A group of private investors borrowed $30 million to build 320 new luxury apartm

Question

A group of private investors borrowed $30 million to build 320 new luxury apartments near a large university. The money was borrowed at 55% annual interest, and the loan is to be repaid in equal annual amounts(principal and interest) over a 30-year period. Annual operating, maintenance, and insurance expenses are estimated to be $4,500 per apartment, and these expenses are incurred independently of the occupancy rate for the apartments. The rental fee for each apartment will be $12 000 per year, and the worst-case occupancy rate is projected to be 75%.

a. How much profit (or loss) will the investors make each year with 75% occupancy?

b. Repeat Part (a) when the occupancy rate is 90%.

Compound Interest Factors Single Payment Uniform Payment Series Arithmetic Gradient Compound Present Compound Amount Factor Present Sinking Worth Factor Capital Recovery Gradient Uniform Series Find A Gradient Present or Amount Factor un Factor Find A Given F or Factor Find P Given A Factor in in in Given P Given F Given A Given G 9524 9070 0.952 4878 .3172 0.488 0.967 5378 2.050 0.907 2820 3.546 7835 5.526 8.237 1970 5.076 2.805 9.549 11.027 12.578 16.232 20.970 26.127 6768 6446 1547 1407 1.629 0795 5847 5568 5303 43.624 49.988 56.553 63.288 70.159 ·0628 13 1065 9.599 2.079 4581 4363 0423 0387 0355 0327 23.657 10.838 6.474 6.842 7.203 0887 0855 0827 0802 0780 2.407 84.204 30.539 12.462 98.488 105.667 112.846 120.008 127.140 12.821 38.505 8.573 3256 44.502 47.727 0725 9.214 14.375 141.258 2678 0683 54.669 58.402 62.323 66.439 3.920 14.898 10.411 10.694 0.969 11.238 11.501 1.757 12.006 168.622 175.233 31 15.593 16.003 16.374 2204 75.299 80.063 85.067 0133 1999 0625 188.135 194.416 5.253 00828 00626 00478 13.377 14.364 0583 229.545 159.699 209.347 0872 277.914

Explanation / Answer

Average profit per year for 30 years at Occupancy of 75%= (12000*320*75%) - (320*4500) = 1,440,000

Present value of all the profit for 30 years = 1,440,000 * 18.256 (refering the above table)

= 26,288,640

Cash Outflow at year 0 i.e. currently is $ 30 million while the present value of all profit earned during the period of 30 years is only 26.29 million. Hence, there is net loss of 3,711,360 in present terms.

At 90% Occupancy, annual profit = (12000*320*90%) - (320*4500) = 2,016,000

Present value of all the profit for 30 years = 2,016,000 * 18.256 (refering the above table)

= 36,804,096

Net gain in present terms = 36,804,096 - 30,000,000 = 6,804,096

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