90 0 0 135,90 0 Yr. 5 135,900 129,996 0 135,900 0 135,900 Yr. 6 135,90 0 133,89 6 0 135,90 0 0 135,90 0 Sale price at the end of Yr. 8: = [NOI (yr9) / Terminal cap rate] = $134,606 / 0.10 = $1,346,060 Yr. 7 137,913 34,478 103,435 0 103,435 Yr. 8 142,05 0 11,364 130,68 6 0 130,68 6 Yr. 9 146,311 11,705 134,60 6 0 134,60 6 Cash Flows: CF1 = 114,300 CF2 = 135,900 CF3 = 135,900 CF4 = 135,900 CF5 = 135,900 CF6 = 135,900 CF7 = 103,435 CF8 = 1,476,746 (130,686+1,346,060) PV of Cash Flows @ 11 percent = $1,246,090