The following questions are an assignment and would appreciate if it would be answered,

thank you

Real Estate Finance and Investments - Fall 2016 Homework 1 Due date: Sep 21 Question 1 In a 200,000 SF office building complex, the lease contracts are renewed every 5 years. The first contract is just signed for $25/SF/year (current market rent) with rents paid in arrears (at the end of the year) annually. The rent is fixed during the contract period, but expected to be adjusted to the market rent between the leases. The market rent is expected to increase by 3% per year.1 The discount rate is 10%/year. a. What is the value of this office building, assuming that the building is sold at the end of year 10 and the cap rate at that time is expected to be 10%? What is the implied cap rate at time 0? b. What is the value of this office building, assuming that the building is sold at the end of year 10 and the cap rate at that time is expected to be the same as today? What is the implied cap rate at time 0 and 10? c. What is the value of this office building, assuming that the building will be held and rented indefinitely (perpetually)? What is the implied cap rate at time 0? d. What is the value if the rents are paid in advance (at the beginning of the year) and the building is rented perpetually? Question 2 An acre (43,560 SF) of land in the CBD is being used as an open parking lot. The land currently brings $28/SF/year rent, paid in arrears, and the rent is expected to increase by 2% annually. The discount rate for the parking lot rents is 8%. An investment project that is being considered is building a 100,000 SF office building on the land. The construction will cost $2,000,000 and the building will have a 30 year productive life after it is built (after 30 years, it is assumed that the building can be demolished and the land can be converted to a parking lot without additional cost). The construction will take one year2 . The resulting office space is expected to be rented for net $22/SF/year (in arrears) starting next year, and the rent is expected to increase by 1% annually. The required rate of return on office buildings is 11%. Is this a good investment project? Question 3 Consider a 100,000 sqf office building with the following cash flows: The gross rent in year 1 is $30/sqf/year and the rents are expected to grow at 2% per year. The operating expenses in the first year are $5/sqf/year and are expected to increase at 3% per year. All cash flows are in arrears. The discount rate for the property is 9%. 1 Please start with a time line to understand the pattern of cash flows. Once a contract is signed, the rents are fixed for 5 years. In the mean time the market rents rise every year. When the next contract is signed, annual rents jump to the new market rent level. 2 Hint: No rents will come from the office building during the construction period. 1 a. What is the value of the building if the building will be held and rented indefinitely? What is the implied cap rate at time 0? b. What is the value of the building if the building is sold at the end of 10 years at a 8% cap rate? What is the implied cap rate at time 0? Question 4 The equity REIT A currently (current time is end of 2005) trades at $120/share. In the past year, the realized rate of return on A has been 10%, and A's cap rate at the beginning of year was 13%. REIT A distributed all of its NOI in the past year to its shareholders in the form of dividends. What was the trading price of A at the beginning of 2005?3 Question 5 Consider the following projected cash flows (including reversion) for Property A and Property B for the following 10 years. A B 1 $1.0000 $1.0000 Annual net cash flow projections for two properties ($ millions) 2 3 4 5 6 7 8 9 $1.0050 $1.0100 $1.0151 $1.0202 $1.0253 $1.0304 $1.0355 $1.0407 $1.0200 $1.0404 $1.0612 $1.0824 $1.1041 $1.1262 $1.1487 $1.1717 10 $12.7252 $14.7395 a. What is the annual growth rate in operating cash flows for each building during the first nine years? b. If both properties sell at cap rates (initial and terminal cash yields) of 9%, what is the expected annual return on a 10-year investment in each property? c. If the 9% cap rate represents a fair market value for each property, then which property is the more risky investment (and how do you know)? Question 6 You are considering investing in Property B in question 5. The listing price of the property is $11 million. You know that the historical annual returns on this type of property has been 10%, and the historical risk premium on this type of property has been 5.5%. In alternative investments tools, the prices of zero coupon treasury bonds are as follows: Prices of zero coupon treasury bonds (denomination = $1,000) Maturity(yr) 1 2 3 4 5 6 7 8 9 Price $971 $934 $889 $839 $784 $725 $665 $604 $544 10 $485 How much is the property worth? Is this a good investment opportunity?4 3 Hint: Start with the definition of return. Write the return to REIT A in 2005. The answer will be staring at you ... 4 Hint: You can calculate the risk free rates at different maturities from the Treasury bond prices; i.e., 1000 Pt = (1+rf t. t) 2