Engineering Economic Analysis

FIGURE 2-7 An example cash flow
diagram (CFD).
(+)

+

(-)

$100 $100 ~nd of Period 2

tD~":~~ 1

i

IS also Beginning

~ of Period 3. $50

/0-1-2-3-4-J

Time0!

("today") $100 j j

$150 $150

Categories of Cash Flows

The expenses and receipts due to engineering projects usually fall into one of the following
categories.

First cost=expense to build or to buy and install

Operations and maintenance (O&M)=annual expense, such as electricity, labor, and

minor repairs

Salvage value=receipt at project termination for sale or transfer of the equipment (can

be a salvage cost)

Revenues=annual receipts due to sale of products or services

Overhaul=major capital expenditure that occurs during the asset's life

Individual projects will often have specific costs, revenues, or user benefits. For ex-
ample, annual operations and maintenance (O&M) expenses on an assembly line might be
divided into direct labor, power, and other. Similarly, a public-sector dam project might
have its annual benefits divided into flood control, agricultural irrigation, and recreation.

Drawing a Cash Flow Diagram

The cash flow diagram shows when all cash flows occur. Look at Figure 2-7 and the $100

positive cash flow at the end of period 2. From the time line one can see that this cash flow
can also be described as occurring at thebeginningof period 3. Thus, in a CFD the end
ofperiod t is the saI}letime as the beginning ofperiod t+ 1. Beginning-of-period cash
flows (such as rent, lease, and insurance payments) are thus easy to handle: just draw your
CFD and put them in where they occur. Thus O&M, salvages, revenues, and overhauls are
assumed to be end-of-period cash flows.
The choice of time 0 is arbitrary. For example, it can be when a project is analyzed,
when funding is approved, or when construction begins. When construction periods are
assumed to be short; first costs are assumed to occur at time 0, and the first annual revenues
and costs start at the end of the first period. When construction periods are long, time 0 is
usually the date of commissioning-when the facility comes on stream.
Perspective is also important when one is drawing a CFD. Consider the simple trans--
action of paying $5000 for some equipment. To the firm buying the equipment, the cash
fJ,owis a cost and hence negative in sign. To the firm selling the equipment, the cash flow
is a revenue and positive in sign. This simple example shows that a consistent perspective
is required when one is using a CFD to model the cash flows of a problem. One person's
cash outflow is another person's inflow.
Often two or more cash flows occur in the same year, such as an overhaul and an O&M
expense or the salvage value and the last year's O&M expense. Combining these into one