E

which can be written as:

Inserting sum formula 2.7 for the geometric series gives:

The net present value NPVFj over the future of project j is:

where:

where:

LFj = future lifetime of project j;

rf = cost of capital over the future lifetime of project j; p = profit;

EFj = yearly net exploitation result of project j over the future lifetime Lpj, in money units at the start of the project.

Inserting sum formula 2.7 for the geometric series of the last term gives:

We are interested in the profit p for NPV = 0. This means that we have to find the root x from:

Rearranging terms gives:

Table 2.3 Characteristics portfolio of real estate projects

Project

Estimate

D

Eh

Tw

Ad

Rd

Nk

low

9

9

9

9

9

9

Investment

best

10

10

10

10

10

10

high

13

12

14

14

14

14

low

3%

3%

3%

2%

3%

3%

Interest

best

4%

4%

4%

3.5%

5%

5%

high

5%

5%

5%

5%

6%

6%

low

1.2

1.2

1.2

1.0

1.2

1.2

Revenues

best

1.4

1.3

1.35

1.1

1.3

1.3

high

1.5

1.4

1.5

1.3

1.4

1.4

low

1.8

1.8

1.8

1.8

1.8

1.8

Rest value

best

2.0

2.0

2.0

2.0

2.0

2.0

high

2.1

2.1

2.1

2.1

2.1

2.1

Life time (Past/Future)

4/26

6/34

5/25

9/31

9/31

The Equation 2.13, of the form x = f (x), can be solved using Wegstein's iterative procedure (Wegstein, 1958). The routine can also be found in Open Design, a Collaborative Approach to Architecture (page 80).

The Monte Carlo simulation for the entire portfolio can then be conducted in the same way as for a single investment project. The input for this option of our software package consists of the number of projects N and for each project:

2. Ranges (three values) for EF and rF .

The output gives the probability distribution of the expected return (profit) for the portfolio.

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