RE I: Class Note #2
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Real Estate Investments I
(Business 33450)
Winter Quarter, 2023
Instructor: . Pagliari, Jr.
Key Take-Aways:
• Applications of “mainstream” finance to commercial real estate:
Net present value,
Internal rate of return,
Modified internal rate of return, and
Look-back IRR.
• The commercial real estate pro forma.
• Misconceptions in pricing.
• Fees → a “drag” on returns.
Real Estate Investments I
Business 33450
Instructor: . Pagliari, Jr.
Class Notes – Week #2:
Investment Decision Making: Part I
Table of Contents
I. Generalized Investment Model ………………………………………………………………………….. 2
II. Three Common Approaches to Discounted Cash Flow Analyses ………………………….. 3
III. Typical Application to “Core” Real Estate ……………………………………………………….. 12
IV. DDM ← Corporate Finance Model Applied to Real Estate ………………………………… 27
V. Misconceptions in Pricing: ……………………………………………………………………………… 32
VI. A Look at Current Pricing ……………………………………………………………………………….. 48
VII. Note on the “Drag” of Fees on Returns ……………………………………………………………. 56
VIII. A Look at Private “Retail” Real Estate Equity …………………………………………………… 58
IX. Note on Catch-Up Provisions ………………………………………………………………………….. 62
X. Note on Look-back IRRs ………………………………………………………………………………… 63
XI. Proof of Dividend Discount Model…………………………………………………………………… 66
XII. Appendix – Limited Partnership Offering …………………………………………………………. 68
As noted in the Syllabus, this is another attempt to blend theory
and practice. As with future classes, let’s start with “mainstream”
finance and then apply these concepts to real estate investing.
I. Generalized Investment Model
Reminder: Through the mid-term exam, we will examine unlevered cash flows (k = ka).
A. Like most ex ante investment analyses, real estate begins with forecasting operating and
reversionary cash flow:
B. For simplicity, we generally assume all cash flows occur at year-end and therefore:
1. the initial investment is made in year 0,
2. the operating cash flows are received at the end of years 1 through N, and
3. the reversionary (or sale) proceeds are received at the end of year N (where: N = the
investment’s holding period).
C. At least through the midterm exam, we will not devote much time to how k (the periodic
discount rate) is to be determined.
D. Moreover, “beta” (β ) is not typically used in private real estate. Indeed, it might be plausibly
argued that private real estate investors have demonstrated something less than an ideal pricing
of risk (e.g., see week #3 notes with regard to the historical risk/return performance of core
properties).1 Accordingly, a better understanding of risk (see week #9) may lead to your
competitive advantage.
1 As another example, see: and , “Stocks Are from Venus, Real Estate Is from Mars,”
Journal of Portfolio Management, Special Issue 2007, pp. 134-144. The authors find that, while a multifactor
approach prices (private) real estate quite well, the weightings almost completely contradict the results of
. Fama and . French, “The Cross-Section of Expected Stock Returns, Journal of Finance,
June 1992, pp. 427-465. More specifically, Pai and Geltner find: “… the market beta has a zero risk
premium…” and “…a return premium on larger rather than smaller assets and on a higher-tier MSA locations.
These results are exactly the opposite of the Fama and French findings of higher returns on smaller stocks and
of the greater return premium on stocks with a higher book/market ratio.”
1 2(Future )
where: initial price,
equal, discrete time periods,
length of total holding period,
cash flow received at end of per
CF CF CF CF = PV CFs P
(1+k (1+k (1+k (1+k) ) ) )
= = + + +∑
periodic discount rate.
Operating cash flows + sale proceeds
II. Three Common Approaches to Discounted Cash Flow Analyses
{This section should be a review of material from an earlier finance course.2}
A. Net present value (NPV) – see Exhibit I for a real estate application:
1. given k and CFn, solve for P0 (or NPV) of cash flows as the unknown,
2. recall:3
(a) if NPV [i.e., PV(CF) – P0] > 0, accept the project,
(b) if NPV [i.e., PV(CF) – P0] < 0, reject the project 3. problem: what discount rate (k) to select? (a) may get different rankings with various discount rates, and (b) these different rankings are a function of the timing of cash flows. 2 These old-fashioned corporate finance models (assuming constant expected returns) fit unlevered, core real estate (with its relatively slow-moving cash flows) fairly well. If instead you would like to consider time-varying expected returns, see: . Campbell and . Shiller, “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors,” Review of Financial Studies, Autumn 1988, pp.195-228. And/or if you would like to consider price-to-book effects, see: . Fama and . French, “The Anatomy of Value and Growth Stock Returns,” Financial Analysts Journal, November 2007, pp.44-54. 3 Assumes an infinite supply of investable funds. 0 5 10 15 20 25 30 Time Periods (n ) Illustration of Projects with Varying Cash Flows 0.0% 2.5% 5.0% 7.5% 10.0% 12.5% 15.0% Discount Rates (k ) Illustration of Present Value of Cash Flows Given Varying Discount Rates Project A has front-ended cash flows, while Project B has back-ended Q: What does this graph (about the NPV of each) imply? A: As k ↑, Project B is less attractive relative to Project A Let’s arbitrarily assume the same price (P0 = $6) for each project. Exhibit I: NPV Approach Major Assumptions: Purchase Price (P 0 ) $10,000 Initial Cash Flow (CF 0) $900 Growth in Cash Flow (g ) 4.00% Transaction Costs: Acquisition 1.00% Disposition 2.00% Holding Period (N ) 10 years Discount Rate (k ) 13.00% Reinvestment Rate 5.00% Property Sale: Initial Cap Rate plus 75 basis points Property Cash Flows Discount Net Present Year Acquisition Operations Reversion Total Rate Value 0 ($10,100) ($10,100) 1.0000 ($10,100) 1 $936 936 0.8850 828 2 973 973 0.7831 762 3 1,012 1,012 0.6931 702 4 1,053 1,053 0.6133 646 5 1,095 1,095 0.5428 594 6 1,139 1,139 0.4803 547 7 1,184 1,184 0.4251 503 8 1,232 1,232 0.3762 463 9 1,281 1,281 0.3329 426 10 1,332 13,391 14,723 0.2946 4,337 Total ($10,100) $11,238 $13,391 $14,528 ($290) Let’s make these financial concepts operative in a (private) real estate context Used to price or re-price transactions In practice: • We spend a lot of time debating what these forecasted numbers ought • You need to be competent in both the techniques (NPV, IRR, etc.) & the forecasting of E[CFn] – the latter comes with experience NPV < 0; so, either reject the proposed acquisition or renegotiate the price For now, we’ll continue to assume that: NOIn = CFn See next page for derivation of these numbers Recall: NOICap Rate Exhibit I: NPV Approach Major Assumptions: Purchase Price (P 0 ) $10,000 Initial Cash Flow (CF 0) $900 Growth in Cash Flow (g ) 4.00% Transaction Costs: Acquisition 1.00% Disposition 2.00% Holding Period (N ) 10 years Discount Rate (k ) 13.00% Reinvestment Rate 5.00% Property Sale: Initial Cap Rate plus 75 basis points Property Cash Flows Discount Net Present Year Acquisition Operations Reversion Total Rate Value 0 ($10,100) ($10,100) 1.0000 ($10,100) 1 $936 936 0.8850 828 2 973 973 0.7831 762 3 1,012 1,012 0.6931 702 4 1,053 1,053 0.6133 646 5 1,095 1,095 0.5428 594 6 1,139 1,139 0.4803 547 7 1,184 1,184 0.4251 503 8 1,232 1,232 0.3762 463 9 1,281 1,281 0.3329 426 10 1,332 13,391 14,723 0.2946 4,337 Total ($10,100) $11,238 $13,391 $14,528 ($290) Let’s take a closer look at the interplay of the assumptions and the forecasted cash flows “trailing” cap rate = 9.0% “round-trip” transaction costs (typically, much higher internationally) {Seller typically pays the brokerage fee} =f(aging, obsolescence) [sometimes used to proxy transaction costs] NA for NPV = P0 + transaction costs @ 1% CF1 = CF0 (1+g)1 = CF2 = CF0 (1+g)2 = CF3 = CF0 (1+g)3 = = CF1 (1+k)-1 = CF2 (1+k)-2 = CF3 (1+k)-3 = P10 – transaction costs {see Exhibit V} A note on potential price renegotiation (assumes all other cash flows remain as is): Initial Cost $10,100 Net Present Value (290) Revised Cost $9,810 1 + Transaction Costs (%) ÷ 101% Revised Price $9,713 B. Internal rate of return (IRR) – see Exhibit II: 1. given P0 and CFn, solve for k (such that NPV = 0) as the unknown4, and 2. recall:5 (a) if k [i.e., P0 = PV(CFs)] > “hurdle rate,” accept the project,
(b) if k [i.e., P0 = PV(CFs)] < “hurdle rate,” reject the project, 3. problems:6 (a) what "hurdle rate" to select if unlimited investment capital, (b) possible multiple solutions7 (see Exhibit III) with reversal of cash flow signs, and (c) IRR = implied reinvestment rate, which may be problematic – often under two conditions: i. heavy tax shelter – front-end tax deductions push after-tax investment towards zero (and, therefore, expected after-tax returns towards infinity), and ii. highly levered transactions – these types of investments often take on option-like both possibilities are characterized by: ♦ high expected return increases as a result of small equity contribution, and ♦ high expected return – substantially in excess of available reinvestment rates. 4 Solving for k generally must be done iteratively (i.e., there’s no algebraic solution); this iteration is performed by your computer and/or calculator. 5 Assumes an infinite supply of investable funds. 6 For other potential infirmities, see "Sins of the IRR" by . Brown, Journal of Real Estate Portfolio Management, Vol. 12, No. 2, 2006, pp. 195-199 – also found on the course's Canvas site. 7 For those (and only those?) who are mathematically inclined, consider the example presented in Exhibit III; it is a two-period model which can be solved using the quadratic formula: + + = ⇒ = , where: [In the context of Exhibit III, a = –10,000, b = 10,000 and c = –1,600; therefore, x1 = .20 ⇒ k1 = 400% and x2 = .80 ⇒ k2 = 25%.] Exhibit II: IRR Approach Major Assumptions: Purchase Price (P 0 ) $10,000 Initial Cash Flow (CF 0) $900 Growth in Cash Flow (g ) 4.00% Transaction Costs: Acquisition 1.00% Disposition 2.00% Holding Period (N ) 10 years Discount Rate (k ) 12.52% Reinvestment Rate 5.00% Property Sale: Initial Cap Rate plus 75 basis points Property Cash Flows Discount Net Present Year Acquisition Operations Reversion Total Rate Value 0 ($10,100) ($10,100) 1.0000 ($10,100) 1 $936 936 0.8887 832 2 973 973 0.7898 768 3 1,012 1,012 0.7019 710 4 1,053 1,053 0.6237 657 5 1,095 1,095 0.5543 607 6 1,139 1,139 0.4926 561 7 1,184 1,184 0.4378 518 8 1,232 1,232 0.3891 479 9 1,281 1,281 0.3458 443 10 1,332 13,391 14,723 0.3073 4,524 Total ($10,100) $11,238 $13,391 $14,528 $0 Assumptions/parameters are unchanged; therefore, forecasted cash flows are unchanged; the only difference is k. Used generally when talking about RE deals (as IRRs are scale-free, while NPVs are not) and informs our judgment about what: • the hurdle rate ought to be used in IRR decisions, and • the discount rate ought to be used in NPV decisions. NA for IRR the IRR requirement Before you turned on your computer, you should have known that the IRR < 13%. A: Exhibit I has same cash flows and with k = 13% produced an NPV < 0. ∴ Need to lower k such that NPV = 0. {this is the only difference from Exhibit 1} Q: Is this a good deal? (IRRs of 25% and 400% sound really good. So, it must be good – right?) A: Depends on your reinvestment rate (recall: IRR implicitly assumes a reinvestment rate = IRR). • If your reinvestment rate < 25%, then this is a negative NPV project (see next graph). • For example, assume your reinvestment rate = 5%; then: Without this RE investment: $1,600 (1.05)2 = $1,764. With this RE investment: $10,000 (1.05)1 – $10,000 (1.05)0 = $500. [In both cases, you initially invest $1,600.] Exhibit III: Multiple Solutions to IRR Problem IRR @ 25% IRR @ 400% Project's Discount Net Present Discount Net Present Sign Year Cash Flow Factor Value Factor Value Negative 0 ($1,600) 1.0000 ($1,600) 1.0000 ($1,600) Positive 1 10,000 0.8000 8,000 0.2000 2,000 Negative 2 -10,000 0.6400 -6,400 0.0400 -400 Total ($1,600) $0 $0 Suppose that you are offered an industrial property for $1.6 million. The property has one year remaining on its original ten-year lease. This lease pays $10.0 million at the end of each year. However, the site has significant environmental problems which are expected to cost $10.0 million to clean up. This cost will come due one year after collecting the final lease installment. Your job is to determine the project's internal rate of return. When CFs flip sign more than once An example of why some investors consider reinvestment rates and MIRR (see next § and Exhibit IV). 0% 100% 200% 300% 400% 500% 600% Discount Rates (k ) Illustration of NPVs, Given Varying Discount Rates Recall: IRR @ NPV = 0 25% 400% Any reinvestment rate < 25% (which seems certain) produces a negative NPV. A mathematical aside: This is an example of Descartes' Rule of Signs, which asserts that the number of positive roots of a polynomial is at most the number of sign changes in the sequence of polynomial's coefficients. https://en.wikipedia.org/wiki/Descartes%27_rule_of_signs https://en.wikipedia.org/wiki/Polynomial C. Modified internal rate of return (MIRR) – see Exhibit IV: 1. given an assumed reinvestment rate, P0 and CFn, solve for k (such that P0 = PV(CFs), when discounted at the MIRR, = 0) as the unknown8, 2. recall:9 (a) if k [i.e., P0 = > “target rate”, accept the project,
(b) if k [i.e., P0 = < “target rate”, reject the project, and 3. problems: (a) which reinvestment rate to select? typically, a “safe” rate (e.g., Treasuries, mortgage rates, etc.), as a f(horizon), is used. (b) which target rate to select? 8 In the case of the MIRR, k can be solved algebraically. There are two (equivalent) ways of doing so (they differ only in terms of their compounding frequencies – the former is periodic and the latter is continuous): Method #1: Method #2: {When simply not deferring to Excel (or some other spreadsheet application), this method is the one most frequently used in practice – it is also illustrated on the following page.} + = = − 9 Assumes an infinite supply of investable funds. NP MIRR FV+ = Exhibit IV: Modified IRR Approach Major Assumptions: Purchase Price (P 0 ) $10,000 Initial Cash Flow (CF 0) $900 Growth in Cash Flow (g ) 4.00% Transaction Costs: AcquisitionAcquisition 1.00% DispositionDisposition 2.00% Holding Period (N ) 10 years Discount Rate (Modified IRR) 10.46% Reinvestment Rate 5.00% Property Sale: Initial Cap Rate plus 75 basis points Property Cash Flows Reinvestment Future and Ending Year Acquisition Operations Reversion Total Rate Value Values 0 ($10,100) ($10,100) 1.0000 ($10,100) 1 $936 936 1.5513 1,452.0 0 2 973 973 1.4775 1,437.6 0 3 1,012 1,012 1.4071 1,424.0 0 4 1,053 1,053 1.3401 1,411.1 0 5 1,095 1,095 1.2763 1,397.5 0 6 1,139 1,139 1.2155 1,384.5 0 7 1,184 1,184 1.1576 1,370.6 0 8 1,232 1,232 1.1025 1,358.3 0 9 1,281 1,281 1.0500 1,345.1 0 10 1,332 13,391 14,723 1.0000 14,723 $27,304 Total ($10,100) $11,238 $13,391 $14,528 $27,304 We can compute the Modified IRR in either of two (equivalent) ways: 1) a standard IRR calculation with the intervening years recorded as zeros, or 2) recognize that the (geometric mean) return can be computed directly: Assumptions/parameters are unchanged; therefore, forecasted cash flows are unchanged This only matters for MIRR Before you turned on your computer, you should have known that the MIRR < IRR. A: Because the reinvestment rate < IRR. ∴ MIRR < IRR. At least one national CRE firm, uses this technique as part of their testing new candidates Solve for MIRR: PV MIRR FV In Excel: N x = x ^ (1/N ) Two new columns III. Typical Application to “Core” Real Estate A. Most typically, real estate investors use NPV to negotiate prices and IRR approach to rank B. Holding period: 5 - 10 years [ = f(high transaction costs)], C. Growth rates: 2 - 4% per annum [if market’s in equilibrium, then typically same rate for both revenues and expenses and that rate approximates the inflation rate], D. Reversionary capitalization rate: 50 - 100 basis points higher than going-in capitalization rate [ = f(aging, obsolescence, declining useful lives)], E. Going-in capitalization rate (where: NOI = net operating income): NOI = rate cap i. In certain settings and to simplify things, the capitalization rate can also be based on NOI0 (as used in many of the following analyses) see Exhibit V. ii. See Exhibit VI (which uses Dollars & Cents of Apartments – similar resources exist for other property types) for numerical examples of comparative underwriting. iii. For now, we’ll repeat the mistake often observed in practice: trea 程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com