Annual cash flows

Time is taken into account by discounting the annual cash flow Acf with the rate of interest to obtain the anitual discounted cash flow -Adcf- Thus, at the end of year 1,... 

In Section 13.2, a number of economic indicators were derived from the annual cash flow the most useful being the economic life of the project, determined when the annual cashflow becomes permanently negative. 

Net Present Va.Iue, Each of the net annual cash flows can be discounted to the present time using a discount factor for the number of years involved. The discounted flows are then all at the same time point and can be combined. The sum of these discounted net flows is called the net present value (NPV), a popular profit criterion. Because the discounted positive flows first offset the negative investment flows in the NPV summation, the investment capital is recovered if the NPV is greater than zero. This early recovery of the investment does not correspond to typical capital recovery patterns, but gives a conservative and systematic assumption for investment recovery. 

Internal Return Rate. Another rate criterion, the internal return rate (IRR) or discounted cash flow rate of return (DCERR), is a popular ranking criterion for profitabiUty. The IRR is the annual discounting rate that makes the algebraic sum of the discounted annual cash flows equal to zero or, more simply, it is the total return rate at the poiat of vanishing profitabiUty. This is determined iteratively. 

Different cash flow patterns are used in Figures 4—6 to illustrate advantages of the NRR as a profitabihty parameter. These ventures have input data identical to Venture A except for the values given in Table 4 the resulting annual cash flow patterns are quite different. 

In modern methods of profitability assessment, cash flows are more meaningful than profits, which tend to be rather loosely defined. The net annual cash flow after tax is given by... 

The relationships among the various annual costs given by Eqs. (9-1) through (9-9) are illustrated diagrammaticaUy in Fig. 9-1. The top half of the diagram shows the tools of the accountant the bottom half, those of the engineer. The net annual cash flow Acp, which excludes any provision for balance-sheet depreciation Abd, is used in two of the more modern methods of profitability assessment the net-present-value (NPV) method and the discounted-cash-flow-rate-of-return (DCFRR) method. In both methods, depreciation is inherently taken care of by calculations which include capital recoveiy. 

Let us consider projects A and B, having net annual cash flows as listed in Table 9-2. Both projects have initial fixed-capital expenditures of 100,000. On the basis of payback period, project A is the more desirable since the fixed-capital expenditure is recovered in 3 years, compared with 5 years for projec t B. However, project B runs for 7 years with a cumulative net cash flow of 110,000. This is obviously more profitable than project A, which runs for only 4 years with a cumulative net cash flow of only 10,000. 

In the final year of the project, the working capital and the laud are recovered, which in this case cost a total of 100,000. Thus, in the final year of the project, Afc = — 100,000 and —Afc = + 100,000. From Eq. (9-4), it is seen that any capital recoveiy makes a positive contribution to the net annual cash flow. 

Time is taken into account by using the annual discounted cash flow Adcf, which is related to the annual cash flow Acf and the discount factor by... 

TABLE 9-4 Annual Cash Flows and Discounted Cash Flows for a Project... 

At the end of Year 10, the working capital (C vc = 90,000) and the cost of land (Cl = 10,000) are recovered, so that the annual expenditure of capital Atc in Year 10 is — 100,000 per year. Hence, the net annual cash flow (after tax) for Year 10 must reflect this recovery. By using Eq. (9-4),... 

TABLE 9-5 Annual Cash Flows, Straight-Line Depreciation, and 10 Percent Discount Factor... 

Atc = total annual capital expenditure. Acf Aci — Aij — Atc net annual cash flow. f = discount factor at 10%. 

Maximum discounted cumulative expenditure on the project Cumulative net annual cash flow X Acf... 

Let us consider the net annual cash flows (after tax) Acf foi projects E, F, and G, hsted in Table 9-6. The cumulative annual cash flows X Acf 3.nd cumulative discounted annual cash flows X dcf, using a discount of 10 percent for these projec ts, are also hsted in Table 9-6. We notice that the cumulative annual cash flow for each project is -i- 1000. 

When to Scrap an Existing Process Let us suppose that a company invests 50,000 in a manufacturing process that has positive net annual flows (after tax) Acp of 10,000 in each year. During the third year of operation, an alternative process becomes available. The new process would require an investment of 40,000 but would have positive net annual cash flows (after tax) of 20,000 in each year. The cost of capital is 10 percent, and it is estimated that a market will exist for the product for at least 6 more years. Should the company continue with the existing process (project H), or should it scrap project H and adopt the new process (project 1) ... 

The net annual cash flows Acp and cumulative discounted annual cash flow X Aocf discount factor of 10 percent are hsted in Table 9-7 for the two projec ts. At the end of Year 9, the net present values are... 

Both projects have lives of 10 years and constant positive net annual cash flows Acf of 2069 and 1558 for projec ts J and K respec tively. The corresponding (NPV)s at a discount factor of 10 percent are + 2710 and + 2560 respectively. These data are summarized as follows ... 

In this case, the lives of the machines are unequal, and the comparison is conveniently made on the basis of capitalized cost. This puts lives on the same basis, which is an infinite number of years. The net annual cash flows generated by each machine are equal. 

Relationship between (PBP) and (DCFRR) For the case of a single lump-sum capital expenditure Cpc which generates a constant annual cash flow Acf in each subsequent year, the payback period is given by the equation... 

Equations (9-59), (9-60), (9-61), and (9-62) may be used as they stand to assess expenditure on energy-conservation measures since a constant amount of energy is saved in each year subsequent to the capital outlay. However, the annual cash flows Acf corresponding to the energy savings remain constant only if there is no inflation or if the money values are corrected to their purchasing power at the time of the capital expenditure. 

To recover this amount of capital and interest in 3 years, the average net annual cash flow Acr required is... 

In effec t, in computing the average net annual cash flow per dollar invested, the value of f p of Eq. (9-46) has been obtained for this example. From tables of the annuity present-worth factor/ p the value of the interest rate is found to be = 0.25 when f p = 0.5124 with n = 3 years. 

Equation (9-110) enables all the net annual cash flows to be corrected to their purchasing power in Year 0. If the inflation rate is zero, Eq. (9-110) becomes identical with Eq. (9-109). 

Ejfect of Inflation on (DCFRB.) A net annual cash flow Acpvvill have a cash vaJue of Acf(1 + i) 1 year later if invested at a fractional interest rate i. If there is inflation at an annual rate h, then an effective rate of return or interest rate can be defined by the equation... 

Instead of using Eq. (9-113), it is unfortunately common practice to try to obtain the true or effective rate of return by calculating the nominal (DCFRR), based on actual net annual cash flows uncorrected for inflation, and then subtracting the inflation rate from it as if... 

We shall consider the simple case of(l) a single capital expenditure made immediately before the start of production and (2) equal positive net annual cash flows Acp in all the productive years of the project. For this case, Eq. (9-109) can be rewritten in terms of the payoack period and the (DCFRR) as follows ... 

Here, p is the number of payback periods that have elapsed since the project started to generate positive net annual cash flows Acp up to any given year n since project startup. It is given by... 

In this method each year s savings need to take account of the fact that, as the equipment gets older, the cost of maintenance and repairs is likely to increase. The effect of inflation can also be allowed for in assuming the annual cash flows through the life of the equipment. 

Economic analysis can determine the discounted profitability criteria in terms of payback period (PBP), net present value (NPV), and rate of return (ROR) from discounted cash flow diagram, in which each of the annual cash flow is discounted to time zero for the LHS system. PBP is the time required, after the construction, to recover the fixed capital investment. NPV shows the cumulative discounted cash value at the end of useful life. Positive values of NPV and shorter PBP are preferred. ROR is the interest rate at which all the cash flows must be discounted to obtain zero NPV. If ROR is greater than the internal discount rate, then the LHS system is considered feasible (Turton et al., 2003). 

Payback time Payback time is the time that elapses from the start of the project (A in Figure 2.2) to the breakeven point (F in Figure 2.2). The shorter the payback time, the more attractive is the project. Payback time is often calculated as the time to recoup the capital investment based on the mean annual cash flow. In retrofit, payback time is usually calculated as the time to recoup the retrofit capital investment from the mean annual improvement in operating costs. 

A company has the option of investing in one of the two projects A or B. The capital cost of both projects is 1,000,000. The predicted annual cash flows for both projects are shown in Table 2.14. For each project, calculate the ... 

A Absorption factor in absorption (-), or annual cash flow ( ), or constant in vapor pressure correlation (N-m 2, bar), or heat exchanger area (m2)... 

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