Question

A construction and development project has estimated expenses that start today for $3,000,000. The expenses decrease at 10% per month after the first expense. The construction starts today and finishes after 24 expenses. The expenses are the land acquisition, development cost charges, consultants’ costs, marketing costs, construction costs, and other costs. The project revenues consist of selling the first luxury homes during the months 26 to 30 at the same equal price per month, X. The other stream of revenues consist of selling the rest of the units at month 33 at $2,600,000 and then increasing at 5% after month 33 for 6 additional months. If the expected return of the construction and development investment is 1.65% per month, what is the value (X) of the units during the months 26 to 30?

Create cash flow diagram.

Answer 1

In case, the cost of capital is r, we've,

NPV of total expenses: -

On solving, we've: -

NPV of total expenses: -

Also, NPV of total revenues: -

Putting in r = 1.65%, and equating the NPVs, X = 1,622,800.09

Cash flow diagram is shown in the figure below.