Final Examination
Real Estate Investments I
Winter Quarter, 2023
Copyright By PowCoder代写 加微信 powcoder
Instructor: . Pagliari, Jr.
Instructions:
1. This is a closed-book/closed-note exam (subject to the formulae provided in the
appendix to this exam). For instance, you are not permitted to use the class-provided
spreadsheets in preparation of your solutions.
2. Please use the Instructor-provided “solution form” (found on Chalk) as, at a minimum,
your cover sheet – though, pasting your Excel-generated solution into this Word
document may be preferable. Completing the footer will automatically place your name
on subsequent pages and indicate the number of pages you used to complete this
examination: “1 of _.”
3. If you do not use a computer to prepare your solution set, you will have two hours to
complete the examination. If you do use a computer, you will have two and a half hours
to complete the examination (i.e., an additional 30 minutes will be permitted for
formatting, printing, etc.).
4. Do not write in the exam; instead, provide your solution set on separate paper. If you
do not use a computer to prepare your answers, write your answers legibly (using only
one side of the page). If you use a computer, make sure that your file prints your
solution set professionally.
5. Whether or not you use a computer, show all supporting calculations (as partial credit
will be given) and label clearly each of the questions you answer. Make sure your
responses are submitted in the proper sequence.
6. The weighting used to grade each question is equal to the amount of time allocated to
that question.
7. If the question calls for a multi-part answer (e.g., name three Illinois cities), credit will
only be given for the first corresponding number of replies (e.g., only the first three
named cities) – and the remainder will be ignored.
8. Unless the problem notes otherwise, assume that all cash flows are received at year’s end
and that interest, discount and/ or inflation rates are annual.
9. You are expected to observe the Booth Honor Code (including, but not limited
to, maintaining the contents of this exam strictly confidential.)
10. Good luck!
1. You are contemplating the purchase of a $5.0 million dollar (assume transaction costs are zero)
apartment building which last year had operating cash flow (i.e., CF0 or net income after
replacements) of $350,000. As part of the potential financing for this property, you approach
several lending institutions about the parameters under which they would make a first mortgage
loan. They consistently provide you with the following parameters:
Interest rate: 6.40%
Loan fees: 2.0%
Amortization period: 30 years
Loan maturity: 10 years
Maximum loan amount equals the lesser of:
1.2:1 debt-coverage ratio,* or
80% loan-to-value ratio.
* based on CF0.
For purposes of this problem, assume the annual compounding of interest (i.e., ignore
monthly compounding).
A. Compute the annual loan constant.
(5 minutes)
B. Compute the maximum loan† you could borrow against this property.
(5 minutes)
C. Assuming you hold the property for five years (at which time you sell the property and
pay off the loan), calculate the effective annual interest rate (ε) rate – using an exact
approach (rather than an approximation).
(5 minutes)
D. Comment on how and why the effective interest rate (ε) were to change as your holding
period changes.
(5 minutes)
† Rounded to the nearest $10,000.
E. Assuming that you believe that the property’s growth in cash flows to be 2% per annum
and the property’s ending capitalization rate will be the same as its beginning cap rate
(and that kd is as you computed in 1.C. above‡), present the components of return (or
return attribution) for this levered (ke) transaction.
(5 minutes)
‡ If you did not compute a value for 1.C., then assume that kd = 7.0% (note: this is not the
correct answer to 1.C.).
F. You understand that the use of leverage increases the riskiness of your equity
investment. Consequently, you are interested in calculating the “break-even” growth rate
(such that ka = kd assuming no shifts in capitalization rates).
i. Determine the break-even growth rate.
ii. Given what you know about current conditions in today’s real estate market, how
confident (and why) do you feel in achieving this rate?
(10 minutes)
G. Due to real estate’s high transaction costs, you also want to consider owning this asset
for the long-term (e.g., at least as long as the 5 years estimated in 1.C. above).
Accordingly, you have some concerns about the proposed loan’s “rollover” risk (i.e., the
ability of the loan to be refinanced, when it “balloons” or matures in ten years, should
interest rates and/or capitalization rates rise significantly).
i. For the loan constant to approach the value of the interest rate, what does this
imply about the length of the amortization period?
ii. Please comment on the general nature of when – under what cap rate/loan constant
conditions – the lender’s two loan underwriting tests (i.e., the LTV and DCR tests)
produces approximately the same maximum loan amount and when one test will act
as the binding constraint. That is, in some market environments, the loan-to-value
ratio will determine the lower of the two possible indicated loan amounts (i.e., it will
act as the binding constraint); in other environments, the debt-coverage ratio will
represent the governing test. When?
(10 minutes)
2. You have been asked by an old friend to estimate the risk/return profile of two competing real
estate investments. You discuss the expected economic landscape over the investor’s anticipated
holding period. This friend feels that there is 75% likelihood of a low inflationary environment.
In the low inflationary environment, this friend feels that 2% represents the long-term average
inflation rate. Conversely, if we have a high inflationary environment, the rate is expected to be
6%. Given the uncertainties facing the stock and bond markets and the slope of the yield curve,
you feel that there is a 60% likelihood of an increasing capitalization rate environment and a
40% likelihood of a decreasing cap rate environment. Based on the various combinations of
these possibilities, you have computed the following real (i.e., inflation-adjusted) after-tax
Scenario: Project #1 Project #2
Low Inflation, Decreasing Cap Rates 9.5% 12.5%
Low Inflation, Increasing Cap Rates 4.5% 3.5%
High Inflation, Decreasing Cap Rates 8.0% 10.5%
High Inflation, Increasing Cap Rates 5.5% 4.0%
You feel confident that all other significant investment variables have a reasonably small range
of potential outcomes.
A. Based on the subjective estimates of you and your family friend, prepare a joint
probability matrix concerning the economic variables of importance.
(5 minutes)
B. Compute the mean and standard deviation of the expected return for Project #1 (only).
(5 minutes)
C. Assuming that the mean and standard deviation of Project #2’s expected return are
7.0% and 4.0%, respectively (note: these are only approximations of the specific
statistics), what is the probability that Project #1 will generate a real, after-tax return that
is at least equal to 4.50% (i.e., your old friend’s weighted average estimate of the long-
term inflation rate plus a cushion of 150 basis points)? What is the probability for
Project #2? Based on this criterion, which project would you select?
(10 minutes)
D. Assuming that your family’s friend can afford to invest in both of these properties, what
should you look for in the pattern of returns between these two properties? Why?
(5 minutes)
3. The typical, GAAP-based financial statements of publicly traded companies are often found
wanting for real estate investment trusts. Accordingly, most REITs also present “funds from
operations” (FFO) as supplemental information.
A. Based on the following GAAP-based income statement, what should XYZ Company
report as its FFO?
(10 minutes)
B. Most analysts augment FFO with their own calculation of “funds available for
distribution”(FAD) – also sometimes referred to as “cash available for distribution”
(CAD) or “adjusted funds from operations” (AFFO). What items – whether or not
evident in the exhibit above – make up the transition from FFO to FAD? (Note: You’re
not asked to make the calculation – but rather generally identify the items that make up
the transition from FFO to FAD.)
(5 minutes)
XYZ Company
An Apartment-Oriented REIT
Selected Year-End Financial Statement Disclosure
Property Revenues $270,000,000
Property Expenses 110,000,000
General & Administrative Expenses 5,000,000
Depreciation Expense 45,000,000
Interest Expense 50,000,000
Net Income $60,000,000
Net Income $60,000,000
Plus: Depreciation 45,000,000
Less: Principal Amortization -10,000,000
Changes in Working Capital -5,000,000
Total of Cash Provided from Operations $90,000,000
Income Statement
Statement of Changes in Financial Position
C. Assuming that the XYZ owns 25,000 apartment units and that a reasonable replacement
reserve is $300 per unit, prepare a presentation of levered, operating cash flows as if XYZ
were a private real estate entity. (Further assume that only half of the General &
Administrative Expense would be necessary if the entity were to be privately operated.)
(5 minutes)
D. Despite a retreat in prices and returns during 1998-99 and again during the 2007-08
financial crisis, equity REITs have enjoyed remarkable success since the early 1990s.
Nevertheless, it can be argued that there ought to be a “clientele” effect for REITs. Please
i. this clientele effect as it relates to REITs,
ii. four instances of when/how the REIT “platform” might matter, and
iii. four instances of when/how the REIT “platform” might not matter.
(10 minutes)
DO NOT WRITE ANSWERS IN THE EXAMINATION
Note: This sample examination totals 100 minutes (and, therefore, 100 points);
the actual examination will also total 120 minutes (and, therefore, 120 points).
Summary of Generalized Equations
1. Monthly Level-Payment, Self-Amortizing Loan:
2. Present Value of an Annuity and Series:
a. Finite Annuity:
− + =
b. Infinite Annuity:
c. Infinite Series:
g)+(1 CF = P
3. One-Period Leverage Model:
LTVk k = k
4. Volatility of Leverage Equity (assuming fixed-rate financing):
e = 1 LTV
5. Single-Period Return:
value market Beginning
value market in change + Income
6. Multiple-Period Return:
a. Arithmetic Average:
k + + k + k + k = k N321
b. Geometric Average:
( ) ( ) ( ) ( )1 2 31 1 1 1 1N Nk k k k … k= + + + + −
c. Approximation of Geometric Average:
7. Measures of Risk:
a. Historical Variance:
)k k( + + )k k( + )k k( + )k k( =
b. Forecasted Variance:
w )k k( + + w )k k( + w )k k( + w )k k( = N
k ⋅⋅−⋅−⋅− …σ
c. Standard Deviation:
8. Z-Score:
Z Score =
9. Conditional Expectations (Two-Variable Case: x and y):
a. Expected Return:
YXY xxYE µσ
b. Variance:
( )2 ,22| 1 YXYxY ρσσ −=
c. Covariance:
( )( ) YXYX
YnXnYX yxN
d. Correlation:
10. Portfolio Volatility → 2-Variable Case:
1 1 1 1 1 1 1 1
1 1 2 2 1 2 1 2 1 2 1 1 2 2 1 2 1 22 2P , ,w w w w w w w wσ σ σ ρ σ σ σ σ σ= + + = + +
11. Approximate Portfolio Volatility → N-Variable Case:
where: σ = average volatility of a single asset (or variable),
ρ = average correlation between any two assets in the portfolio, and
N = the number of total assets in the portfolio.
{assumes: ,
, 1, 2,… , and ,i i i ji N w i jN
σ σ ρ ρ= ∀ = = = ∀ ≠ }
[Instructor’s Note: You are responsible to memorize any other equation(s) you feel relevant.]
Final Examination
Business 33450: Real Estate Investments I
Winter Quarter, 2023
Instructor: . Pagliari, Jr.
SOLUTION SET
Please observe the Booth Honor Code: These solutions and the exam
are to remain confidential; you are not to share them (directly or
indirectly) with any other student who will be taking this course.
1. Loan Interest Rate 6.40%
Loan Fees 2.0%
Amortization Period (years) 30
Maturity Period (years) 10
Annual Monthly
Compounding Compounding
A. Loan Constant 7.579% 7.506%
B. LTV Test:
Value $5,000,000 $5,000,000
TV 80.0% 80.0%
Estimated Loan Amount $4,000,000 $4,000,000
CF0 $350,000 $350,000
Minimum DCR 1.20:1 1.20:1
Available for Debt Service 291,667 291,667
Loan Constant 7.579% 7.506%
Estimated Loan Amount $3,848,599 $3,885,744
Maximum Loan Amount (rounded) $3,850,000 $3,890,000
C. Loan Payoff (years) 5 5
Annual Loan Payment $291,773 $291,986
Ending Loan Balance $3,592,178 $3,637,250
Gross Loan Amount $3,850,000 $3,890,000
Loan Origination Fees (77,000) (77,800)
Net Loan Proceeds 3,773,000 3,812,200
Loan Payment – Year 1 -291,773 -291,986
Loan Payment – Year 2 -291,773 -291,986
Loan Payment – Year 3 -291,773 -291,986
Loan Payment – Year 4 -$291,773 -291,773 -291,986
Loan Payment – Year 5 -$3,592,178 -3,883,951 -3,929,236
Effective Interest Rate (k d ) 6.898% 6.888%
D. Effective interest rate (k d ) decreases as holding period lengthens.
Why? Because amortizing the loan fee over a longer period of time.
Supplement
E. Components of Return:
Initial Cap Rate (CF 1/P 0) 7.14% 7.14%
Growth Rate (g ) 2.00% 2.00%
Cap Rate-Shift Effect (∆) 0.00% 0.00%
Asset-Level Return (k a ) 9.14% 9.14%
Leverage Effect (k e – k a ) 6.89% 7.23%
Equity-Level Return (k e ) 16.03% 16.37%
Degree of Leverage:
Asset Value $5,000,000 $5,000,000
Loan Amount – Gross (3,850,000) (3,890,000)
Loan Fees 77,000 77,800
Loan Amount – Net (3,773,000) (3,812,200)
Equity Requirement $1,227,000 $1,187,800
Loan-to-Value Ratio 75.5% 76.2%
F. i) Break-even growth rate:
g = -0.095% -0.105%
Ought to feel favorably towards the possibility of achieving at least a zero-percent growth rate.
The two tests will indicate identical (maximum) loan amounts when the capitalization rate
approximately equals the loan constant. When the capitalization rate exceeds the loan constant,
the LTV test will represent the binding constraint. When the loan constant exceeds the
capitalization rate, the DCR test will represent the binding constraint.
The loan constant approaches the interest rate as the amortization period lengthens substantially
(e.g. , 30 or more years).
LTVk k = k
Low High Total
Increasing 45% 15% 60%
Decreasing 30% 10% 40%
75% 25% 100%
Inflation rate (ρ ) 2% 6%
Probability
Deviations
B. Low Inflation, Decreasing Cap Rates 30% 9.50% 2.850% 0.0270%
Low Inflation, Increasing Cap Rates 45% 4.50% 2.025% 0.0180%
High Inflation, Decreasing Cap Rates 10% 8.00% 0.800% 0.0023%
High Inflation, Increasing Cap Rates 15% 5.50% 0.825% 0.0015%
Total 100%
Mean 6.500%
Variance 0.049%
Standard Deviation 2.208%
Therefore, the expected returns of Project #1 ~ N(6.50%,2.21%^2).
C. Target Return 4.50%
Project #1 Project #2
Mean 6.500% 7.000%
Standard Deviation 2.208% 4.000%
Z Score -0.91 -0.63
Probability of Less Than Target 18.25% 26.60%
Probability of More Than Target 81.75% 73.40%
Therefore, select Project #1.
Inflation Rates
Project #1
Note: Not looking for
students to produce such
a graphic on the exam.
Instead, this graphic is
provided as an aid to the
students’ understanding
of the problem.-10% -5% 0% 5% 10% 15% 20% 25%
Potential Returns
Return Distributions: Projects #1 & #2
Target Return Project #1 Project #2
3. XYZ Company
An Apartment-Oriented REIT
Selected Year-End Financial Statement Disclosure
Property Revenues $270,000,000
Property Expenses 110,000,000
General & Administrative Expenses 5,000,000
Depreciation Expense 45,000,000
Interest Expense 50,000,000
Net Income $60,000,000
Net Income $60,000,000
Plus: Depreciation 45,000,000
Less: Principal Amortization -10,000,000
Changes in Working Capital -5,000,000
Total of Cash Provided from Operations $90,000,000
A. Net Income $60,000,000
Depreciation Expense 45,000,000
Funds from Operations (FFO) $105,000,000
B. Determinants of FAD:
Funds from Operations
* Straight-line Rents
* “Cap Ex”
– Tenant Improvements
– Leasing Commissions
– Building Improvements/Replacement Reserve(s)
* Principal Amortization
* Preferred Dividends
* Minority-Interest Payments/Distributions
Funds Available for Distributions (FAD)
Income Statement
Statement of Changes in Financial Position
C. Property Revenues $270,000,000
Property Expenses 110,000,000
Management Fees (G&A) Adjustment 2,500,000
Interest Expense 50,000,000
Principal Amortization 10,000,000
Replacement Reserves 7,500,000
Operating Cash Flow $90,000,000
# Apartment Units 25,000
Replacement Reserve per Unit $300
Net Income $60,000,000
Depreciation Expense 45,000,000
Funds from Operations (FFO) 105,000,000
Management Fees (G&A) Adjustment 2,500,000
Principal Amortization (10,000,000)
Replacement Reserves (7,500,000)
Operating Cash Flow $90,000,000
Alternative Presentation
D. i) The “clientele” effect:
To the extent that REITs can be bought at below asset value.
To the extent that REITs can be bought at above asset value.
The reasons why the platform does not matter:
To the extent the benefits of the REIT platform (e.g ., liquidity, disclosure, investor
governance, etc .) can be easily negotiated within the context of private-market vehicles by
large (primarily, institutional) investors in private-market vehicles. The one exception to this
line of reasoning is liquidity. However, liquidity may be less important to large institutional
investors and the degree of liquidity for large investors may be quite illusive.
To the extent that many of these large investors will have to relinquish certain “control”
provisions (e.g ., the amount of discretion permitted in a separate account) in order to avail
themselves of the purported REIT benefits – clearly this tradeoff may not be worthwhile to
these large investors (who can privately negotiate these same benefits).
To the extent that the REIT marketplace offers certain property types (e.g ., apartments,
office, industrial, etc .) which are easily obtained by large (and small) investors in private-
market vehicles.
Small (primarily, individual) v. large (primarily, institutional) investors vis-à-vis issues of
negotiating strength, need for (availability of) liquidity, depth of real estate expertise,
desire for control, etc.
The reasons why the platform matters:
To the extent that the REIT platform provides certain benefits (e.g. , liquidity,
disclosure, investor governance, etc. ) not easily obtained by sm
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com