A real estate developer and operator plans to build a new high-rise office build

Question

A real estate developer and operator plans to build a new high-rise office building in North Dallas. Comparable buildings last 60 years, but the developer plans to sell it after 20 years for 40% of the construction cost. For the first 20 years it can be leased as Class A office space. When the building is sold, then the land's cost will be recovered in full (land value is estimated to go up 2% per year). Here are the estimated cost:

$20M Land
$41M Building (500,000 square foot)
$6.4M Annual operating and maintenance - end of year payment 3% Annual property tax and insurance (% of initial investment)

- end of year payment

(a) If the company wants a 12% rate of return, what is the required annual leasing income for the whole building? Use the method of annual cash flow or the
method of NPW [3 points] to find the solution.

(b) Assuming an expected average occupancy rate of 90% (i.e., on average 10% of the building are vacant at all times), what is the minimum leasing price per square foot

and year [.5 point]? Is this a reasonable price [.5 point]? (check the Web!)

Explanation / Answer

We will use NPW method

Initial investment = 20 + 41 = $ 61 million

Land value at the end of 20 year = 20*(1+.02)^20 = $29.72 million

And 40% of building cost = 40%*61 = $24.4 million

So total sale value (TS)= 29.72 + 24.4 = $54.12 million

MARR = 12%

Now the PW of TS = 54.12/(1.12)^20 = $5.61 million

(Annual operation and maintenance + 3% (annual property tax +insurance)) AM = 6.4+3%*61 = $8.32 million

PW of total AM = 8.32/(1.12)^1 + 8.32/(1.12)^2 + 8.32/(1.12)^3 + 8.32/(1.12)^4...............+ 8.32/(1.12)^20. So this is Geometric progression (gp) SUMgp = a(1-r^n)/(1-r) here a = 8.32/1.12 = 7.43; r = 1/1.12 = .89 and n = 20

PW of total AM = $60.98 million

Now Initial investment + PWAM - PWTS - PW of leasing income = 0

L = Annual leasing income

PWLI = L/(1.12)^1 + L/(1.12)^2 + L/(1.12)^3 + L/(1.12)^4.............................+ L/(1.12)^20. So this is Geometric progression (gp) SUMgp = a(1-r^n)/(1-r) here a = L/1.12; r = 1/1.12 = .89 and n = 20

PWLI = L*7.33

So 61 - 5.61 + 60.98 - L*7.33 = 0 So Annual leasing income L = $15.88 million

b) Occupied building area = 90% of 500000 = 450000

So minimum leasing price per square foot per year = 15880000/450000 = $35.29

In comparision to the rates searched on wed this is very high

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