Question

J&M Company is a real-estate developer considering a 40-unit apartment complex in a growing college town. As the area is also booming with foreign automakers locating their US assembly plants, the firm expects that the apartment complex, once built, will enjoy a 90% occupancy for an extended period. The firm already compiled some of the critical financial information related to the development project as follows:  Land price (1 acre) = $1,200,000  Building (40 units of single bedroom) = $4,800,000  Project life = 25 years  Building maintenance per unit per month = $100  Annual property taxes and insurance = $400,000 Assuming that the land will appreciate at an annual rate of 5%, but the building will have no value at the end of 25 years (it will be torn down and a new structure would be built), determine the minimum monthly rent that should be charged if a 12% return (or 0.9489% per month) before tax is desired.

Answer 1

Step-by-step explanation:

Salvage value = price(1+i)^n; i -interest rate; n-time period

Salvage value = 1,200,000*(1+0.05)^25 = 4,063,680

Monthly rent = ((price+building cost) - salvage value)*(i(1+i)^n/[(1+i)^n-1]) +

+ i*salvage value + maintenance cost*12*number of buildings + insurance and property tax) * (return/[(1+i)^n-1]) =

((1,200,000+4,800,000)-4,063,680)*(0.12*(1+0.12)^25/[(1+0.12)^25 -1]) + 0.12*4,063,680 + (100*12*40) +400,000)*(0.009489/[(0.009489 +1)^12 -1]) =

= (6,000,000 - 4,063,680)*2/16 + 487,641.6+ 48,000 + 400,000) * 0.0791 =

=( 1,936,320 * 0.125 + 487,641.6 + 448,000) * 0.0791 =

= (249,398.016 +487,641.6+448,000)*0.0791 = 97.636.63

So the minimum monthly rate is 97.636.63