Page 93 - Principles of Applied Reservoir Simulation 2E

78 Principles of Applied Reservoir Simulation

is operating at a loss. The loss is usually associated with initial capital invest-
ments and operating expenses that are incurred before the project begins to
generate revenue. The reduction in loss and eventual growth in positive NPV
is due to the generation of revenue in excess of expenses. The point in time on
the graph when the NPV is zero after the project has begun is the payout time.
The concept of payout time applies to either discounted or undiscounted cash
flow. Payout time on Figure 9-1 is approximately 1.5 years.
The discounted cash flow return on investment (DCFROI) and payout time
are measures of the economic viability of a project. Another measure is the
profit-to-investment ratio. The profit-to-investment (PI) ratio is a measure of
profitability. It is defined as the total undiscounted cash flow without capital
investment divided by total investment. Unlike DCFROI, the PI ratio does not
take into account the time value of money. The definitions of several commonly
used economic measures are presented in Table 9-2. Useful plots include a plot
of NPV versus time and a plot of NPV versus discount rate.

Table 9-2
Definitions of Selected Economic Measures
Discount Rate Factor to adjust the value of money to a base
year.

Net Present Value Value of cash flow at a specified discount rate.
(NPV)
DCFROI or IRR Discount rate at which NPV = 0.
Payout Time Time when NPV = 0.

Profit-to-Investment Undiscounted cash flow without capital invest-
(PI) Ratio ment divided by total investment.

The ideas discussed above are quantified as follows. Net present value
is the difference between the present value of revenue R and the present value
of expenses £, thus

NPV = R-E (9.1)
If we define AE(&) as the expenses incurred during a time period k, then E may
be written as