Monte Carlo simulation of a portfolio of real estate investments

Real estate investors are primarily interested in the risk profile (probability distribution of expected return) of their portfolio of projects. What we need, therefore, is a method to conduct a Monte Carlo simulation for a portfolio of projects with different starting dates, different lifetimes and different risk profiles.

Any project, j, of a portfolio of N projects has a past (indicated by subscript P) and a future (indicated by subscript F).

The NPV is the sum of the NPV over the past and the NPV over the future:

The NPVpj over the past - at the present time, in money units of the present time - of project j is:

where:

cost of capital over the past lifetime of project j; past lifetime of project j;

investment made at the start of project j, in money units of that point in time;

rest value of project j, at the end of its lifetime, in money units at the start of the project; selling price of premises at the end of LFj is VPj(1 + r)Lpj+LF; yearly net exploitation result of project j over the past lifetime Lpj, in money units at the start of the project.

The sum of the geometric series 1- xn n-1

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