Question

You are considering a luxury apartment building project that requires an investment of $12,500,000. The building has 35 units. The firm expects that the maintenance cost for the apartment building will be $250,000 in the first year, and to rise to $300,000 in the second year, and to continue to increase by $50,000 in subsequent years. The cost to hire a manager for the building is estimated to be $80,000 per year. After four years of operation, the apartment building can be sold for $14,000,000. What annual rent per apartment unit will provide a return on investment of 10%? Assume that the building will remain fully occupied during the four years.

Answer 1

ANSWER:

I = 10%

N = 4

In order to find the rent per unit we will equate the pw to zero.

let the rent per unit be x.

pw = initial investment + maintenance cost per building per year(p/a,i,n) + increase in maintenance cost per building per year(p/g,i,n) + manager hiring cost per year(p/a,i,n) + rent per unit * no of units (p/a,i,n) + salvage value(p/f,i,n)

0 = -12,500,000 - 250,000(p/a,10%,4) - 50,000(p/g,10%,4) - 80,000(p/a,10%,4) + x * 35(p/a,10%,4) + 14,000,000(p/f,10%,4)

12,500,000 + 250,000 * 3.17 + 50,000 * 4.378 + 80,000 * 3.17 = 35x * 3.17 + 14,000,000 * 0.683

12,500,000 + 792,500 + 218,900 + 253,600 = 110.95x + 9,562,000

13,765,000 = 110.95x + 9,562,000

110.95x = 13,765,000 - 9,562,000

110.95x = 4,203,000

x = 4,203,000 / 110.95

x = 37,881.928

so the rent per unit will be $37,881.928