Valuation Problem:

Question 1

Consider a 200,000 SF oce building complex, with NOI of $25/SF/year with rents and operating expenses paid in arrears (at the end of the year) annually, and no capital expenditures The rent will increase by 3% per year. The discount rate is 10%/year.

a. What is the value of this oce 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 cap rate at time 0?

b. What is the value of this oce 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 cap rate at time 0 and 10?

c. What is the value of this oce building, assuming that the building will be held and rented indenitely (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 Central Business District (CBD) is being used as an open parking lot. The land currently brings an operating cash

ow of $28/SF/year, paid in arrears, which 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 oce 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 identical to the one we currently own, without additional cost). The construction will take one year1. The resulting oce space is expected to produce operating cash ows of $22/SF/year (in arrears) starting next year, and the rent is expected to increase by 1% annually. The required rate of return on oce buildings is 11%. Is this a good investment project?

Question 3

Consider a 100,000 sqf oce building with the following cashfows: 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 rest year are $5/sqf/year and are expected to increase at 3% per year. There are no capital

expenditures. All cash ows are in arrears. The discount rate for the property is 9%.

a. What is the value of the building if the building will be held and rented indenitely?

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?

1Hint: No rents will come from the oce building during the construction period.

1

Question 4

Consider the following projected cash

ows (including reversion) for Property A and Property

B for the following 10 years. Assume that operating cash

ows (excluding reversion) = NOI,

there are no capital expenditures.

Annual net cash

ow projections for two properties ($ millions)

1 2 3 4 5 6 7 8 9 10

A $1.0000 $1.0050 $1.0100 $1.0151 $1.0202 $1.0253 $1.0304 $1.0355 $1.0407 $12.7252

B $1.0000 $1.0200 $1.0404 $1.0612 $1.0824 $1.1041 $1.1262 $1.1487 $1.1717 $14.7395

a. What is the annual growth rate in operating cash

ows for each building during the rst

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?