Cash Flows: Estimation and Diagramming
As mentioned in earlier sections, cash fl ows are the amounts of money estimated for future projects or observed for project events that have taken place. All cash fl ows occur during specifi c time periods, such as 1 month, every 6 months, or 1 year. Annual is the most common time period. For example, a payment of $10,000 once every year in December for 5 years is a series of 5 outgoing cash flows. And an estimated receipt of $500 every month for 2 years is a series of 24 incoming cash flows. Engineering economy bases its computations on the timing, size, and direction of cash fl ows.
Cash infl ows are the receipts, revenues, incomes, and savings generated by project and business activity. A plus sign indicates a cash infl ow.
Cash outfl ows are costs, disbursements, expenses, and taxes caused by projects and business activity. A negative or minus sign indicates a cash outfl ow. When a project involves only costs, the minus sign may be omitted for some techniques, such as benefi t/cost analysis.
Of all the steps in Figure 1–1 that outline the engineering economy study, estimating cash fl ows (step 3) is the most diffi cult, primarily because it is an attempt to predict the future. Some examples of cash fl ow estimates are shown here. As you scan these, consider how the cash infl ow or outfl ow may be estimated most accurately.
Cash Infl ow Estimates
Income: + $150,000 per year from sales of solar-powered watches
Savings: + $24,500 tax savings from capital loss on equipment salvage
Receipt:
Savings: + $150,000 per year saved by installing more effi cient air conditioning
Revenue: + $50,000 to $75,000 per month in sales for extended battery life iPhones
Cash Outfl ow Estimates
Operating costs:- $230,000 per year annual operating costs for software services
First cost: - $800,000 next year to purchase replacement earthmoving equipment
Expense: - $20,000 per year for loan interest payment to bank
Initial cost: - $1 to $1.2 million in capital expenditures for a water recycling unit
All of these are point estimates , that is, single-value estimates for cash fl ow elements of an alternative, except for the last revenue and cost estimates listed above. They provide a range estimate, because the persons estimating the revenue and cost do not have enough knowledge or experience with the systems to be more accurate. For the initial chapters, we will utilize point estimates. The use of risk and sensitivity analysis for range estimates is covered in the later chapters of this book.
Once all cash infl ows and outfl ows are estimated (or determined for a completed project), the net cash fl ow for each time period is calculated.
where NCF is net cash fl ow, R is receipts, and D is disbursements.
At the beginning of this section, the timing, size, and direction of cash fl ows were mentioned as important. Because cash fl ows may take place at any time during an interest period, as a matter of convention, all cash fl ows are assumed to occur at the end of an interest period.
The end-of-period convention means that all cash infl ows and all cash outfl ows are assumed to take place at the end of the interest period in which they actually occur. When several infl ows and outfl ows occur within the same period, the net cash fl ow is assumed to occur at the end of the period.
In assuming end-of-period cash fl ows, it is important to understand that future (F) and uniform annual (A) amounts are located at the end of the interest period, which is not necessarily December 31. If in Example 1.7 the lump-sum deposit took place on July 1, 2011, the withdrawals will take place on July 1 of each succeeding year for 6 years. Remember, end of the period means end of interest period, not end of calendar year.
The cash fl ow diagram is a very important tool in an economic analysis, especially when the cash fl ow series is complex. It is a graphical representation of cash fl ows drawn on the y axis with a time scale on the x axis. The diagram includes what is known, what is estimated, and what is needed. That is, once the cash fl ow diagram is complete, another person should be able to work the problem by looking at the diagram.
Cash fl ow diagram time t 0 is the present, and t 1 is the end of time period 1. We assume that the periods are in years for now. The time scale of Figure 1–4 is set up for 5 years. Since the end-of-year convention places cash fl ows at the ends of years, the “1” marks the end of year 1.
While it is not necessary to use an exact scale on the cash fl ow diagram, you will probably avoid errors if you make a neat diagram to approximate scale for both time and relative cash fl ow magnitudes.
The direction of the arrows on the diagram is important to differentiate income from outgo. A vertical arrow pointing up indicates a positive cash fl ow. Conversely, a down-pointing arrow indicates a negative cash fl ow. We will use a bold, colored arrow to indicate what is unknown and to be determined. For example, if a future value F is to be determined in year 5, a wide, colored arrow with F ? is shown in year 5. The interest rate is also indicated on the diagram. Figure 1–5 illustrates a cash infl ow at the end of year 1, equal cash outfl ows at the end of years 2 and 3, an interest rate of 4% per year, and the unknown future value F after 5 years. The arrow for the unknown value is generally drawn in the opposite direction from the other cash fl ows; however, the engineering economy computations will determine the actual sign on the F value.
Before the diagramming of cash fl ows, a perspective or vantage point must be determined so that or – signs can be assigned and the economic analysis performed correctly. Assume you borrow $8500 from a bank today to purchase an $8000 used car for cash next week, and you plan to spend the remaining $500 on a new paint job for the car two weeks from now. There are several perspectives possible when developing the cash fl ow diagram—those of the borrower (that’s you), the banker, the car dealer, or the paint shop owner.
The cash fl ow signs and amounts for these perspectives are as follows.
 |
| Figure 1–6 Cash fl ows from perspective of borrower for loan and purchases. |
One, and only one, of the perspectives is selected to develop the diagram. For your perspective, all three cash fl ows are involved and the diagram appears as shown in Figure 1–6 with a time scale of weeks. Applying the end-of-period convention, you have a receipt of $8500 now (time 0) and cash outfl ows of $8000 at the end of week 1, followed by $500 at the end of week 2.
EXAMPLE 1.9 - Cash Flows: Estimation and Diagramming
EXAMPLE 1.10 - Cash Flows: Estimation and Diagramming
EXAMPLE 1.11 - Cash Flows: Estimation and Diagramming
Categories:
THE FUNDAMENTALS
0 comments:
Post a Comment