**1i.**Zenith Investment Company is considering the purchase of an office property. It has done an extensive market analysis and has estimated that based on current market supply/demand relationships, rents, and its estimate of operating expenses, annual NOI will be as follows:

A market that is currently oversupplied is expected to result in cash flows remaining flat for the next three years at $1,000,000. During years 4, 5, and 6, market rents are expected to be higher. It is further expected that beginning in year 7 and every year thereafter, NOI will tend to reflect a stable, balanced market and should grow at 3 percent per year indefinitely. Zenith believes that investors should earn a 12 percent return (r) on an investment of this kind.

**a.**Assuming that the investment is expected to produce NOI in years 1–8 and is expected to be owned for seven years and then sold, what would be the value for this property today? (Hint: Begin by estimating the reversion value at the end of year 7. Recall that the expected IRR = 12% and the growth rate (g) in year 8 and beyond is estimated to remain level at 3%.)

**b.**What would the terminal capitalization rate (RT) be at the end of year 7?

**c.**What would the “going-in” capitalization rate (R) be based on year 1 NOI?

**d.**What explains the difference between the “going-in” and terminal cap rates?

**1ii.** What is the economic rationale for the cost approach? Under what conditions would the cost approach tend to give the best value estimate?

**2i.** Ace Investment Company is considering the purchase of the Apartment Arms project. Next year’s NOI and cash flow is expected to be $2,000,000, and based on Ace’s economic forecast, market supply and demand and vacancy levels appear to be in balance. As a result, NOI should increase at 4 percent each year for the foreseeable future. Ace believes that it should earn at least a 13 percent return on its investment.

**a.**Assuming the above facts, what would the estimated value for the property be now?

**b.**What “going-in” cap rates should be indicated from recently sold properties that are comparable to Apartment Arms?

**c.**Assuming that in part (a) the required return changes to 12 percent, what would the value be now?

**d.**Assume results in part (c). What should the investor now be observing regarding the price of “comparable” sales? What market forces may be accounting for the differences in value between (a) and (c)?

**2ii.** What is the economic rationale for the sales comparison approach? What information is necessary to use this approach? What does it mean for a property to be comparable?

**3i.** Acme Investors is considering the purchase of the undeveloped Baker Tract of land. It is currently zoned for agricultural use. If purchased, however, Acme must decide how to have the property rezoned for commercial use and then how to develop the site. Based on its market study, Acme has made estimates for the two uses that it deems possible, that is, office or retail. Based on its estimates, the land could be developed as follows:

Which would be the highest and best use of this site?

**3ii.**What is a capitalization rate? What are the different ways of arriving at an overall rate to use for an appraisal?

**4i. **Ajax Investment Company is considering the purchase of land that could be developed into a class A office project. At the present time, Ajax believes that the site could support a 300,000 rentable square foot project with average rents of $20 per square foot and operating expenses equal to 40 percent of that amount. It also expects rents to grow at 3 percent indefinitely and believes that Ajax should earn a 12 percent return (r) on investment. The building would cost $100 per square foot to build:

**a.**What would the estimated property value and land value be under the above assumptions?

**b.**If rents are suddenly expected to grow at 4 percent indefinitely, what would the property value and land value be now? What percentage change in land value would this be relative to the land value in (a)?

**c.**Instead of (b), suppose rents will grow by only 1 percent because of excessive supply. What would land value be now? What percentage change would this be relative to the land value in (a)?

**d.**Suppose the land owner is asking $12,000,000 for the land. Under assumptions in part (a) would this project be feasible?

**e.**If the land must be acquired for $12,000,000, returning to the assumptions in (a), how much of a change in the following would have to occur to make the project feasible? (Consider each item one at a time and hold all other variables constant.)

**(1)** Expected return on investment (r).

**(2)** Expected growth (g) in cash flows.

**(3)** Building cost.

**(4)** Rents.

**4ii.**If investors buy properties based on expected future benefits, what is the rationale for appraising a property without making any income or resale price projections?

**5i.** Armor Investment Company is considering the acquisition of a heavily depreciated building on 10 acres of land. It expects to rent the building as a storage facility and expects to collect cash flows equal to $100,000 next year. However, because depreciation is expected to increase, Armor expects cash flows to decline at a rate of 4 percent per year indefinitely. Armor expects to earn an IRR on investment return (r) at 13 percent.

**a.**What is the value of this property?

**b.**Assume that after 5 years the building could be demolished and the land could be redeveloped with a strip retail improvement. The latter would produce NOI of $200,000 per year, grow at 3 percent per year, and cost $1 million to build. Investors currently earn a 10 percent IRR on such investments. How would this affect your estimate of value in (a)?

**5ii.**What is the relationship between a discount rate and a capitalization rate?

**6i.** Athena Investment Company is considering the purchase of an office property. After a careful review of the market and the leases that are in place, Athena believes that next year’s cash flow will be $100,000. It also believes that the cash flow will rise in the amount of $7,000 each year for the foreseeable future. It plans to own the property for at least 10 years. Based on a review of sales of properties that are now 10 years older than the subject property, Athena has determined that cap rates are in a range of .10. Athena believes that it should earn an IRR (required return) of at least 12 percent.

**a.**What is the estimated value of this office property (assume a .10 terminal cap rate)?

**b.**What is the current, or “going-in,” cap rate for this property?

**c.**What accounts for the difference between the cap rate in (b) and the .10 terminal cap rate in (a)?

**d.**What assumptions are being made regarding future economic conditions when using current comparable sales to estimate terminal cap rates?

**6ii.** What is meant by a unit of comparison? Why is it important?

**7i.** An investor is considering the purchase of an existing suburban office building approximately five years old. The building, when constructed, was estimated to have an economic life of 50 years, and the building-to-value ratio was 80 percent. Based on current cost estimates, the structure would cost $5 million to reproduce today. The building is expected to continue to wear out evenly over the 50-year period of its economic life. Estimates of other economic costs associated with the improvement are as follows:

The land value has been established at $1 million by comparable sales in the area. The investor believes that an appropriate opportunity cost for any deferred outlays or costs should be 12 percent per year. What would be the estimated value for this property?

**7ii.**Why do you think appraisers usually use three different approaches when estimating value?

**8i.** ABC Residential Investors, LLP, is considering the purchase of a 120-unit apartment complex in Steel City, Pennsylvania. A market study of the area reveals that an average rental of $600 per month per unit could be realized in the appropriate market area. During the last six months, two very comparable apartment complexes have sold in the same market area. The Oaks, a 140- unit project, sold for $9 million. Its rental schedule indicates that the average rent per unit is $550 per month. Palms, a 90-unit complex, is presently renting units at $650 per month, and its selling price was $6.6 million. The mix of number of bedrooms and sizes of units for both complexes is very similar to that of the subject property, and both appear to have normal vacancy rates of about 10 percent annually. All rents are net as tenants pay all utilities and expenses.

**a.**Based on the data provided here, how would an appraiser establish an estimate of value?

**b.**What other information would be desirable in reaching a conclusion about the probable value for the property?

**8ii.** Under what conditions should financing be explicitly considered when estimating the value of a property?

**9i.** The NOI for a small income property is expected to be $150,000 for the first year. Financing willbe based on a 1.2 DCR applied to the first year NOI, will have a 10 percent interest rate, and will be amortized over 20 years with monthly payments. The NOI will increase 3 percent per year after the first year. The investor expects to hold the property for five years. The resale price is estimated by applying a 9 percent terminal capitalization rate to the sixth-year NOI. Investors require a 12 percent rate of return on equity (equity yield rate) for this type of property.

a.What is the present value of the equity interest in the property?

**b.**What is the total present value of the property (mortgage and equity interests)?

**c.**Based on your answer to part (b), what is the implied overall capitalization rate?

**9ii.** What is meant by depreciation for the cost approach?

**10i.**Sammie’s Club wants to buy a 320,000-square-foot distribution facility on the northern edge of a large midwestern city. The subject facility is presently renting for $4 per square foot. Based on recent market activity, two properties have sold within a two-mile distance from the subject facility and are very comparable in size, design, and age. One facility is 350,000 square feet and is presently being leased for $3.90 per square foot annually. The second facility contains 300,000 square feet and is being leased for $4.10 per square foot. Market data indicate that current vacancies and operating expenses should run approximately 50 percent of gross income for these facilities. The first facility sold for $9.4 million, and the second sold for $7.9 million.

**a.**Using a “going-in” or direct capitalization rate approach to value, how would you estimate value for the subject distribution facility?

**b.**What additional information would be desirable before the final direct rate (R) is selected?

**10ii.**When may a “terminal”cap rate be lower than a “going in”cap rate? When may it be higher?

**11i.** Refer to the highest and best use analysis in Exhibit 10–9. Suppose the warehouse income would grow at 3 percent per year instead of 2 percent. Does this change the highest and best use of the site? If so, what is the new implied land value?

(For Reference Exhibit 10-9)

**11ii.** In general, what effect would a reduction in risk have on “going in”cap rates? What would this effect have if it occurred at the same time as an unexpected increase in demand? What would be the effect on property values?

**12i.** You are an analyst with Perception Partners and have been asked to make pricing recommendations regarding the acquisition of Rose Garden Apartments. This project was built five years ago and contains 250 units in a suburban market area. The broker that brought the project to your attention indicates that the asking price will be $27,000,000. She has also provided the attached information based on a market survey showing data from three sales of comparable apartment properties that have occurred in a one-mile radius of Rose Garden during the past six months (see table below).

Perception believes that market returns (IRR) should be in a range of 8 percent (compounded annually) for this type of investment. Perception (1) plans to own the property for five years and then sell it and (2) believes that rents will grow at 3 percent per year. At the present time,

Perception believes that the sale price that it hopes to achieve at the end of year 5 should be based on a “going-out” cap rate that will be .005 greater than the “going-in” cap rate. The property is to be acquired on an “all cash” basis.

**a.**Prepare an analysis of Rose Garden with the three comparable properties. Based on this analysis, do you think that the “going-in” cap rate today for Rose Garden should be higher or lower than the cap rates shown for the comparables?

**b.**If Rose Garden is acquired for $27,000,000, what would be the “going-in” cap rate at that price? How does this compare to cap rates for the comparables?

**c.**If Rose Garden is acquired for $27,000,000, would the 8 percent required return be achieved over the five-year period of ownership?

**12ii.**What are some of the potential problems with using a “going in” capitalization rate that is obtained from previous property sales transactions to value a property being offered for sale today?

**13i.** An investor is considering the purchase of a small office building. The NOI is expected to be the following: year 1, $200,000; year 2, $210,000; year 3, $220,000; year 4, $230,000; year 5, $240,000. The property will be sold at the end of year 5 and the investor believes that the property value should have appreciated at a rate of 3 percent per year during the five-year period. The investor plans to pay all cash for the property and wants to earn a 10 percent return on investment (IRR) compounded annually.

**a.**What should be the property value (REV) at the end of year 5?

**b.**What should be the present value of the property today?

**c.**How can the value at the end of year 5 be estimated today if the present value today is unknown?

**d.**Based on your answer in (b), if the building could be reproduced for $2,300,000 today, what would be the underlying value of the land?

**13ii.** When estimating the reversion value in the year of sale, why is the terminal cap rate applied to NOI for the year after the holding period?

**14i.** Spreadsheet Problem. Refer to the Ch10_Mort Eq Cap tab in the Excel Workbook provided on the Web site. This replicates the example discussed on page 314 of the book.

**a.**Suppose there is an aggressive lender that is willing to allow the debt coverage ratio (DCR) to be as low as 1.0. Keep all other assumptions, including the loan interest rate and equity discount rate (before-tax equity yield), the same. How does this affect the amount that can be borrowed and the property value?

**b.**Refer to part (a). Is it reasonable to assume that the loan interest rate and equity discount rate would be the same? If not, would you expect each to be higher or lower? Why?

**14ii.**Is a cap rate the same as an IRR? Which is generally greater? Why?

**15i.** Spreadsheet Problem. Refer to the Ch10_H&BU tab in the Excel Workbook provided on the Web site, which replicates the highest and best use analysis example in the chapter.

**a.**Suppose the construction cost is $3.5 million for office, $6.5 million for retail, $2.5 million for apartment, and $3.5 million for warehouse. How does this change the highest and best use of the site and the land value?

**b.**Use the same construction costs as part (a) but assume that office income would increase by 4 percent per year instead of 3 percent per year. Does this change the highest and best use of the site and the land value?

**15ii.** Discuss the differences between using (1) a terminal cap rate and (2) an appreciation rate in property value when estimating revision values.

**16.**Spreadsheet and ARGUS Problem. Use the Oakwood Apartments.SF file provided on the book Web site to use with ARGUS. This replicates the Oakwood Apartments example in the book. This same example is also solved with Excel in the Ch10_Apartment tab in the Excel Workbook provided on the Web site. Suppose investors required only a 9 percent rate of return (discount rate) instead of 11 percent and the terminal cap rate used to estimate the resale price was 8 percent instead of 9 percent.

**a.**Use the Excel template to see how your answer would change.

**b.**Use ARGUS to see how your answer would change.

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