RE I_ Weeks # 6 & 7
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Real Estate Investments I
(Business 33450)
Winter Quarter, 2023
Instructor: . Pagliari, Jr.
Classes #6 & #7
Key Take-Aways:
• Mortgage mechanics.
• Mortgage underwriting.
• Debt’s impact on:
Equity returns (ke)
Volatility (σe)
• Strategic use of leverage.
• CMBS/securitization.
• Bridge equity loans.
• Levered loans.
Not well understood by
most practitioners
Real Estate Investments I
Instructor: . Pagliari, Jr.
Class Notes – Weeks #6 & 7:
Mortgage Debt/Use of Financial Leverage
Table of Contents
I. General Parameters of Loan Types ……………………………………………………………………. 1
II. Loan Benchmarks/Ratios/ Terminology …………………………………………………………… 2
III. Construction v. Permanent Financing ………………………………………………………………… 5
IV. Basic Loan Mathematics ………………………………………………………………………………….. 7
V. A Note on the Effective Interest Rate ………………………………………………………………. 17
VI. A Few Points to be Made about Loan Pricing …………………………………………………… 23
VII. Loan-to-Value Ratio v. Debt-Coverage Ratio ……………………………………………………. 28
VIII. Leverage and Investment Considerations …………………………………………………………. 41
IX. Interest Rate/Adjusted Cap Rate Spread ………………………………………………………….. 43
X. An Overview of the CMBS Market …………………………………………………………………… 47
XI. Highly Levered Transactions ………………………………………………………………………….. 73
XII. An Introduction to the Strategic Use of Leverage ………………………………………………. 77
XIII. Levered Loans ……………………………………………………………………………………………….. 88
XIV. Volatility of Levered Equity When Considering Bankruptcy ……………………………… 106
XV. Key Relationships between Asset Returns and Cost of Indebtedness …………………. 109
These notes were partly prepared based on discussions with:
My former colleagues at BlackRock Realty Group
(in particular: , (’90) & ),
(’10) & – CBRE
(AB ’78) – HTLF Financial Services.
However, any remaining mistakes or omissions are the fault of the Instructor.
I. General Parameters of Loan Types
A. Concerned with “permanent” loans (see graphic on p.3).
B. Payments: level v. graduated,
C. Amortization: self-amortizing v. balloon v. interest-only,
D. Rate: fixed v. floating,
E. Contingent Interest: no v. yes; if yes, based on:
1. gross income,
2. net operating income, and/or
3. reversion (via sale, refinance, appraisal, etc.),
F. Collateral/ Guaranty:
1. recourse (“joint & several”) v. non-recourse, and
2. mortgage lien position (1st, 2nd, wrap, etc.):
Illustration of Hypothetical Lien Priorites
$1,000 Position Position
First Mortgage Loan
Second Mortgage Loan
(or Mezzanine Financing)
G. Prepayment: prohibited v. allowed (with penalty) – while prepayment without penalty is
generally permitted for residential mortgages, this is not the case for commercial mortgages.
Particularly favored when ρ
is high and/or uncertain.
Capital Stack
(or “cap stack”)
Consider Pagliari and Pritzker,
as “joint & several” guarantors.
Unsurprisingly, expected return
[E(ki)] and risk (σi) increase as
you move up the capital stack.
II. Loan Benchmarks/Ratios/ Terminology
A. Debt-Coverage Ratio (DCR):
* estimated NOI (less reserves) divided by debt service,
B. Loan-to-Value Ratio (LTV):
* loan amount divided by property value,
C. Debt Service:
* annual principal and interest payments,
D. Loan Constant:
* annual debt service divided by current loan amount,
E. Loan Origination Fees and Costs (“Points”)
* expressed as a percentage of initial loan amount.
F. Lenders typically underwrite the collateral based on trailing earnings (i.e., NOI0), as befits
their risk/return tradeoff (i.e., the lender’s maximum return is essentially the loan’s interest
rate). However, some lenders will “reach” for volume (i.e., new business) in “hot” markets by
underwriting the collateral based on forward earnings (i.e., NOI1) – in some cases, they will
even use “stabilized” earnings.1
1 At a higher leverage ratios, current earning may be insufficient to fully service the debt payments; if so, then
an interest reserve is typically established (i.e., held back from the loan disbursement) to fund the anticipated
shortfall(s). It is expected that property’s income will stabilize before the interest reserve is exhausted (e.g., see
the State & Main – Part II case). Of course, this is not always the case (e.g., see Village in Real
Estate II (#33451)).
For underwriting purposes, lenders set maximum DCR and
LTV thresholds and then make loans based on the lower of
these two hurdles – examples to follow.
Overview of Real Estate Debt Finance
Apartments
Condominiums Hotels
Co-operatives Industrial
Single-family Homes Residential Commercial Office
Townhomes Retail
Others Others
Short-Term Short-Term
Acquisition & Development (A&D) Loans Construction Loans
Construction (Revolver) Loans
Long-Term Long-Term
Permanent/End Loans Permanent/Take-Out Loans
Securitized –> MBS Securitized –> CMBS
Unsecuritized –> Portfolio Loans Unsecuritized –> Whole Loans
This is mostly
commercial
banks commercial
“agencies”
Ways to stratify the lending market:
• Residential v. commercial, and
• Short-term (construction) v. long-term (permanent).
Often accompanied by a change of ownership:
• from builder to homeowner,
• from one homeowner to another, or
• refinancing of existing (permanent) loan.
Often accompanied by a change of ownership:
• from developer to investor,
• from one investor to another, or
• refinancing of existing (permanent) loan.
Income-Producing RE: Owner-Occupied Housing:
Overview of Real Estate Debt Finance
Apartments
Condominiums Hotels
Co-operatives Industrial
Single-family Homes Residential Commercial Office
Townhomes Retail
Others Others
Short-Term Short-Term
Acquisition & Development (A&D) Loans Construction Loans
Construction (Revolver) Loans
Long-Term Long-Term
Permanent/End Loans Permanent/Take-Out Loans
Securitized –> MBS Securitized –> CMBS
Unsecuritized –> Portfolio Loans Unsecuritized –> Whole Loans
Income-Producing RE (weeks #1-9).
Most often, “take-out” loans are
made specifically to refinance a
construction loan once the project is
completed (this is case #3).
{aka balance-sheet lenders}
Land + Buildings
Build, Inventory & Sell RE.
Land & Infrastructure
Buildings: Homes
Non-Recourse
Note: “take-out” loans are a subset
of permanent loans.
III. Construction v. Permanent Financing
A. Mortgage lending differs: residential v. commercial financing.
B. Mortgage lending also differs: construction v. permanent financing:
1. The general nature of construction loans:
a. Interest rate – floats (tied to prime or SOFR (or LIBOR2)),
b. Maturity – short term (18 to 36 months),3
c. Amortization – none (or, interest-only),
d. Loan amount – 65-80% of cost (dependent upon a variety of factors: pre-leasing,
developer’s track record, market strength, etc.),
e. Recourse – personal liability4 to developer, and
f. Sources – commercial banks, credit companies, etc.
2. The general nature of “permanent” loans:
a. Interest rate – fixed (tied to long-term Treasuries) or floats (tied to short-term
Treasuries or LIBOR),
b. Maturity – intermediate term (5 to 10 years),
c. Amortization – often based on 30 years,
d. Loan amount – 65-80% of value (dependent upon a variety of factors: tenants’
credit-worthiness, lease rollover, property type, market strength, etc.),
e. Recourse – none (i.e., non-recourse), and
2 In 2017 (and following the scandals surrounding the London inter-bank offer rate (LIBOR)), the Federal
Reserve System decided that, in June 2023, LIBOR is to be replaced as the reference rate with the secured
overnight financing rate (SOFR, which is not without its own complications and nuances – e.g., see:
“Understanding LIBOR Alternatives in CRE Loans,” , November 12, 2021) in the U.S.
and the sterling overnight index average (SONIA) in Europe. While the real estate lending market is
transitioning to these alternative reference rates, some earlier-originated loan documents retain the reference
to LIBOR (which was first published in 1986).
3 On occasion, it may be longer; loan length = f(project size, complexity, expected lease-up, etc.).
4 The developer may be able to negotiate certain limitations: construction-cost only guarantees, top x% of the
loan, etc.
https://www.federalreserve.gov/newsevents/pressreleases/files/bcreg20221216a1.pdf
https://www.chathamfinancial.com/insights/understanding-libor-alternatives-in-cre-loans?utm_source=re+newsletter&utm_medium=email&utm_campaign=cre+market+update
f. Sources – insurance companies, CMBS (commercial mortgage-backed securities)
market, governmental agencies (for apartments), etc.
3. Overview of commercial mortgage market lending share:
Source: “Top Banks’ Loan Books Grew 5% Last Year,” Commercial Mortgage Alert, April 29, 2022.
Hedge funds,
opportunity funds,
REITs, etc. [are an
increasingly
important segment
of high-yield debt]
The commercial
banks are the
primary source for
construction loans.
IV. Basic Loan Mathematics
A. As indicated in week #4, a level-payment, self-amortizing mortgage loan is a finite annuity:
In some loan documents, you will see language that describes this present-value process (you
may even see some form of the equation itself – as in case #3).
Lenders quote interest rates on an annual basis; however, the computations are generally
made on a monthly basis (i.e., a 30-day month and a 360-day year). For example, a 6.0% loan
fixed for 30 years → 0.5% per month for 360 months (a 12.0% loan → 1.0%/month, etc.).
B. Level (monthly) payment is that annuity amount which over the term of the mortgage loan
has a present value (when discounted at the loan’s stated interest rate) equal to the initial loan
amount – this is a finite-annuity problem.
C. Equation (1) can be re-written as a finite annuity:5
= L
D. From Equation (2), we can write the formula for the monthly loan constant:
E. The above must be multiplied by 12, in order to obtain the annual loan constant (LC ):
Annual Loan Constant
5 Same mathematics as in the week #4 notes. More commonly in practice, the payment amount (and/or any
of the other parameters) is produced by using a calculator/computer. In Excel, the function is:
=PMT(i/12, Nx12, L0).
This figure is used in practice to “size”
loans and to determine CF leverage:
• positive (CF1/P0 > LC), or
• negative (CF1/P0 < LC)
infinite annuity
infinite annuity
starting after
loan maturity
F. Some examples:
Compare N = 15 years v. N = 30 years.
For example, if the initial loan amount (L0) = $100,000 and the interest rate (i) = 8.5%,
then the annual loan constant at 15 years equals:
Annual Loan Constant
Assume as above that the initial loan amount (L0) = $100,000 and the interest rate (i) =
8.5%, then the annual loan constant at 30 years equals:
Annual Loan Constant
To foreshadow (§IV.J):
Loan Constant .118169
Interest Rate -.085000
Principal Reduction .033169
To foreshadow (§IV.J):
Loan Constant .092270
Interest Rate -.085000
Principal Reduction .007270
While debt service remains
constant over the life of the loan,
the portion representing accrued
interest declines and the portion
representing principal
amortization increases.
payment is
relative to
initial loan
G. An Aside: While most loans are based on monthly compounding (and a 360-day year), the
frequency of the compounding period matters:
Example of Various Compounding Periods
Compounding
Frequency 4.0% 8.0% 12.0% 16.0%
Annual 4.000% 8.000% 12.000% 16.000%
Semi-Annual 4.040% 8.160% 12.360% 16.640%
Quarterly 4.060% 8.243% 12.551% 16.986%
Monthly 4.074% 8.300% 12.683% 17.227%
Daily 4.081% 8.328% 12.747% 17.347%
Continuously 4.081% 8.329% 12.750% 17.351%
∆ |Monthly - Annual 0.074% 0.300% 0.683% 1.227%
Equivalent Rate for a Stated Rate of:
Note: The equivalent rate6 = (1 + i/n)n – 1, where: n = number of compounding periods per
year (e.g., a 12.0% annual rate with monthly compounding → (1 + .12/12)12 – 1 = .12683).
6 In Excel, the stated interest rate (i) is referred to as the “nominal” rate; two interrelated functions are
available (as stated in Excel): a) =NOMINAL(effect_rate, npery) and b) =EFFECT(nominal_rate, npery),
where: npery = the number of compounding periods per year.
Of course (and as shown in earlier in these class notes), these two functions are related to one another
(again, as stated in Excel):
Nominal_Rate
EFFECT 1 1
Debt Equity
∆ increases with i
{w.r.t. the preferred return (or “pref”)}
H. The loan's unpaid principal balance at any time (T ) is simply equal to the present value of
the remaining debt service payments discounted at the stated interest rate. It can be
determined via:
where: T = year of loan repayment.
I. The existence of loan origination fees and costs (or, "points") causes the loan's effective
interest rate (ε ) to rise above the stated interest rate. The solution for the effective interest
rate is a combination of the points and the period of time the borrower keeps the loan
outstanding. It is determined as follows:
12Net Loan Proceeds
+ +
− +
+
Pyt L = + L
L = Pyt +
ε – must be iteratively solved, via IRR-like techniques.
As Points ↑, ε ↑.
J. Mortgage and underwriting mechanics: see Exhibits 1 – 5 for examples.
This is important
when prepaying a
self-amortizing
loan or making a
balloon payment.
If, e.g., the loan has an amortization
period of 30 years, but “balloons” in
the 10th year, then the loan balance
upon maturity is:
Note: Pyt and LT are determined based on i, L0 and N
(and are independent of the “points”)
ε is the new element, for which we must solve
Exhibit 1: Illustration of Various Loan Parameters
Major Assumptions: #1 #2 #3
Interest Rate (i ) 8.50% 8.50% 8.50%
Loan Origination Fees (Pts ) 1.50% 1.50% 1.50%
Amortization Period (N ) 30 Years 30 Years 15 Years
Term (or, Maturity) 10 Years 10 Years 10 Years
Net Operating Income (NOI 0) $1,000,000 $1,000,000 $1,000,000
Debt Coverage Ratio (DCR ) 1.05 :1 1.15 :1 1.15 :1
Loan-to-Value Ratio (LTV ) 95.0% 85.0% 85.0%
Purchase Price (P 0) $12,500,000 $12,500,000 $12,500,000
Transaction Costs 1.0% 1.0% 1.0%
Capitalization Rate [(NOI 0 = CF 0)/P 0 ] 8.0% 8.0% 8.0%
Annual Loan Constant:
Monthly Loan Constant 0.77% 0.77% 0.98%
Annual Loan Constant (LC ) 9.23% 9.23% 11.82%
Tests for Maximum Loan Amount:
1) Debt-Coverage Test:
Net Operating Income $1,000,000 $1,000,000 $1,000,000
Debt Coverage Ratio ÷ 1.05 :1 ÷ 1.15 :1 ÷ 1.15 :1
Available for Debt Service $952,381 $869,565 $869,565
Annual Loan Constant ÷ 9.23% ÷ 9.23% ÷ 11.82%
Loan Amount $10,321,718 $9,424,177 $7,358,673
$10,320,000 Rounded $9,420,000 Rounded $7,360,000 Rounded
2) Loan-to-Value Test:
Purchase Price $12,500,000 $12,500,000 $12,500,000
Loan-to-Value Ratio x 95.00% x 85.00% x 85.00%
Loan Amount $11,875,000 $10,625,000 $10,625,000
$11,880,000 Rounded $10,630,000 Rounded $10,630,000 Rounded
Maximum Loan Amount $10,320,000 $9,420,000 $7,360,000
Annual Debt Service:
Loan Amount $10,320,000 $9,420,000 $7,360,000
Annual Loan Constant 9.23% 9.23% 11.82%
Annual Debt Service $952,222 $869,180 $869,722
Equity Requirement:
Purchase Price $12,500,000 100.0% $12,500,000 100.0% $12,500,000 100.0%
Transaction Costs 125,000 1.0% 125,000 1.0% 125,000 1.0%
Gross Acquisition Cost 12,625,000 101.0% 12,625,000 101.0% 12,625,000 101.0%
Loan Amount (10,320,000) -82.6% (9,420,000) -75.4% (7,360,000) -58.9%
Loan Fees 154,800 1.2% 141,300 1.1% 110,400 0.9%
Net Loan Proceeds (10,165,200) -81.3% (9,278,700) -74.2% (7,249,600) -58.0%
Equity Requirement $2,459,800 19.7% $3,346,300 26.8% $5,375,400 43.0%
This is an oversimplified set of examples (e.g., i ≠ f(N, DCR
or LTV). For now, just looking for some basic intuition.
Loan “balloons”
in year 10
from §IV.F)
A form of “reverse engineering”:
L0 x DC x DCR = NOI (less RR)
loan amount
is the lesser
of test #1
and test #2
The only items
that change across
alternatives are the
parameters found
in the boxes.
Arithmetic inverses
of one another.
conservative
conservative
An increase of ≈ $3 million (or nearly 25% of the purchase price)
used in the following
amortization schedule
Exhibit 2 Loan Amortization Schedule
15-Year Amortizing Mortgage Loan 30-Year Amortizing Mortgage Loan
Beginning Debt Accrued Principal Ending Beginning Debt Accrued Principal Ending
Month Balance Service Interest Amortization Balance Balance Service Interest Amortization Balance
1 $7,360,000 $72,477 $52,133 $20,343 $7,339,657 $7,360,000 $56,592 $52,133 $4,459 $7,355,541
2 7,339,657 72,477 51,989 20,488 7,319,169 7,355,541 56,592 52,102 4,490 7,351,051
3 7,319,169 72,477 51,844 20,633 7,298,536 7,351,051 56,592 52,070 4,522 7,346,529
4 7,298,536 72,477 51,698 20,779 7,277,757 7,346,529 56,592 52,038 4,554 7,341,975
5 7,277,757 72,477 51,551 20,926 7,256,831 7,341,975 56,592 52,006 4,586 7,337,388
6 7,256,831 72,477 51,403 21,074 7,235,757 7,337,388 56,592 51,973 4,619 7,332,770
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