Final Exam – REE 6045 – Fall 2018 – Dr. Beracha
To complete this final examination you will need to answer the 15 questions listed below. All
questions must be answered in the Excel spreadsheet titled “Final Exam REE6045 – Excel file”
that is provided to you. Moreover, your answers must fit within the designated space (highlighted
in yellow) for each answer within each of the Excel tabs.
This final exam is due on or before October 10
th at 11:55 pm EST. By that time you should submit
an electronic copy (via email) of your assignment. If you turn your assignment late, 10% will be
deducted from your grade for every calendar-day delay.
All the work on this final exam must be 100% your own work. You are not allowed to discuss
the exam with any of your classmates or any other person prior to the deadline. A failing
grade in the course will automatically be assign to a student that helps or seeks help from
another person while working on the exam. You are allowed, however, to use the textbook,
classroom notes, review lectures and use any “non-interactive” websites while working on
1. (5 points, 5*1)
a. According to the rule of 72, how many times your money will be doubled over a 40-
year period if it earns a rate of return of 9% per year? Show your work.
b. Using the rule of 72, estimate the value of an initial investment of $60K at the end of a
40-year period if it earns a rate of return of 9% per year? Show your work.
c. According to the 4% rule, what the size of your investment portfolio needs to be in
order for you to withdraw an initial annual amount of $300K? Show your work.
d. Referring to part c, what will be your 4th annual withdrawal amount if the inflation rate
during the 3 years since your initial withdrawal averaged 2.5% per year? Show your
2. (8 points, 4+4) Consider the “buy vs. rent” Excel spreadsheet provided to you in tab A2.
a. According to the assumptions made in that spreadsheet, should the average individual
buy or rent? Briefly explain.
b. Using “Goal Seek” alter the “buy vs. rent” Excel spreadsheet so that it shows the
minimum rate of price appreciation the homeowner must receive in order to be better
off buying than renting. Highlight in yellow the cell that includes this price appreciation
3. (7 points, 4+3) Consider the levered DCF model provided to you in tab A3 of the Excel
a. Calculate the maximum price that an investors with the assumptions made in the model
should be willing to pay for that property. Show this maximum price in cell C8.
b. If you expect a general increase in the risk premium for real estate investments over the
next 8 years, how would this affect the expected levered return on this property? Briefly
4. (7 points, 3+2+2) Using the headers in tab A4 of the Excel spreadsheet and the input values
included in the green “box”:
a. Create a monthly amortization schedule for a fixed rate 15-year mortgage. Make sure
that any value that the user (me in this case) changes in the green “box” will be reflected
in your amortization schedule. Your monthly payment calculation should be included
in cell J5 and should also automatically change with any changes to the values in the
b. Next to the amortization schedule, create an Excel graph that shows the remaining
mortgage balance overtime. Make sure that your graph is labeled appropriately.
c. Include a vlookup function in cell L7 that will reflect the remaining mortgage balance
associated with the end of the month entered by the user into cell J7. For example, if
the user enters 34 into cell J7, cell L7 will automatically show the remaining mortgage
balance after 34 months.
5. (8 points, 0.5*16) Calculate the nominal and real annual rate of housing price appreciation
rate for Miami and for Houston for the requested different time periods using the housing
price index data and the inflation index data provided to you in tab A5 of the Excel
spreadsheet. In total, you need to calculate 16 values that will appear in the 16 yellow cells
of that Excel tab.
6. (6 points, 3+3) Given your results from the previous problem:
a. What can you say about the magnitude and the volatility of housing price appreciation
in the short, medium and long run?
b. Are the results from question 5 consistent with the theory of price appreciation we
discussed in the beginning of this course? Briefly explain.
7. (8 points, 4+4) Consider a REIT that holds high quality office buildings in some of the best
locations in the US. The REIT is currently traded at a price of $68/share and there are 120
million shares outstanding. Using the information below answer the following questions:
Expected next year total revenue: $750M
Expected next year total expenses (including interest and depreciation): $360M
Expected next year depreciation: $90M
Expected next year interest: $70M
Total debt: $1.8B
Current office CAP in the US: 4.5% to 6.0% depending on quality and location.
a. What is your estimation for a fair market value for a share of the REIT described? Show
b. What is your estimation for a fair price to pay for a share of the REIT described, if you
require an 8.0% rate of return on an unlevered basis and expect the REIT to increase
NOI at an average rate of 2.5%? Should you buy shares of that REIT? Show your work!
8. (6 points, 2+2+2) PLAM and ARM:
a. What is the main difference between a PLAM and an ARM? Briefly explain.
b. Under which economic circumstances a PLAM type loan is greatly needed? Briefly
c. What is the main difference between negatively amortized mortgage and reversed
9. (7 points, 1*7) For each of the factors listed below indicate whether the factor,
independently, is likely to cause a particular income producing property to trade for a
lower or higher CAP rate compared with an average property. For this question, no
explanation is needed. Indicating “higher” or “lower” for factors a through g is sufficient.
a. Lower volatility in rent prices and occupancy rates.
b. Worse location
c. High inflation environment
d. High risk premium environment
e. High expected NOI growth
f. Lower construction quality
g. High quality tenants
10. (8 points, 4+4) Consider an income producing property that according to your assumptions
and estimations is currently worth $4M on an unlevered basis when a 7.5% required rate
of return is applied. One of the assumptions that you have made when arriving at that
estimate is that you will sell the property in 6 years for a CAP of 8%, which translates to
$4.4M at that future point in time.
a. At what price will you sell the property in 6 years if all your assumptions materialized
except that you will sell the property for a CAP of 7% instead of 8%? Show your
b. All other things equal, by how much the situation described in part a affects the current
value of the property. Show your calculations.
11. (6 points, 2*3) According to the Truth-in-Lending-Act (TILA) lenders must provide
borrowers with an APR in addition to the interest rate to be charged on the loan.
a. What is the purpose of providing borrowers with an APR? Briefly explain.
b. What is the main problem with APR? Briefly explain.
c. Consider a potential borrower who evaluates two mortgages options. One with higher
upfront fees and the other with lower upfront fees, but the two options have the same
APR. Which option would you advise the borrower to take if the borrower expects to
stay in the home for a relatively short time period? Briefly explain.
12. (6 points, 2*3) Real estate market inefficiency:
a. Briefly describe 5 factors that cause the stock market to be more efficient than the real
b. Can investors make money in an efficient market? Briefly explain.
c. Do educated and informed investors rather operate in an efficient or inefficient market?
13. (7 points, 3+2+2) DCR:
a. Calculate the DCR for an income producing property to be acquired at a price of $7M
and a CAP of 5.5%. The down payment on the property is 30% of the property value
and the mortgage on the remaining balance is a fixed-rate interest only loan at a rate
b. What is the meaning of a DCR of 1.30, for example? Please explain.
c. List and briefly explain three different factors that are likely to cause the lender to
require a higher DCR from investors?
14. (6 points, 2*3) Four years ago, when you were 24, you graduated from college and landed
a good paying job. At that time you purchased your “starter home” for $200K. Since then,
the housing market in the city where your home is located experienced unusually high rate
of price appreciation and a local real estate agent informed you that if you were to put your
home on the market today, you will be able to sell it for about $350K.
a. Did the recent abnormal housing price appreciation benefited you? Explain in 3-4
b. What kind of individuals benefited the most from the recent price appreciation
described in this question? Explain in 2-3 sentences.
c. What kind of individuals suffered the most from the recent price appreciation described
in this question? Explain in 2-3 sentences.
15. (5 points) Which single real estate topic covered in this course you found to be most
interesting and/or informative? Please explain why in a couple sentences. Is there a
particular topic we covered that you found irrelevant? Is there a particular topic that wasn’t
covered, which you expected to be covered in this intro course? Please explain.
ONE Excel file named “LastName_FirstName_Final Exam”.