编程辅导 RE I: Week #3

RE I: Week #3

The information contained in this document is confidential, privileged and only for
the information of the intended recipient and may not be used, published or

redistributed without the prior written consent of the Instructor.

Real Estate Investments I
(Business 33450)

Winter Quarter, 2023
Instructor: . Pagliari, Jr.

Key Take-Aways:
• IRR Attribution (components of return).
• Capitalization-rate shifts.
• Empirical results:

 historical return-generating process, and
 performance by property types.

• Forecasting future returns.
• Determining capitalization rates.

• FYI: Broker’s “book” (outlet mall) ← helpful for case #2
• FYI: Investment-Committee memoranda

For your own edification
(and not to be tested)

Real Estate Investments I

Instructor: . Pagliari, Jr.

Class Notes – Week #3

Investment Decision Making: Part II

Table of Contents

I. IRR ATTRIBUTION: …………………………………………………………………………………………… 1

II. IRR ATTRIBUTION – THE MECHANICS: …………………………………………………………….. 20

III. EMPIRICAL RESULTS: “TWENTY YEARS OF THE NCREIF INDEX” ………………………… 32

IV. FORECASTING FUTURE RETURNS: …………………………………………………………………….. 79

V. BROKER’S “BOOK”: PRIME OUTLETS AT EDINBURGH ………………………………………… 100

VI. PRINCIPAL’S ANALYSIS: INVESTMENT COMMITTEE MEMORANDUM …………………….. 147

These notes were partly prepared based on skillful assistance from:

(KAS Computer Sciences, LLC).

However, any remaining mistakes or omissions are the fault of your Instructor.

I. IRR Attribution:

A. Recall the dividend discount model (DDM): 10

B. Recall its simplifying assumptions:
1. constant growth: ( )1 1,2,…,nn oCF CF g n N= + ∀ = , which implies an income stream

like that shown on the following pages.

2. constant discount rate (k)

C. Simplifying assumptions are not always met in practice.

D. However, the violations of the simplifying assumptions yield additional information.

E. Consider some “real world” violations of the DDM’s assumptions {see Exhibit 2 from

“Inside the Real Estate Yield”}:

1. construction period,

2. lease-up period,

3. rental concessions,

4. fixed leases,

5. market disequilibrium:

, x = g if

6. operating frictions,

7. the volatility of growth (σg),

See following illustrations.

Each deviation from the
DDM’s simplifying

assumptions represents a
violation that can be

quantified with respect to its
impact on total return

Don’t want
MBA “robots”

(who run to
their computer

with every
change to the

pro forma);
instead, want

some intuition

generating

8. change in capitalization rates | ∆ = f(∇,N) – see Exhibits 1 – 3,

a) an exact solution is given by the differences in the IRRs:

∆ = IRR with ∇ – IRR without ∇

b) an approximations of the effect1 of changing capitalization rates is given by:

1 -1; where:

∆ ≈ − = ∇ =

c) see digression on changing capitalization rates

9. disposition costs,

10. costs of leverage,

11. costs of income taxes, and

12. costs of partners/advisors.

F. Can be used on an ex ante (prospective) or ex post (historical) basis.

G. The solution to Homework Problem #1 is another example.

1 This approximation holds exactly for one-year holding periods and works reasonably well for longer holding
periods and, particularly so, when capitalization rates are rising. However, a variation of this equation, 1 N− ∇ ,
produces slightly better approximations when capitalization rates are falling and the holding period is longer than,
say, three years. While both approximations tend to overstate the (absolute value of the) difference from the exact

effect as the holding period lengthens, these differences are, on balance, better approximated by 1 1N −

accordingly, we will use this form throughout these notes. [An aside: Typical holding period of a core property for
an institutional investor is 5 to ten years (and shorter still for non-core properties).]

← After the midterm.

Impact Distance Time

[ = Ending/Beginning ]

1 11 21 31 41 51 61 71 81 91

Time Periods (n )

Illustration of the Constant-Growth Assumption Underlying the DDM

Note: We’ve used the discrete version of the model in class.
If you prefer, you can use a continuous version of the
model: CFn = CF0eγn, where: γ = ln(1+g)

( )0 1 1, 2, …,

nCF CF g n N= + ∀ =

1 11 21 31 41 51 61 71 81 91

Time Periods (n)

Illustration of the Constant-Growth Assumption Underlying the DDM,
But with a Construction/Development Period

Construction/
Development

1 11 21 31 41 51 61 71 81 91

Time Periods (n)

Illustration of the Constant-Growth Assumption Underlying the DDM,
But with a Lease-Up Period

1 11 21 31 41 51 61 71 81 91

Time Periods (n)

Illustration of the Constant-Growth Assumption Underlying the DDM,
But with Rental Concessions

Concessions

e.g., “free rent”

1 11 21 31 41 51 61 71 81 91

Time Periods (n)

Illustration of the Constant-Growth Assumption Underlying the DDM,
But with Fixed-Rate Leases

Fixed-rate leases having the same
NPV as floating-rate leases.

Long-term leases (here, having the
same PV as the short-term leases).

1 11 21 31 41 51 61 71 81 91

Time Periods (n)

Illustration of the Constant-Growth Assumption Underlying the DDM,
But with Market Disquilibrium (λ < 1) Inflation Index ( )0 1 1, 2, ..., nCF CF n Nλρ= + ∀ = {Clearly, this example presumes λ < 1} Recall: g = λ ρ ; where: g = growth rate, λ = inflation pass-thru rate, and ρ = inflation rate. While g ≠ ρ is not a violation of DDM’s constant- growth requirement (provided g1 = g2 =…), it can be helpful to identify those instances when g ≠ ρ (as an indication of market disequilibrium). Clearly, this example presumes λ < 1. 1 11 21 31 41 51 61 71 81 91 Time Periods (n) Illustration of the Constant-Growth Assumption Underlying the DDM, But with Operating Frictions (σg > 0)

An aside/recall:

≈ − ; where:

x = geometric average of x,
x = arithmetic average of x, and
σ2 = variance of x.

H. An aside: Variability in the components of returns:

1. Volatility in the components contributes to an increase in the “other” effects.

2. Consider the following example, assuming a 20-year investment horizon:2

Major Assumptions:
P 0 = $100.00

NOI 0 = $5.00

Component Mean Volatility
g 2.5% 1.5%
b 70.0% 2.5%
∇ 0.990 0.10

So, the 20-year effect is ∇ equal to 0.818

With Without
IRR Attribution Volatility Volatility Difference
Initial Income Yield 5.16% 5.13% 0.03%
Dividend Payout Ratio 70.00% 70.00% 0.00%
Cash Flow Yield 3.61% 3.59% 0.02%
Income Growth 2.46% 2.50% -0.04%
Fundamental Return 6.07% 6.09% -0.02%
Effects of Capitalization Rate Shifts (∇ ) (a ) (b) 1.12% 0.75% 0.37%
Other Effects (c ) 0.59% -0.03% 0.63%
Total Return (d ) (e ) 7.77% 6.80% 0.97%

(a ) This represents the exact solution; the approximate solution equals 1.50%.
(b ) The ending (trailing) cap rate equals 3.71% while the beginning (trailing) cap rate equals 5.00%.
(c ) If the approximate solution were to be used, then the Other Effects would equal 0.23%.
(d ) This represents the geometric mean; the arithmetic mean equals 8.31%.
(e ) The (sample) standard deviation of this return equals 11.02%.

Illustration of IRR Attribution with Volatile Components

Note: This value (∇) is applied every year. ‘

2 The table above is taken from the “Dynamic” tab in this week’s accompanying Excel spreadsheet. By repeatedly
pressing F9, you will observe that numbers presented above represent just one sample path out of an infinite
number of possibilities.(Of course, you can also change the parameter values – shown in a blue font above.)

[= DDM = CF1/P0 + g ]

[CF1/P0 + g + ∆ + ε ]

I. More broadly, let’s consider an illustration of IRR Attribution (i.e., components of return):

Exhibit 1 from “Inside the Real Estate Yield”
IRR Attribution for Two Hypothetical Investments

To-Be-Developed Existing
Office Apartment

Building Complex

Stabilized yield (cap rate) a 10.0% 7.0%
Inflationary expectation 4.0% 4.0%
Base Yield 14.0% 11.0%

Construction period (0.3%) –
Lease-up period (0.4%) –
Rent concessions (0.6%) –
Fixed leases (0.5%) –
Market disequilibrium (1.0%) 0.2%
Operating frictions (1.0%) –
Change in cap rates 1.6% (0.8%)
Disposition costs (0.2%) (0.2%)
Real Estate Yield 11.6% 10.2%

Costs of leverage – –
Costs of income taxes – –
Cost of partners/advisors (1.5%) (1.0%)

Investor’s Nominal Yield b 10.1% 9.2%

Investor’s Real Yield 5.9% 5.0%

b The amount attributed to each of the “frictions” (i.e. , violations of the DDM) is computed by sequentially layering
the frictions onto the cash flow pattern used to generate the base yield. A new IRR is computed at each iteration.
This difference in the IRR provides the amount attributed to that element. The amount attributed to each friction is
slightly dependent upon the sequence chosen by the real estate analyst; however, this discrepancy is usually quite
small. In the future, perhaps some standardized convention can be widely adopted in order to assure comparability
among analyses.

a Based on CF1 which, for commercial properties, ignores leasing commissions and tenant improvements.

=f(supply,

post-midterm

J. Digression on the effects of capitalization rate shifts:

1. Cap rate shifts – general effects:
a) If cap rates rise over your holding period, then the value of your real estate falls (and,

conversely, falling cap rates increases the value of your real estate).
b) As a simple example – assuming constant NOI – consider the following:

Rising Cap Rates:
NOI $600 $600
Cap Rate 6.0% 8.0% 1.33x
Price $10,000 $7,500

k = CF 1/P 0 + g + ∆
= 6.0% + 0.0% + -25.0%

Falling Cap Rates:
NOI $600 $600
Cap Rate 8.0% 6.0% 0.75x
Price $7,500 $10,000

k = CF 1/P 0 + g + ∆
= 8.0% + 0.0% + 33.3%

For simplicity, assume NOI = CF

Recall: ∆ = f (∇, N )

Note: The 1:1 correspondence between
%∆ Price and ∆ is a special case,
– which requires:
* one-year holding period, &
* constant NOI (i.e ., g = 0).

Note: A 200 bps-
increase in cap rates
produces a smaller
effect (in absolute

terms) than a 200 bps-
decrease in cap rates.

Note: The earlier
approximation of the
cap-rate-shift effect:

holds precisely in a
one-period model:

∆ ≈ − = − =

c) The relationship between interest rates and bond prices is like that of cap rates and
(commercial) real estate prices: If interest rates rise, the value of the bond falls – so is
the case for cap rates and real estate prices – and, conversely, if interest rates fall, the
value of the bond rises (and, again, so is the case for cap rates and real estate prices).
However, a better analogy to cap rates is that of common stock’s earnings-to-price ratio.

d) Movements in capitalization rates: sellers v. buyers:

Cap Rate Movements
Seller Unfavorable Favorable
Buyer Favorable Unfavorable

e) Capitalization rates move3 due to two sets of forces:

a. Capital-market forces – changes in the market’s consensus estimates of the
required risk premia, forecasted growth rates, etc. (as indicated later in these
notes), and

b. Property-specific forces – consider two sources:

i. changes in the property’s forecasted cash-flow growth (e.g., markets
located in the “oil patch”), and

ii. changes in the property’s risk profile:

1. e.g., “credit” tenants, like and Enron, suddenly
go bankrupt, and

2. e.g., value-add/redevelopment “plays” (which “de-risk” the
investment)

f) ∆ = f(∇,N) – Exhibit 2 emphasizes the interplay of the shift (∇) and the holding period
(N), where the effect (∆) of the cap rate shift can be thought of as the distance between
the blue line (where ∇ = 1.0 and, therefore, ∆ = 0) and the green curves (when cap rates
are falling) or red curves (when cap rates are rising). Clearly, the cap rate shift (∇≠1.0)
and the effect (∆) of the cap-rate shift are important when the investor’s holding period
(N) is short but less important when the holding period lengthens.

g) Exhibits 3 and 4 provide detailed results for those summarized in Exhibit2.

2. IRR Attribution – an expanded version: 1

3 In corporate finance (and investments more generally), we often think about shifting pricing multiples in the
context of a two-stage dividend discount model (which is, equivalently, the real estate case of shifting cap rates):

0 1 0 12 2

1 11 2 1 2

1 1 beginning cap rate

CF g CF gk g

Such cases often

involve some
start-up business,

where it is
presumed that:

unfavorable

(generally)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Holding Period (Years)

Exhibit 2 – Total Annual Return Based Upon Various
Capitalization Rate Shifts and Holding Periods

.90 Cap Rate Shift

.95 Cap Rate Shift

1.00 Cap Rate Shift

1.05 Cap Rate Shift

1.10 Cap Rate Shift

Cap Rate Expansion:
NOI0/P0 < NOIN/PN Cap Rate Compression: NOI0/P0 > NOIN/PN

k = CF1 / P0 + g Everywhere Else:
k = CF1 / P0 + g + ∆

compression

← ∇ < 1.0 ← ∇ > 1.0

{e.g., pre-GFC era & since ≈ 2010}

{e.g., following the GFC}

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Holding Period (Years)

Exhibit 2 – Total Annual Return Based Upon Various
Capitalization Rate Shifts and Holding Periods

.90 Cap Rate Shift

.95 Cap Rate Shift

1.00 Cap Rate Shift

1.05 Cap Rate Shift

1.10 Cap Rate Shift

Cap Rate Expansion:
NOI0/P0 < NOIN/PN Cap Rate Compression: NOI0/P0 > NOIN/PN

k = CF1 / P0 + g

Development & Redevelopment Deals:
→ Value-Added & Opportunsitic

Stabilized Deals:
→ Core & Core Plus Funds

Everywhere Else:
k = CF1 / P0 + g + ∆

 try to make the “magic”
happen quickly

Fairly de minimus effect

Exhibit 3 – Summary of IRR Calculations for
Various Capitalization Rate Shifts and Holding Periods

Assumptions:

Purchase Price (P 0) $1,000

Initial Cash Flow (CF 0) $68

Growth Rate (g ) 3.0%

Lease Term 1 Year(s)

Initial Capitalization Rate (CF 0/P 0) 6.80%

Holding IRR Based on Capitalization Rate Shift () of:

Period (Years) 0.90x 0.95x 1.00x 1.05x 1.10x 1.15x 1.20x

0.25 54.68% 31.11% 10.00% -9.29% -26.74% -42.67% -57.27%

1 21.44% 15.42% 10.00% 5.10% 0.64% -3.43% -7.17%

2 15.40% 12.59% 10.00% 7.60% 5.37% 3.29% 1.35%

3 13.45% 11.66% 10.00% 8.45% 7.00% 5.63% 4.35%

4 12.49% 11.20% 10.00% 8.87% 7.82% 6.82% 5.88%

5 11.93% 10.93% 10.00% 9.13% 8.31% 7.54% 6.81%

6 11.55% 10.75% 10.00% 9.30% 8.64% 8.02% 7.43%

7 11.28% 10.62% 10.00% 9.42% 8.87% 8.36% 7.87%

8 11.08% 10.52% 10.00% 9.51% 9.05% 8.62% 8.21%

9 10.93% 10.45% 10.00% 9.58% 9.19% 8.81% 8.46%

10 10.81% 10.39% 10.00% 9.64% 9.29% 8.97% 8.67%

11 10.71% 10.34% 10.00% 9.68% 9.38% 9.10% 8.83%

12 10.62% 10.30% 10.00% 9.72% 9.45% 9.20% 8.97%

13 10.56% 10.27% 10.00% 9.75% 9.51% 9.29% 9.09%

14 10.50% 10.24% 10.00% 9.78% 9.57% 9.37% 9.18%

15 10.45% 10.22% 10.00% 9.80% 9.61% 9.43% 9.27%

Note: Asymmetric differences when cap-rate shifts are compared on an additive basis (e.g., ∇ =

0.9 v. ∇ = 1.1 – as each compared to ∇ = 1.0); asymmetric differences are eliminated
when cap-rate shifts are compared on a multiplicative basis (e.g., ∇ = 0.9 v. ∇ = 1/0.9 ≈
1.11 – as each compared to ∇ = 1.0).

from earlier

graph, due to
volatility

.068 1.03 .03

expansion compression

Exhibit 4 – Underlying Calculations

2-Year Hold
IRR Based on Capitalization Rate Shift of:

0.90 0.95 1.00 1.05 1.10 1.15 1.20
0 ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0)
1 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2 $1,250.9 $1,188.8 $1,133.0 $1,082.5 $1,036.6 $994.6 $956.2

3-Year Hold
IRR Based on Capitalization Rate Shift of:

4-Year Hold
IRR Based on Capitalization Rate Shift of:

0.90 0.95 1.00 1.05 1.10 1.15 1.20
0 ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0)
1 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2 72.1 72.1 72.1 72.1 72.1 72.1 72.1
3 74.3 74.3 74.3 74.3 74.3 74.3 74.3
4 $1,327.1 $1,261.2 $1,202.0 $1,148.4 $1,099.7 $1,055.2 $1,014.4

5-Year Hold
IRR Based on Capitalization Rate Shift of:

0.90 0.95 1.00 1.05 1.10 1.15 1.20
0 ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0)
1 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2 72.1 72.1 72.1 72.1 72.1 72.1 72.1
3 74.3 74.3 74.3 74.3 74.3 74.3 74.3
4 76.5 76.5 76.5 76.5 76.5 76.5 76.5
5 $1,366.9 $1,299.1 $1,238.1 $1,182.9 $1,132.7 $1,086.9 $1,044.8

6-Year Hold
IRR Based on Capitalization Rate Shift of:

0.90 0.95 1.00 1.05 1.10 1.15 1.20
0 ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0)
1 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2 72.1 72.1 72.1 72.1 72.1 72.1 72.1
3 74.3 74.3 74.3 74.3 74.3 74.3 74.3
4 76.5 76.5 76.5 76.5 76.5 76.5 76.5
5 78.8 78.8 78.8 78.8 78.8 78.8 78.8
6 $1,407.9 $1,338.0 $1,275.2 $1,218.3 $1,166.7 $1,119.5 $1,076.2

7-Year Hold
IRR Based on Capitalization Rate Shift of:

0.90 0.95 1.00 1.05 1.10 1.15 1.20
0 ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0)
1 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2 72.1 72.1 72.1 72.1 72.1 72.1 72.1
3 74.3 74.3 74.3 74.3 74.3 74.3 74.3
4 76.5 76.5 76.5 76.5 76.5 76.5 76.5
5 78.8 78.8 78.8 78.8 78.8 78.8 78.8
6 81.1 81.1 81.1 81.1 81.1 81.1 81.1
7 $1,450.1 $1,378.2 $1,313.5 $1,254.9 $1,201.7 $1,153.0 $1,108.5

8-Year Hold
IRR Based on Capitalization Rate Shift of:

0.90 0.95 1.00 1.05 1.10 1.15 1.20
0 ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0) ($1,000.0)
1 70.0 70.0 70.0 70.0 70.0 70.0 70.0
2 72.1 72.1 72.1 72.1 72.1 72.1 72.1
3 74.3 74.3

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