Question

A group of private investors borrowed $30,657,286million to build 300 new luxury apartments near a large university. The money was borrowed at 5% annual interest, and the loan is to be repaid in equal annual amounts over a 40-year period. Annual operating and maintenance expenses are estimated to be $4,195 per apartment. This expense will be incurred even if an apartment is vacant. The rental fee for each apartment will be $12,305 per year, and the worst case occupancy rate is projected to be 82%. Investigate the sensitivity of annual profit (or loss) to changes in occupancy rate. Express your answer in percent rounded to the nearest hundedths.

Answer 1

Annual loan payment = 30657286 * (A/P,5%,40)

= 30657286 *0.058278

= 1786645.31

Annual maint. cost = 4195 * 300 = 1258500

Rental income at 82% occupancy rate = 0.82 *300 * 12305 = 3027030

Profit / Loss at 82% occupancy rate = 3027030 - 1786645.31 - 1258500 = -18115.31

Let Breakeven occupancy rate be p%, then

Rental income at P% occupancy rate = P *300 * 12305 = P*3691500

As per given condition

P*3691500 = 1786645.31 + 1258500

P = (1786645.31 + 1258500) / 3691500 = 0.8249 ~ 82.49%

Above occupancy rate of 82.49%, there will be profit