## Financial return

Financial return on investment, allowing trade-offs between benefits and costs, always plays a role in Open Design problems. As mentioned in Chapter 4, we recommend using discounted cash flow analysis with a preference for using the Internal Rate of Return (IRR) criterion over the Net Present Value (NPV) criterion.

The Net Present Value of a project is:

Ci = cash flow (positive or negative) in year i; r = (yearly) cost of capital (as a fraction of that capital); m = life time of the project in years.

In general, the cost of capital r is closely linked with inflation.

The Internal Rate of Return, IRR, is the value for r which would give NPV= 0:

In real estate financing, the cash flows can be characterised by:

• A large investment I, i.e. negative cash flow, at the start of the project;

• A yearly net exploitation result E, i.e. the difference between the yearly exploitation revenues and costs;

• A rest value V at the end of the project. In real estate investments V constitutes the selling price at the end of the lifetime.

The formulae for NPV and IRR can then be simplified to:

The profit P is defined as the return made above the cost of capital (or inflation) r, so:

Usually, it is this profit P in which we are primarily interested. P should be sufficient to reward the financier for the risk involved compared to investment alternatives. If that reward is too low, the project cannot be financed.

It should be noted that in equation (8.2) the rest value V - i.e. the selling price of the premises at the end of the lifetime - is taken into account by discounting for inflation but not for profit above the cost of capital. The reason for doing so is that we wish to trade off investment against return from exploitation, not from land speculation. To include speculation profit on the sales of premises, the last term in equation (8.2) must be replaced by V/(1 + IRR)m. In practice the difference is negligible. The profit P has to be found from:

where

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

which can be written as:

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