Money cash flow

Net present value (NPV). Since money can be invested to earn interest, money received now has a greater present value than money received at some time in the future. The net present value of a project is the sum of the present values of each individual cash flow. In this case, the present is taken to be the start of a project. 

The project cashflow s constructed by performing the calculation for every year of the project life. Atypical project cashflow is shown in Figure 13.9, along with a cumulative cashflow showing how cumulative revenue is typically split between the capex, opex, the host government (through tax and royalty) and the investor (say the oil company). The cumulative amount of money accruing to the company at the endof the project is the cumulative cash surplus or field life net cash flow. 

The project cashflow discussed so far follows a pattern typical of E P projects a number of years of expenditure (giving rise to cash deficits) at the beginning of the project, followed by a series of cash surpluses. The annual cashflows need to be evaluated to incorporate the timing of the cash flows, to account for the effect of the time value of monef. The technique which allows the values of sums of money spent at different times to be consistently compared is called discounting. 

Ref 91. Discounted cash-flow models account for use of capital, working capital, income taxes, time value of money, and operating expenses. Real after-tax return assumed to be 12.0%. Short-rotation model used for sycamore and poplar. Herbaceous model used for other species. Costs ia 1990 dollars. Dry tons. 

DecoveTj of Capital. In Figure 1, the annual book depreciation is used to retire the fixed capital investment. Whereas this accounting model does not correspond to the typical money flow, it is one possible model for recovery of capital. This model assumes that the investment is reduced each year by the amount of the annual depreciation. Another model (22) assumes that a uniform yearly book depreciation payment is made to an interest-bear sinking fund that accumulates to the depreciable fixed capital amount at the end of the venture. Using this second model, the investment is outstanding throughout the lifetime of the project. This also does not correspond to the actual money flow in most cases. ProfitabiUty analysis utilizes a third model based on discounted cash flows. 

If money is borrowed, interest must be paid over the time period if money is loaned out, interest income is expected to accumulate. In other words, there is a time value associated with the money. Before money flows from different years can be combined, a compound interest factor must be employed to translate all of the flows to a common present time. The present is arbitrarily assumed often it is either the beginning of the venture or start of production. If future flows are translated backward toward the present, the discount factor is of the form (1 + i) , where i is the annual discount rate in decimal form (10% = 0.10) and n is the number of years involved in the translation. If past flows are translated in a forward direction, a factor of the same form is used, except that the exponent is positive. Discounting of the cash flows gives equivalent flows at a common time point and provides for the cost of capital. 

Numerically, the difference between continuous and annual compounding is small. In practice, it is probably far smaller than the errors in the estimated cash-flow data. Annual compound interest conforms more closely to current acceptable accounting practice. However, the small difference between continuous and annual compounding may be significant when apphed to very large sums of money. 

Discounted Cash Flow The present value P of a future sum of money F is given by... 

Thus, cash flow in the early years of a project has a greater value than the same amount in the later years of a project. Therefore, it pays to receive money as soon as possible and to delay paying out money for as long as possible. 

The cost of capital may also be considered as the interest rate at which money can be invested instead of putting it at risk in a manufacturing process. Let us consider the process data listed in Table 9-4 and plotted in Fig. 9-10. If the cost oi capital is 10 percent, then the appropriate discounted-cash-flow curve in Fig. 9-10 is abcdef. Up to point e, or 8.49 years, the capital is at risk. Point e is the discounted breakeven point (DEEP). At this point, the manufacturing process... 

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. 

For many years, companies and countries have lived with the problem of inflation, or the faUing value of money. Costs—in particular, labor costs—tend to rise each year. Failure to account for this trend in predicting future cash flows can lead to serious errors and misleading profitabihty estimates. 

The same questions may then be asked for different values of the probabilities p and po. The answers to these questions can give an indication of the importance to the company of P at various levels of risk and are used to plot the utility curve in Fig. 9-25. Positive values are the amounts of money that the company would accept in order to forgo participation. Negative values are the amounts the company woiild pay in order to avoid participation. Only when the utihty value and the expected value (i.e., the straight line in Fig. 9-25) are the same can net present value (NPV) and discounted-cash-flow rate of return (DCFRR) be justified as investment criteria. 

It is also possible to combine (MSF) considerations with evaluation of the true discounted-cash-flow rate of return (DCFRR) by using Eq. (9-62). The relationship of Eq. (9-59) is independent of inflation if all money values are based on those prevailing in the startup year. For this case, Fig. 9-34 shows the true (DCFRR) reached in a given time, expressed as the number of elapsed payback periods for various values of the payback period. 

As indicated in Section 30.7, energy-conservation measures cost money, and in spite of the likely results indicated by any of the methods available (simple payback, discounted cash flow, etc.) it is possible that the organization s funds are not available for such schemes. Alternatives that should be considered are ... 

Expenditure on corrosion prevention is an investment and appropriate accountancy techniques should be used to assess the true cost of any scheme. The main methods used to appraise investment projects are payback, annual rate of return and discounted cash flow (DCF). The last mentioned is the most appropriate technique since it is based on the principle that money has a time value. This means that a given sum of money available now is worth more than an equivalent sum at some future data, the difference in value depending on the rate of interest earned (discount rate) and the time interval. A full description of DCF is beyond the scope of this section, but this method of accounting can make a periodic maintenance scheme more attractive than if the time value of money were not considered. The concept is illustrated in general terms by considering a sum of money P invested at an... 

A prerequisite to a corrodable material being used is that it is known to have a useful and reasonably predictable life. Planned, or unplanned downtime costs money and the intervals between planned replacements must be of reasonable duration. In practice, the replacement interval is usually conservative at first and then as experience accumulates, the intervals between planned replacements will usually extend. The main reason for choosing a planned maintenance policy is that on a discounted cash flow (DCF) calculation over the life of the plant, the cost of regular replacements including maintenance labour and downtime is less than the extra initial capital cost of a more durable material. 

These arrows show us how the reaction took place. For most of the reactions that you will see this semester, the mechanisms are well understood (although there are some reactions whose mechanisms are still being debated today). You should think of a mechanism as bookkeeping of electrons. Just as an accountant will do the bookkeeping of a company s cash flow (money coming in and money going out), the mechanism of a reaction is the bookkeeping of the flow of electrons. 

Discounted cash flow (time value of money)... 

The money earned in any year can be put to work (reinvested) as soon as it is available and start to earn a return. So money earned in the early years of the project is more valuable than that earned in later years. This time value of money can be allowed for by using a variation of the familiar compound interest formula. The net cash flow in each year of the project is brought to its present worth at the start of the project by discounting it at some chosen compound interest rate. 

The rate of return is often calculated for the anticipated best year of the project the year in which the net cash flow is greatest. It can also be based on the book value of the investment, the investment after allowing for depreciation. Simple rate of return calculations take no account of the time value of money. 

Inflation depreciates money in a manner similar to, but different from, the idea of discounting to allow for the time value of money. The effect of inflation on the net cash flow in future years can be allowed for in a similar manner to the net present worth calculation given by equation 6.9, using an inflation rate in place of, or added to, the discount rate r. However, the difficulty is to decide what the inflation rate is likely to be in future years. Also, inflation may well affect the sales price, operating costs and raw material prices differently. One approach is to argue that a decision between alternative projects made without formally considering the effect of inflation on future earnings will still be correct, as inflation is likely to affect the predictions made for both projects in a similar way. 

Net future worth NFW , Simple. When plotted as cash-flow diagram, shows timing of investment and income Takes no account of the time value of money... 

The other indices to be described, net present value and discounted cash flow return, are more comprehensive because they take account of the changing pattern of project net cash flow with time. They also take account of the time value of money. 

As a more complete picture of the project emerges, the cash flows through the project life can be projected. This allows more detailed evaluation of project profitability on the basis of cash flows. Net present value can be used to measure the profit taking into account the time value of money. Discounted cash flow rate of return measures how efficiently the capital is being used. 

Various other evaluation schemes based on the concept of time value of money are also sometimes used. These, together with the Net Present Value and Rate of Return methods, are all grouped together under the title of discounted cash flow methods. 

The key to the discounted cash flow methods is the determination of a proper interest rate. For this, two factors must be known. One is how much does it cost to obtain money The second is what is a reasonable amount of profit to expect from a plant The first depends on the source of money. This can be corporation earnings, the sale of stock, the issuance of bonds, the selling of assets, or borrowing from some outside source. The second depends on economic conditions. 

For an example of the kinds of decisions that involve the time value of money, examine the advertisement in Figure 3.1. For which option do you receive the most value Answers to this and similar questions sometimes may be quickly resolved using a calculator or computer without much thought. To understand the underlying assumptions and concepts behind file calculations, however, you need to account for cash flows in and out using the investment time line diagram for a project. Look at Figure 3.2. 

Does not properly consider the time value of money and distributed investments or cash flows... 

Net present value (NPV) the present value (including the time value of money) of initial and future cash flows given by Equation (13.4). 

Where CF is the cash flow from operation, HR is the hurdle rate or required minimum return and II is the initial investment. Advantages of NPV are that it accounts for the time-value of money, provides a value estimate for the lifetime of the project (10 years) and can always be calculated (unlike IRR). Hurdle rates are set by central finance groups or, in some cases, the project team. If a positive NPV is obtained at a given hurdle rate a project is considered profitable and should be executed based on competing priorities. 

Pi is the cash flow for the year i, and r is the relevant discount rate, which can be thought of either as the interest of borrowing money to start the company, or as the return from an alternate opportunity for a safe investment. This equation considers that 1 next year is worth only 1/(1 + r) dollars this year. The value of the NPV is the sum of all the cash flows for the n year, discounted by the power of compound interest. We give here the values of NPV for a number of values of r ... 

When r = 0, we take the position that future money is worth just as much as current money, so that NPV is equal to the sum of the cash flows. When r = 0.05, or a discount rate of 5%, the NPV equals 128 a positive NPV means that this investment is better than putting our investment of 350 into a safe alternate investment to earn 5% interest. When r = 0.25, NPV = -72 a negative NPV means we are better off investing our 350 into a safe alternate investment to earn 25% interest. The NPV for each investment is computed and compared, and the investment with the highest NPV has the most merit. Note that NPV is sensitive to the value of r, so that the winner when interest rates are low need not be the winner when interest rates are high. 

Continuous Compound Interest In some companies, namely petroleum, petrochemical, and chemical companies, money transactions occur hourly or daily, or essentially continuously. The receipts from sales and services are invested immediately upon receipt. The interest on this cash flow is continuously compounded. To use continuous compounding when evaluating projects or investments, one assumes that cash flows continuously. 

This model does not take into account the time value of money, and no consideration is given to cash flows that occur in a project s later years after the depreciable investment has been recovered. A variation on this method includes interest, called payout period plus interest (POP + I) and the net effect is to increase the payout period. This variation accounts for the time value of money. 

Net Present Worth Method The NPW method allows the conversion of all money flows to be discounted to the present time. Appropriate interest factors are applied depending on how and when the cash flow enters a venture. They may be instantaneous, as in the purchase of capital equipment, or uniform, as in operating expenses. The alternative with the more positive NPW is the one to be preferred. In some instances, the alternatives may have different lives so the cost analysis must be for the least common multiple number of years. For example, if alternative A has a 2-year life and alternative B has a 3-year hfe, then 6 years is the least common multiple. The rate of return, capitalized cost, cash flow, and uniform annual cost methods avoid this complication. 

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