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PLA 4310 Real Estate Finance I – Summer 2023

HOMEWORK QUIZ 2 SOLUTIONS

TO BE COMPLETED & SUBMITTED INDIVIDUALLY

(Attach worksheets, if you wish – not required)

There are TWO SECTIONS: 1 Multiple Choice, 2 Calculations.

Reference to your textbook, class slides and notes are permitted; BUT SHARING ANSWERS IS NOT ADVISED AS IT IS IMPORTANT FOR YOU TO TEST YOUR KNOWLEDGE SO FAR. PLEASE MAINTAIN YOUR PERSONAL INTEGRITY.

Section A. Multiple Choice Questions

Select the best alternative answer, based on what you have learnt in the course.

HIGHLIGHT CORRECT ANSWER FOR EACH QUESTION

(2 points per question : Total points 24)

1. If you deposit $1,000 in an account that earns 5% per year, compounded annually, you will have $1,276 at the end of 5 years. What would be the balance in the account at the end of 5 years if interest compounds monthly?

(a) $1,000

(b) $1,276

(d) $1,294

2. Begin with a single sum of money at period 0. First, calculate a future value of that sum compounded at 12.01%/per annum for any number of periods. Then discount that future value back over the same number of periods to period 0 at 11.99%. In relation to the initial single sum, the discounted future value:

(a) Is greater than the original amount since the Compound Rate is greater than the Discount Rate.

(b) Is less than the original amount since time erodes the value of money.

(d) Cannot be determined with the information that does not define the time period.

3. Which of the following is not a basic component of any compounding problem? (a) An initial amount

(b) An interest rate

(d) A net present value

4. The internal rate of return:

(a) Is also known as the investor’s return

(b) Represents a return on investment expressed as a compound rate of interest

(c) Is calculated by subtracting the price of an investment from the total stream of cash flows it generates and solve for the interest rate

(d) Can be defined by all of the above

5. What is the approximation of the price you would pay for a property which has a current year NOI of $200,000, which will grow at 4% per year, and you have alternative opportunities to invest your money that provide you with a return of r = 11%?

(a) $1,818,182

(b) $2,857,143

(d) Cannot be determined from given information

6. The future value of a single deposit of $1,000 will be greater when this amount is compounded: (a) Annually

(b) Semi-annually

(d) Monthly

7. Which of the following is FALSE regarding expense stops?

(a) Expense stops protect owners against increases in expenses

(b) Expense stops are usually based on expenses during the first term of the lease

(d) Expense stops provide some protection against inflation

8. A building owner charges net rent of $40 in the first year, $42 in the second year, $44 in the third year, $47 in the fourth year, and $50 in the fifth year. Using a 10% discount rate, what is the effective rent over the five years?

(a) $40.00

(b) $44.13

(d) $50.00

9. If the building owner in the previous question offered three months of free rent in the first year as a concession. What is the effective rent over the five years?

(a) $30.00

(b) $41.73

(d) The effective rent is not changed by this concession.

10. A 1,500 square foot office space is leased at $12.00 square foot. The space is vacant one month out of the year. Office expenses are $6.50 per square foot and an expense stop is set at $6.00 per square foot. What is the annual net operating income to the landlord?

(a) $7,500

(b) $6,750

(d) $8,250 if expenses are paid only on occupied space

11. Which of the following is TRUE for a triple net lease?

(a) All expenses are paid by the owner

(b) All expenses are paid by the tenant

(d) All expenses are paid by the investor

12. Normally, what relation should be most common between the expected "going-in" and expected "going-out" cap rate?

(a) The going-in cap rate should be higher than the going out.

(b) The going-out cap rate should be at least as high as the going-in rate.

Section B. Short Answer Questions (FILL IN CORRECT ANSWER FOR EACH QUESTION)

(Total points 26)

Question 1 (6 points: 3 points each)

You are buying a property and are considering taking out a 5% loan amortizing at a 30-year rate with monthly payments. Your first evaluation of the property indicates that it will have CASH FLOW for REPAYING YOUR LOAN of $1,000,000 per year.

(a) What is the maximum conceivable amount that might be loaned (before risk margins, etc. are added) on the property, given this basic information on the available cash flow to repay the loan?

(b) If the Federal Reserve raises the rate on the 10-year Treasury Bond by 2% and your loan interest rate goes up to 7%, how much can you now borrow , assuming the property cash flow stays the same.

Question 2 (10 points)

THE FOLLOWING 5 QUESTIONS CONCERN THE FOLLOWING SITUATION:

You intend to develop a rental apartment building that has 100 units. It is in a good market and you will immediately fill it up, though with people moving in & out, and fixing up apartments between tenants, you have a typical vacancy rate of 5%. Your starting average rent per unit is $12,000 on the typical 1-year lease. You calculate that the operating expenses you will pay on the property will average $5000 (per occupied unit) per year. Both rents and expenses are expected to grow in-line with inflation at an average of 2%.

(a) What is the projected effective gross revenues or Effective Gross Income( EGI) for the property in the first year?

(b) What is the projected net operating income (NOI) for the property in the first year?

(c) If your hurdle rate of return (or Opportunity Cost of Capital (OCC) or Discount Rate (DR)) on your development of this type of project is 11%, what do you calculate to be an approximate estimation of the property’s valuation, given your operating results in the first year?

(d) Suppose you bought the land for $750,000 and your construction costs (hard & soft) totaled $5,500,000

I. Do you achieve your hurdle rate of return?

II. Do you estimate you will make a profit in addition to your Rate of Return and HOW MUCH IS IT?

(e) What quick and dirty estimation of your total rate of return (investment hurdle rate and extra “profit”) could

you make of your project?

Question 3 (10 marks

THE FOLLOWING 5 QUESTIONS CONCERN THE FOLLOWING SITUATION:

After you have built the apartment project (in the previous problem), the markets get stronger and your rental rates grow by 3% for both Year 2 and Year 3. However, then there is a slightly weaker economy and your rental rate growth is just 2% for Year 4 through Year 7. But, as with all cycles, the demand picks up after a few years, and you have strong growth of 4% for Year 8 through Year 10, with Year 11 expected to be the same 4%. On the other hand, you manage the property well and your Operating Expenses (per occupied unit) just continue to grow at a stable 2% per year. To get a clear picture of your project, you do a Proforma of the NOI over these 10 years.

In Year 10, with things looking so good, you decide to sell the property at the end of that year. The markets are indicating a Cap Rate of 9%.

(a) What would be your selling price?

(b) Taking your 10-year Proforma, what would you now more precisely calculate the Valuation of the project to be back in Year 1, compared with how you valued it earlier on that Year 1 NOI (that is, in Ques 2(c))?