REM400 - Real Estate Finance: Final Take-Home Exam Solution

This document presents a comprehensive solution to a Real Estate Finance take-home exam (REM400) from April 2018. The solution meticulously addresses eight questions covering key concepts in real estate finance. The first question calculates the break-even interest rate, while the second determines the before-tax internal rate of return on equity (BTIRRE). Question three computes taxable income. The fourth question utilizes the Gross Income Multiplier (GIM) approach for property valuation. Question five focuses on size adjustments in property valuation. Question six calculates the market capitalization rate. Question seven computes the Internal Rate of Return (IRR), and the final question discusses the implications of a zero Net Present Value (NPV). The solutions include detailed calculations and explanations, providing valuable insights into various financial aspects of real estate.

REAL ESTATE FINANCE
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Question 1
Break even interest rate BEIR = After tax IRR on Investment / (1-Tax rate)
Break even interest rate BEIR = 9%/(1-0.40) = 15%
Question 2
Debt = 85% and Equity = 15%
BTIRRD = 10% and BTIRRp = 10.75%
Now,
BTIRRE = BTIRRP + {(BTIRRp – BTIRRD) * Debt}/Equity
BTIRRE = 10.75 + {(10.75 -10) *85}/15
BTIRRE = 15%
Hence, BTIRRE would be 15.0%.
Question 3
NOI = $100,000
Property purchased = $1,200,000
Debt service for year = $95,000 (out of which interest amount = $93,400)
Annual depreciation = $38,095
Taxable income = NOI – Interest – Depreciation
Taxable income = 100000 – 93400-38095 = -31,495
Hence, taxable income will be -$31,495.
Question 4
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GIM Approach Yield
Comp 2 Comp 3 Comp 3
Price 300000 350000 375000
Effectice gross income 50,000 55,000 60,000
% Operating expense 50% 55% 54%
NOI 25,000 30,000 32,500
GIM (Price / Effectivegross income) 6.00 6.363 6.25
Average GIM = (6 + 6.36 +6.25)/2 = 6.2045
Effective gross income = $53,000 (given)
GIM approach yield = Effective gross income* Average GIM = 6.204 *53000 = $328,840.9
Question 5
In the given case, adjustment is required to be made with regards to size. For that, it is
imperative to choose from the given grid, two properties which are same with regards to age
and exterior so that any difference in property price is on account of size only. Two
properties that fit the description are 1 and 4 where the exterior and age is the same. Hence,
the price difference is only on account of size.
Size of 1 is 1700 sf
Size of 2 is 1900 sf
Difference in size is 200 sf
Difference in price is (126000-116000) = $10,000
Hence, size adjustment factor = (10000/200) = $50 per square feet or $50 psf
Question 6
Property sold = $200,000
85% of overall amount in loan with 10% interest rate for a period of 15 years.
Now,
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85% of amount = 0.8 * 200,000 = $170,000
Annual income A =170,000{ (0.1*(1.1)15)/((1.1)15-1))} = $22,350.54
Before tax, the cash flow - $2000
Net operating income NOI = $22350.54 - $2000 = $20,350.54
Thus,
Capitalization rate = NOI/ Current value of the asset = $20,350.54/$170,000
Capitalization rate = 11.96%
Hence, market capitalization would be 11.96%.
Question 7
Computation of IRR
Step 1: Rate of return of property having NOI
ROR = 10%
Step 2: Net present value of property having NOI
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Step 3: IRR
Hence, the IRR will be 37.91%.
Question 8
Net present value (NPV) of a project indicates the project viability by expressing the net cash
flows in present value terms. Generally, one would select the project which shows positive
NPV value. However, when the NPV of a project comes out to be $0, then it means that the
project would neither result in profit nor loss to the company. Also, at zero NPV the present
value of inflows would be equal to the present value of outflows. However, a company can
undertake a project irrespective of zero NPV value by considering the opportunity costs
associated with the project. The investor can adopt the project if the opportunity of the project
is completely aligned as in that scenario, the project would be earning the discounted cash
flows. However, there would be no extra benefits in monetary terms and the company would
lose any particular investment or opportunity with respect to the opportunity cost. For
example: If a company is willing to purchase computers from a company called XYZ limited
and the NPV of this project is zero then also the company would go ahead with the project
because XYZ limited is the company which offers free smartphones along with the
computers which any other company do not. Hence, the company would be ready to adopt
the project considering that it has opportunity costs of receiving free smartphones. Thus,
getting free smartphones would be considered as opportunity cost for the company if it denies
the offer.
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