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Real Estate Investments I
(Business 33450)
Winter Quarter, 2023
Instructor: . Pagliari, Jr.
Key Take-Aways:
• Financial modeling of long-term, fixed-rate leases:
debt-equity model, and
income-differential model.
• An application of duration to real estate.
• Different financing mechanisms:
sale/leaseback,
ground lease,
master lease, and
infrastructure.
• Adjusting leasing/rental rates for excess TIs, differing credit quality, etc.
Real Estate Investments I
Instructor: . Pagliari, Jr.
Class Notes – Week #4:
Investment Decision Making: Part III
Table of Contents
I. Present Value of a Perpetual (or Infinite) Annuity ……………………………………………….. 2
II. Present Value of a Finite Annuity ………………………………………………………………………. 6
III. The Real (Inflation-Adjusted) Return ………………………………………………………………. 10
IV. Two Views of the Same Rent Pattern ……………………………………………………………….. 10
V. Income-Differential Model ……………………………………………………………………………… 16
VI. Debt-Equity Model ………………………………………………………………………………………… 20
VII. Leases as Adjusted for Tenant Quality ……………………………………………………………… 25
VIII. A Note on REIT Spin-Outs …………………………………………………………………………….. 35
IX. A Class of Real Estate Financing Techniques …………………………………………………… 37
X. Examples of Sale/Leaseback Transactions. ……………………………………………………… 38
XI. Bank of America: A Ground-Lease Example …………………………………………………….. 48
XII. The Empire State Building: First a Ground Lease & Then a Master Lease ………….. 67
I. Present Value of a Perpetual (or Infinite) Annuity
A. The present value of a perpetual or infinite annuity1 is given by:
CFCF = = P
B. As a simple proof of this assertion, consider the special case of the DDM (see week #2 notes)
when g = 0:
Recall the DDM:
When 0, then:
CF g CF CF
C. However, don’t confuse the expression above with: 0
, which assumes g = (or,
equivalently, =1).
D. See Exhibits 1 and 2.
1 It is not necessary that we denote an annuity as 0CF (because 0CF can also represent a particular payment to
be received in perpetuity); nevertheless, 0CF is used for your convenience – to easily denote a fixed annuity
Exhibit 1: Value of a Perpetual Annuity
Major Assumptions:
Initial Cash Flow (CFo/Po) $100
Discount Rate 10.0%
Present Value $1,000
Cumulative
Year Cash Flow Discount Factor Present Value Present Value
0 $0 1.00000 $0.00 $0.00
1 100.0 0.90909 90.91 90.91
2 100.0 0.82645 82.64 173.55
3 100.0 0.75131 75.13 248.69
4 100.0 0.68301 68.30 316.99
5 100.0 0.62092 62.09 379.08
6 100.0 0.56447 56.45 435.53
7 100.0 0.51316 51.32 486.84
8 100.0 0.46651 46.65 533.49
9 100.0 0.42410 42.41 575.90
10 100.0 0.38554 38.55 614.46
11 100.0 0.35049 35.05 649.51
12 100.0 0.31863 31.86 681.37
13 100.0 0.28966 28.97 710.34
14 100.0 0.26333 26.33 736.67
15 100.0 0.23939 23.94 760.61
16 100.0 0.21763 21.76 782.37
17 100.0 0.19784 19.78 802.16
18 100.0 0.17986 17.99 820.14
19 100.0 0.16351 16.35 836.49
20 100.0 0.14864 14.86 851.36
21 100.0 0.13513 13.51 864.87
22 100.0 0.12285 12.28 877.15
23 100.0 0.11168 11.17 888.32
24 100.0 0.10153 10.15 898.47
25 100.0 0.09230 9.23 907.70
26 100.0 0.08391 8.39 916.09
27 100.0 0.07628 7.63 923.72
28 100.0 0.06934 6.93 930.66
29 100.0 0.06304 6.30 936.96
30 100.0 0.05731 5.73 942.69
31 100.0 0.05210 5.21 947.90
32 100.0 0.04736 4.74 952.64
33 100.0 0.04306 4.31 956.94
34 100.0 0.03914 3.91 960.86
35 100.0 0.03558 3.56 964.42
36 100.0 0.03235 3.23 967.65
37 100.0 0.02941 2.94 970.59
38 100.0 0.02673 2.67 973.27
39 100.0 0.02430 2.43 975.70
40 100.0 0.02209 2.21 977.91
50 100.0 0.00852 0.85 991.48
60 100.0 0.00328 0.33 996.72
70 100.0 0.00127 0.13 998.73
80 100.0 0.00049 0.05 999.51
90 100.0 0.00019 0.02 999.81
100 100.0 0.00007 0.01 999.93
1. Recall:
2. Occasionally, you will
hear in practice that the
present value of cash
flows received after 30-40
years has very little impact
on the net present value.
This is certainly the case in
this illustration.
Of course, this outcome is
directly related to the
discount rate:
as k ↑ ⟶ NPV .
$1,000 = $100/.10
{Nothing more than a graph of the values shown in Exhibit 1.}
– =
{Same exhibit as prior page, but with further annotations.}
II. Present Value of a Finite Annuity
A. The present value of a finite annuity is given (as shown on the prior page) by:
CFCF k = = P
B. This equation can also be expressed as:
+ kCF CF = P
C. In a quiet moment, you should examine equation (2.1) when N = 0, 1, or .2
D. This equation can also be expressed as:
= CFP
2 The answers are:
At N = 0:
At N = 1:
At N = ∞:
E. This equation can be used to determine the present value of a constant (net) lease payment
over a fixed, finite period.3 The real estate application is the prevalence of net lease deals:
As an example, the plethora of
Walgreen’s sale/leaseback deals:
F. As a prelude to weeks 6 and 7, it can also be used to determine the monthly (or some other
period) payment necessary to completely amortize a mortgage loan over its amortization period:
Loan Amount = Periodic Payment
E. Note: k > i, due to higher risk premium (i.e., asset > debt).
F. An aside: We can also extend the DDM to the case of finite growth:
0 0 0
CF g CF g CF g
3 As one of many close-to-home examples, consider (Brookfield-backed) Fundamental Income’s purchase of 632 N.
Dearborn – leased to a single-tenant, Tao, for 20 years – for ≈ $30 million. See: , “Brookfield-Backed Firm
Buys River North Landmark,” Crain’s’ Chicago Business, May 25, 2022.
Same idea as above:
The present value of the finite-growth case
equals the present value of the infinite-
growth case less the sale of the reversionary
(at some future period N) infinite-growth
{This approach is utilized in Exhibit 7.}
G. Therefore, we can always find the fixed-rate rental stream (which again, for this purpose, we
will note as 0CF ) which has a present value equivalent to the floating-rate rental stream
(which we will continue to note as 0CF ).
Solve in Terms of Net Rents:
CF gCF k gkP
H. Note that as N ⟶ ¥, then
Instructor’s Note:
Focus on the intuition
(not the mathematics) for
the midterm exam; it’s
meant to merely aid your
intuition.
PV(Finite Fixed Lease) = PV(Finite Floating Lease)
I. The practical application of such an exercise is to consider the fixed-rental-rate properties (like
industrial, office and retail) in comparison to the floating-rental-rate properties (like apartments
and hotels) – such that they both have the same present values.
As an illustration, consider the situation in which the market’s standard 20-year lease is
$100/sq.ft., while a particular tenant (with credit quality equal to the market standard) would
prefer that the initial lease payment is lowered but escalated at some agreed-upon rate over the
term of the lease. As shown below, the equivalent initial rental rate is ≈ $81.47/sq.ft., escalating
at 3.0% per annum thereafter:
J. This example assumes that the discount rate is the same between the two types of leases, but
this too can be easily modified.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Illustration of Equivalence Between Fixed- and Floating-Rate Leases
Produces equivalent present values of $851.36, assuming the discount rate equals 10.0% and the lease length is 20 years.
Fixed-rate lease with annual payments of $100.00
Floating-rate lease with initial payment of $81.47 growing by 3.0% per annum thereafter.
III. The Real (Inflation-Adjusted) Return
A. Recall: The real return (r) has a multiplicative relationship with the inflation rate ():
B. Note: For debt (or, mortgage loans in this particular case), the real-return requirement (r) is
lower than that which is required, ex ante, for equities. However, on an ex post basis, the realized
real return on fixed-income securities can be lower or higher than it was for equity securities.
IV. Two Views of the Same Rent Pattern
A. Fact Pattern: Fixed-rate (net) lease payments, maturing at N, with a one-time “bump” in (net)
rents – see following graph.
B. Two differing real estate valuation approaches:
1. income-differential model, and
2. debt-equity model.4
C. In order to be economical, efficient and arbitrage-free, these two approaches must produce
the same valuation.
D. For an intuitive sense of these two approaches, see the following:
4 Much of this initial discussion is based upon: . Young and D. , “Leases as a Key to
Performance and Value…” in The Handbook of Real Estate Portfolio Management, . Pagliari,
Jr., editor, Irwin/McGraw Hill, 1995 and from , and , “Real Estate:
A Hybrid of Debt and Equity,” Real Estate Review, 1989, pp.54-58.
Illustration of INCOME-DIFFERENTIAL and DEBT-EQUITY Models:
Starting Point: Initial Lease with One “Bump”
This view of the rental stream is
particularly applicable to:
industrial, office & retail,
sale/leaseback
ground leases,
master leases, and
infrastructure investments
Illustration of INCOME-DIFFERENTIAL Model:
Viewed as Two Perpetual Annuities | One Longer-Dated than the Other
Illustration of INCOME-DIFFERENTIAL Model:
Viewed as Two Perpetual Annuities | One Longer-Dated than the Other
= CFN – CF0
Consider this as one possible path of “spot”
market rental rates – which the property taps
into upon the expiration of the initial lease.
If these changes in the spot-market rate are
loosely tied to inflation, then the reversionary
value is loosely indexed to inflation.
This is another
perpetual annuity;
however, we have to
wait N periods before
it begins.
Illustration of DEBT-EQUITY Model:
Current Lease as a Bond| Residual as Longer-Dated Perpetuity
ala Equation (2.2)
These LOBs (Lease-Obligation Bonds) are, essentially, tenant-backed bonds (e.g., see the Apple | Santa Monica deal
on Canvas | Cases and/or consider the value of the Apple store outside the Gleacher Center’s backdoor) and, as
such, the company’s credit worthiness ought to determine the appropriate discount rate.
Illustration of DEBT-EQUITY Model:
Current Lease as a Bond| Residual as Longer-Dated Perpetuity
These RAREs (Real Asset Residual Equity) are, essentially, claims on the property’s
reversionary value – now that is no longer encumbered by the existing tenant’s lease.
V. Income-Differential Model
A. The income-differential model is given by:
CF k = + P
B. This approach values, for example, a single-tenant building with a triple-net, fixed-rate, long-
term lease and assumes that this lease “rolls over” with same parameters but a different (and
presumably higher) rental rate.
Or, alternatively, it measures the individual leases that comprise the building’s tenant roster.
In either case, value is viewed as deriving from a portfolio of existing and future (net) leases.
This approach is often better suited to office, retail and industrial properties (v. apartments
and/or hotels).
C. Mathematically, this approach values the existing lease as a perpetual annuity and the future
lease (CFN) as an increment over the existing lease; the future lease increment (CFN – CF0) is
also viewed as a perpetual annuity – the value of which is discounted to its present worth.
D. Generally, this model is specified with a constant discount rate. However, it is usually more
appropriate to discount the future lease increment at a higher rate reflecting greater uncertainty
(and, therefore, more risk):
CF k = + P
where: k1 < k2 .
k1 = f(tenant’s credit-worthiness) [e.g., Google v. Pagliari, Inc.], and
k2 = f(building quality, location, market strength, etc.).
E. Let’s examine some pragmatic problems with this theoretical approach:
1. It ignores leasing commissions, tenant improvements, etc. However, this problem is easily
remedied; consider the “amortized” cost of such expenditures upon lease expiration:
For example, assume: TIs, LCs & CIs = Cap Ex = $10/sq.ft in year t0 and, for simplicity,
assume the length (N) of this new lease = ∞ for Tenant A, while Tenant B (under
otherwise identical terms) requires no Cap Ex and is willing to pay $20/sq.ft./year in net
To be indifferent (as the building owner) between renting the space to Tenant A or Tenant
B (assuming they are of equal credit worthiness), what should Tenant A pay?
Note: We could make this problem more realistic by assuming that Tenant A’s and B’s
leases have a finite maturity (e.g., 10 years). The effect is to convert the mathematics from
an infinite annuity to a finite annuity; however, the intuition remains the same.5
5 In this simple illustration, N = ¥ and, accordingly, the “amortization” of the up-front capital expenditure vis-
à-vis the present value of the lease 0P requires that the expenditure is “amortized” over the life of the lease
such that the (net) lease amount 0CF takes the form of: 00 0 0CFP CF P k
. In the more practical
case, N < ¥, the amortization of the up-front capital expenditure takes a slightly more complicated form:
. Note: As N ↓, Rent Adjustment ↑.
Assume that Tenant A offers to pay directly the Cap Ex and perform the necessary tenant
improvements and other capital improvements, such that Tenant A would then be
obligated to pay annual (net) rent of $20/sq.ft. Q : As the building owner, are you
indifferent? A : No! Why? You want to control construction quality.
2. Assumes a single lease roll over. However, this problem is also easily remedied; consider
including an additional lease increment term(s):
CF CFCF CF
CF kk = + P
where: k1 < k2 < k3.
F. In addition to risk varying between existing and future leases (i.e., k1 < k2), risk can also vary
between existing tenants – see §VII.
G. Nevertheless, the Income-Differential Model efficiently demonstrates that value is sensitive to
and effected by:
1. the initial rent ( 0CF ),
2. rent level changes (i.e., 0NCF CF ),
3. changes in the discount rate (k), and
4. passage of time (N), which (hopefully) enables "under-rentedness" to roll over (this is
akin to our earlier discussion about loss-to-lease).
H. Q: Given the following fact pattern, which property (otherwise identical buildings, but not
necessarily identical tenants) would you prefer and why?
A: A larger share of Property X’s value is from existing leases (80% v. 60%); therefore, you
would typically prefer X to Y.
Q: What other factor(s) might you consider?
A: In particular, the initial portion of value is a f(creditworthiness of tenant(s)), while the
reversionary value is a f(construction quality, location, etc.)
Ultimately, E[kX ] = f(X) and E[kY ] = f(Y); so, how different is the underlying real estate (i.e.,
Building X (in Market X) v. Building Y (in Market Y))?
Q: What is a possible exception to your preference of Property X over Property Y?
A: If you are concerned about unanticipated increases in the rate of inflation (), then you may
prefer Property Y if the difference in the initial valuations is attributable to the differences in
lease length: NX > NY (because Property Y presumably permits you to sooner rewrite the lease
at the then-prevailing market rental rate).
{This question of cash-flow v. residual value – particularly apt when unanticipated inflation is
high or uncertain – is further explored in the duration discussion of §VII.}
CF N – CF 0
Property k (1+k )N
A 250.00$ 200.00$ 50.00$
B 250.00$ 150.00$ 100.00$
Prices(or Values) per Square Foot
[$200/250 = 80%]
[$150/250 = 60%]
VI. Debt-Equity Model
A. The debt-equity model is given by:
CF k = + P
B. In words, this model says:
Price = Value of Existing Tenant Debt + Reversionary
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