When analysis of an investment proposal by the net present value method indicates that the present?

2.2.7.3 Net present value

Net present value (NPV) can be evaluated by adding the present discount values of the incomes while subtracting the discounted present costs through the useful lifetime of the system [29].

(10)NPV=∑NPVsale_i+∑NPVend_i−Cinvestment−∑NPV r_i−∑NPVO&M_i

where NPVsale_i are the present discounted values of income from the sale i (e.g., electrical energy sold to the grid), NPVend_i are the present discounted values of incomes from the residual value of component at the end of the lifetime of the HES, Cinvestment is the initial total investment cost, NPVr_i are the present discounted cost of future costs of replacing the components throughout the life of the system, NPVO & M_i are the discounted present costs of future costs of operation and maintenance of component i throughout the life of the system.

13.2.5 Economic modeling

The best way to meet the cooling load criteria for optimum COPsys and the maximum economic feasibility is to consider an optimum combination of a hybrid energy powered absorption refrigeration system. The economic analysis methodology is built with a suitable model of the system. The cost analysis of this report is discussed based on the principle of capital cost (CC), operating cost (OC), payback period (PBP), annualized capital cost (ACC), total annual cost (TAC), net present value (NPV), and life cycle cost.

The total cost of the system consists of various costs, such as construction, equipment, and civil works. In some regions, subsidies are given by the government agencies to encourage the installation of the renewable energy-based application. The effect of subsidies is incorporated in the capital cost of the system. The major components considered for measuring the CC are the conversion devices, burners, heat exchangers, energy conversion plants, etc. Dependents on the current market rates as available from the suppliers, the cost factors are determined in the present context. Until the measurement is made, the total cost of each part is taken into account as the construction expense (Edwin et al., 2019; Edwin & Sekhar, 2014b).

(13.13)CCofHRES= capitalcostsofBM,BG,and GGconversionsystem+solarcollector+chillingsystem+gasburnerandheatexchanger−govt.subsidies

The running cost (RC) is calculated from the operational and maintenance cost and annual depreciation. The following assumptions are taken into the cost calculations. Some standard values taken in this study are maintenance cost—2% of the capital cost, lifetime of the system—18 years, annual interest rate (d)—12%, the cost of BM—Rs 0.95 kg−1, the cost of cow dung—Rs 0.40 kg−1, and the cost of BG sources—Rs 0.50 kg−1. Transportation and labor costs are also suitably selected for this study (Edwin et al., 2019; Edwin & Sekhar, 2014b).

(13.14)RCofHES=costsof(energysource+operationandmaintenanceofenergyconversiondevice +operationandmaintenanceofVARS+labor+ depreciation)

The performance of a hybrid energy-powered cooling system requires measuring the PBP to replace the traditional fossil fuel (diesel)-powered vapour compression refrigeration system (VCRS) (Edwin et al., 2019; Edwin & Sekhar, 2014b, 2016).

(13.15)Payback period=Incremental value of capital costAnnual savings(profit)

where incremental value is the difference between CCs of diesel generator-operated vapor compression cooling system and hybrid energy-operated vapor absorption cooling system (Edwin & Sekhar, 2014a).

(13.16)CC of fossil−fuel−operated VCRS=costs of diesel genset and VCRS

Annual savings is the reduction in operating cost due to the implementation of hybrid renewable energy-based chilling system.

(13.17) RC of conventional VCRS=diesel cost+O&MCof VCRS+labor cost+depreciation value

TAC consists of ACC and the annual care and replacement costs. It can be stated as:

(13.18)TAC=ACC+annual cost of operation and maintenance cost

Equivalent annual cost is the annual cost of possessing, operating and maintaining an asset over its entire life span, and it is calculated by:

(13.19) ACC=CC×CRF(i,n)

where n is the life span of the component in years, “I” is the annual interest rate, CRF is the capital recovery factor. The CRF can be calculated from

(13.20)CRFi,n=i.(1+i)n (1+i)n−1

NPV is the actual value of the capital and RCs of a device over its lifespan. NPV is used as a primary economic measure for the evaluation of an energy system. The discrepancy between the actual value of the profits and the expenses resulting from an investment is the net present value of the system (Edwin et al., 2019; Edwin & Sekhar, 2014b, 2016). It is expressed as,

(13.21)NPV=S×(1+i)n−1i(1+i)n −CC

where “S” defines for benefits at the end of the period. Conditions for accepting an investment proposal, as evaluated from the NPV method are:

NPV > 0, proposal can be accepted;

NPV = 0, Proposal is indifferent; and

NPV < 0, proposal cannot be accepted.

3.3.5 Net Present Value (NPV)

NPV is a strong criterion to determine if a project is profitable or not. It considers the interest rate (r), which is usually equal to the inflation rate; therefore the real value of money at every year of operation is considered. NPV is calculated as follows:

(3-16)NPV=∑y=1Lc fy(1+r)y−I

For a project to be profitable, NPV must be positive. The more positive the NPV is, the more profit the project will produce. The CCHP cycle and its components can be designed to achieve a predefined profit of NPV min after L years. The unit of NPV is the unit of the currency used in the economic calculations.

14.10 Net Present Value (NPV)

The NPV of the investment is the difference between the present value of the benefits and the costs resulting from an investment. Following points defines the role of an NPV:

A positive NPV implies that the financial position of the investor will be improved by undertaking the project.

A negative NPV would indicate a financial loss.

Zero or null NPV would mean that the present value of all benefits over the useful lifetime is equal to the present value of all the costs [3].

Mathematically,

(14.96)NPV=∑j=0nBj−Cj1+ij

where Bj is the benefits and Cj is the costs at the end of the period j; n is the useful life of the project and i is the rate of interest.

Eq. (14.96) involves subtraction of the cost from the benefits at any period and then multiplying the result by single payment present worth factor for that period. Eventually, the NPV is determined by algebraically adding the results for all the periods under consideration. It often happens that (Bj − Cj) is constant for all j except for j = 0. In such a case, Eq. (14.96) can be modified as

NPV=B0−C0+∑j=1nBj−Cj1+ij

Since B0, the benefits in the 0th year, are invariably zero and Bj − Cj is constant (= B − C) for j = 1 to n, then

NPV=−C0+B−C∑j=1n11+in

or

(14.97)NPV=−C0+B−C1+in−1i 1+in

where C0 represents the initial capital investment in the project.

Eqs. (14.96), (14.97) are based on the assumption that the interest rate i remains constant over time. Furthermore, the NPV could be estimated with different rates of interest rate over jth period. Thus, from Eq. (14.96), it can be modified for NPV as

(14.98)NPV=B0−C0+ B1−C11+i1+B2−C21+i11+i2+…………+Bj−Cj1+i11 +i2…….1+ij+..…+Bn−Cn1+i11+i2 …….1+in

Eventually, on the basis of NPV method, the acceptance criteria of an investment project is

NPV > 0, agree to consider the project

NPV = 0, remain indifferent

NPV < 0, does not agree to consider the project

A positive NPV represents a positive surplus and the project may be accepted subject to availability of funds, while, a project should not be considered or rejected for negative NPV and the funds can be profitably invested in the other projects. In the case of mutually exclusive alternative investments, the project with highest positive NPV should be preferred.

5.6 Comparison of NPV and IRR in economic evaluation

NPV and IRR serve different purposes while evaluating the profitability. NPV (Fig. 7) is a measure of the cash profit (in terms of the present value) generated by the project after recovering the initial investment. Thus, it is an absolute determinant of the entire project’s profit. The IRR for a project represents the RORI. It is a measure of the efficiency with which the capital is employed and indicates the earning power of the project investment. The NPV requires an estimate of the cost of capital whereas IRR does not require the cost of capital. For a single project considered in isolation, NPV and IRR both lead to the same conclusion if a project has a positive NPV. It is bound to have an IRR above the discount rate used in NPV calculation. If a company has potentially more acceptable projects and limited capital to finance them, projects are usually selected in a way to maximizes the total NPV. The ranking of the projects is done in the decreasing order of IRR. If a choice is to be made between alternative proposals of the same project, then the alternative with the greatest NPV should be selected. Note that although IRR is widely used in economic evaluation of projects, it is more limited than NPV in its applications. NPVs are additive when dealing with multiple project selection whereas IRRs are not additive.

NPV profile

NPV profile is a graphical representation of project’s NPV against various discount rates. Discount rates and NPV are subsequently plotted on the x- and y-axis.

Example

Draw the NPV profile for projects A and B and determine which project is better assuming a cost of capital of 5%.

The first task in this problem is to draw the NPV profile by plotting discount rate (x-axis) vs NPVs for projects A and B (y-axis). IRR is the point at which NPV curves cross the x-axis as shown in Fig. 18.2. There is a point referred to as the crossover point (rate) in Fig. 18.2. Crossover point is the discount rate at which the NPV for both projects is equal (Table 18.12).

Table 18.12. Net present value (NPV) profile

There are three stages in the following NPV profile. The first stage occurs before the crossover point, and in this phase, the NPV of project A is more than the NPV of project B. In this stage, there is a conflict between IRR and NPV since the NPV of project A is more than B, while the IRR of project B is more than A. The company’s cost of capital in this example is given to be 5%. When cost of capital is less than crossover point (rate), a conflict exists. When a conflict exists and the cost of capital is less than the crossover point, the NPV method must be used for decision making. Therefore, project A is superior to project B in this example since the cost of capital is given to be 5%. When the cost of capital is low, delaying cash flows is not penalized as much compared to at a higher cost of capital. When the cost of capital is high (more than the crossover point) delaying cash flows will be penalized.

At the crossover point (second stage), NPV of both projects is equal. Finally, during the third stage, NPV for project B is more than NPV for project A. Please note that if the cost of capital in this problem was given to be 10% instead of 5% (cost of capital > crossover rate), both NPV and IRR methods would have led to the same project selection. It is important to note that it is the difference in timing of cash flows that is causing the crossover between the two projects. The project with faster payback provides more cash flows in the early years for reinvestment. If the interest rate is high, it is vital to get the money back faster because it can be reinvested while if the interest rate is low, there is not such a hurry to get the money back faster.

NPV Versus IRR

NPV basically measures the dollar benefit (added value) of the project to the shareholders but it does not provide information on the safety margin or the amount of capital at risk. For example, if NPV of a project is calculated to be $2 million, it does not indicate the kind of safety margin that the project has. In contrast, IRR measures the annual rate of return and provides safety margin information. All in all, for mutually exclusive projects and ranking purposes, NPV is always superior to IRR. Unfortunately, in the oil and gas industry, IRR is quite often used for making critical decisions. It is recommended to calculate and understand IRR methodology for each project. However, the ultimate decision whether to perform a project should be determined using NPV calculation.

(i) Net Present Value (NPV)

The NPV is defined as the present value equivalent of all cash inflows less all cash outlays associated with a project. If the NPV is greater than zero, the project is worthwhile from an economic standpoint. If a choice has to be made between projects, the project with the greatest NPV should be selected. The NPV method converts payments in the future to present values and makes them comparable. The NPV method can be expressed mathematically as:

where i = the actual year, S = annual savings, 1/(1 + r)i = the discounting factor, r = the discount (interest) rate, and C = the initial outlay (investment).

As shown by the calculations in Table 2 the NPV is + 1,814 SEK for the buttress. Hence, a purchase is acceptable according to the above criterion because the NPV is positive, and the investment is thereby profitable. If a choice among various projects has to be made, because projects are competitive or investment funds are limited, the projects should be ranked for selection purposes in order of their NPVs. That is, the greater the NPV, the higher the ranking of a competing project. If the competing projects differ in capital outlay, the relationship between the absolute difference in outlay and the expected improvement in NPV must be examined.

Table 2. Calculation of the NPV with r = 20%.

NPV = +5,814 – 4,000 = + 1,814 SEK

Note: Advantage: The NPV takes the long-term effect of the project into account. Disadvantage: The NPV criterion can discriminate ‘small’ ergonomic projects in ranking. That is, the projects that require ‘small’ capital outlays.

20.5.2 Net Present Value Method

NPV is another measure of profitability that is based on the present value of cash flows discounted on an average rate of i in excess of the present value of investment. It is defined by Eq. (20.4).

(20.4)NPV=∑x=0nNCFx (1+i)x

where i is the average rate of discount; the rest of the variables have the same meaning as defined earlier in Eq. (20.3). This method introduces the true value of money into the analysis based on an interest rate, i, representative of the company's reinvestment opportunities. If the NPV is a positive value, a viable investment is indicated.

Tables 20.6 and 20.7 show the NPVs for the two methods of drilling and completion, respectively. The interest rate is assumed to be 15%.

Table 20.6. Net Present Value (NPV) for Vertical Wells

Total NPV for 5 years is $302 million which is a bit less than the initial investment of $331 million, but these wells will produce for 30 years or so indicating a higher positive NPV.

Table 20.7. Net Present Value (NPV) for Multilateral Horizontal Wells

Total NVP for 5 years is $304 million. A positive value again indicates that the project is viable.

Table 20.7 shows similar data for the horizontal wells.

1.4 Reservoir Management and Economics

The definition of reservoir management presented previously recognizes the need to consider the economics of resource development. The economic value of a project is influenced by many factors, some of which can be measured. An economic measure that is typically used to evaluate cash flow associated with reservoir management options is net present value (NPV). The cash flow of an option is the net cash generated or expended on the option as a function of time. The time value of money is included in economic analyses by applying a discount rate to adjust the value of money to the value during a base year. Discount rate is the adjustment factor, and the resulting cash flow is called the discounted cash flow. The NPV of the cash flow is the value of the cash flow at a specified discount rate. The discount rate at which NPV is zero is called the discounted cash flow return on investment (DCFROI) or internal rate of return (IRR).

Figure 1.4 shows a typical plot of NPV as a function of time. The early time part of the figure shows a negative NPV and indicates that the project is operating at a loss. The loss is usually associated with initial capital investments 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 where the NPV is zero after the project has begun is the discounted payout time. Discounted payout time in Figure 1.4 is approximately four years.

Table 1.2 presents the definitions of several commonly used economic measures. DCFROI and discounted payout time are measures of the economic viability of a project. Another measure is the profit-to-investment (PI) ratio, which is a measure of profitability. It is defined as the total undiscounted cash flow without capital investment divided by total investment. Unlike the DCFROI, the PI ratio does not take into account the time value of money. Useful plots include a plot of NPV versus time and a plot of NPV versus discount rate.

Table 1.2. Definitions of Selected Economic Measures

The preceding ideas are quantified as follows. NPV is the difference between the present value of revenue R and the present value of expenses E; thus,

(1.4.1)NPV=R−E

If we define ΔE(k) as the expenses incurred during a time period k, then E may be written as

(1.4.2)E=∑k=0N×QΔE(k)(1+i′Q)k

where i′ is the annual inflation rate, N is the number of years of the expenditure schedule, and Q is the number of times interest is compounded each year. A similar expression is written for revenue R:

(1.4.3)R=∑k=0N×QΔR(k)(1+iQ)k

where ΔR(k) is the revenue obtained during time period k, and i is the annual interest or discount rate. Equations (1.4.2) and (1.4.3) include the assumptions that i and i′ are constants over the life of the project, but i and i′ are not necessarily equal. These assumptions let us compute the present value of money expended relative to a given inflation rate i′ and compare the result to the present value of revenue associated with a specified interest or discount rate i.

Net present value takes into account the time value of money. NPV for an oil and/or gas reservoir may be calculated for a specific discount rate using the equation

(1.4.4)NPV=∑n=1NPonQon+PgnQgn−CAPEXn−OPEXn−TAXn (1+r)n

where

N = Number of years

Pon = Oil price during year n

Qon = Oil production during year n

Pgn = Gas price during year n

Qgn = Gas production during year n

CAPEXn = Capital expenses during year n

OPEXn = Operating expenses during year n

TAXn = Taxes during year n

r = Discount rate

In many cases, resource managers have little influence on taxes and prices. On the other hand, most resource managers can exert considerable influence on production performance and expenses. Several strategies may be used to affect NPV. Some strategies include accelerating production, increasing recovery, and lowering operating costs. One reservoir management challenge is to optimize economic measures like NPV.

Revenue stream forecasts are used to prepare both short- and long-term budgets. They provide the production volumes needed in the NPV calculation. For this reason, the asset management team may be expected to generate flow predictions using a combination of reservoir parameters that yield a range of recoveries. Uncertainty analysis is a useful process for determining the likelihood that any one set of parameters will be realized and estimating the probability distribution of reserves.

Reservoir management must consider how much money will be available to pay for wells, compressors, pipelines, platforms, processing facilities, and any other items that are needed to implement the plan represented by the model. The revenue stream is used to pay taxes, capital expenses, and operating expenses. The economic performance of the project depends on the relationship between revenue and expenses. Several economic criteria may be considered in the evaluation of a project, such as NPV, internal rate of return, and profit-to-investment ratio. The selection of economic criteria is typically a management function. Once the criteria are defined, they can be applied to a range of possible operating strategies. The strategies should include assessment of both tangible and intangible factors. A comparative analysis of different operating strategies gives decision-making bodies valuable information for making informed decisions.