A group of private investors borrowed $30 million to build 300 new luxury apartm

ID: 2485772 • Letter: A

Question

A group of private investors borrowed $30 million to build 300 new luxury apartments near a large university. The money was borrowed at 6% annual interest, and the loan is to be repaid in equal annual amounts over a 40-year period. Annual operating, maintenance, and insurance expenses are estimated to be $4,000 per apartment. This expense will be incurred even if an apartment is vacant. The rental fee for each apartment will be $12,000 per year. What is the minimum occupancy rate that would make this investment feasible? (Choose the closest occupancy rate from the answers)

a. 80% b. 95% c. 75% d. 90% e. 85%

Explanation / Answer

Calculation of minimum occupancy rate that would make this investment feasible:

Assuming the minimum occupancy rate is X

At minimum occupancy rate the Present value cash inflow should be equal to Initial Cash outflows:

Annual Rent fees = (300 Apartments * X * $12000) =

$3,600,000*X

Less: Annual expenses = (300 Apartments * $4000)

$ 1,200,000

Annual Net Cash Flows = (A)

$3,600,000*X - $1,200,000

Present value of $ 1(6%, 40 years ) (B)

15.0463

Present value of Cash flows = (C) = A*B =

($3,600,000*X - $1,200,000)*15.0463

Initial Cash Outflows =

$ 30,000,000

Hence,

($3,600,000*X - $1,200,000)*15.0463 = $30,000,000

($3,600,000*X - $1,200,000)= $30,000,000/15.0463

($3,600,000*X - $1,200,000)= $1,993,845.66

($3,600,000*X = $1,993,845.66+$1,200,000

$3,600,000*X = $3,193,845.66

X = $3,193,845.66 /$3,600,000

X = 0.90 (Approx) = 90%

Hence Minimum Occupancy should be = 90%