Which of the following depreciation methods is the least used according to GAAP

Present Value of Net Benefit

The present value of net benefit (PVNB) shows the worth of a P2 project in terms of a present-value sum. The PVNB is determined by calculating the present value of all benefits, doing the same for all costs, then subtracting the two totals. The result is an amount of money that would represent the tangible value of undertaking the project. This comparison evaluates all benefits and costs at their current or present values. If the net benefit (the benefits minus costs) is greater than zero, the project is worth undertaking; if the net is less than zero, the project should be abandoned. This technique is firmly grounded in microeconomic theory and is ideal for a TCA analysis.

Even though it requires a preselected discount rate, which can greatly discount long-term benefits, it assures that all benefits and costs over the entire life of the project are included in the analysis. Once a company knows the present value of all options with positive net values, the actual ranking of projects using this method is straightforward; those with the highest PVNBs are funded first.

There are no hard-and-fast rules as to which factors one may apply in performing a life-cycle cost analysis; however, conceptually, the PVNB method is preferred. However, in many small-scale P2 projects, the benefits are so well defined and obvious that a comparative financial factor as simple as a ROI or the payback period suffices.

Three additional terms useful in a life-cycle cost analysis are:

Double declining balance depreciation is an accelerated depreciation method whereby the first-year depreciation is double the amount of straight-line depreciation.

Straight-line depreciation is the depreciation per year equal to the total facility cost divided by the years of depreciation (usually the facility lifetime).

SYD depreciation stands for sum of years’ digits, a common accelerated depreciation method, where the sum of the digits is the total of the numbers representing the years of depreciation (usually the facility lifetime).

4.1 Maximum dry seaweed price

The process model developed in Aspen Plus was sent to Aspen Process Economic Analyzer for economical evaluations. The total project capital cost is considered to depreciate, via a straight-line depreciation method, over the 10 years of economic Life of the facility. To reach a ROI break-even point after 10 years of operation, dry seaweed cost increased until net present value in 10th year equals to zero. The maximum price for dry seaweed obtained was 160 $/Ton for the base case of 100,000 MT/year of dry seaweeds. Table 3 shows resulting production costs at this break-even point. Figure 2 shows a pie chart of the distribution of operating costs in 10th year. From the chart, it can be seen that the raw materials constitute 68.5% of the total operating costs, and 18% of the operating cost is for utilities. This is in accordance with high raw material costs associated for ethanol production plants using fermentation processes from biomass (Liu & Gu, 2008).

Table 3. Production costs (US$) at a ROI break-even point

Total Project Cost12,901,300Total operating labor and maintenance cost per year1,466,000Total raw material cost per year16,302,200Total product sales per year26,783,400Total utilities cost per year4,449,870

TECHNIQUES FOR EVALUATION OF ENERGY PROJECTS

Typical published calculations of the cost of producing synthetic fuels distinguish between industrial financing and regulated utility financing. In both cases, the computations are usually performed for a specified year with the investment cost, feedstock cost, and other operating costs presented in terms of dollars for that year. Sometimes, it is unclear whether the reported investment is based on hypothetical “overnight” construction or whether account has been taken of the S-shaped curve of investment outlays.

In the case of industrial financing, published computations are usually performed so that a specified discounted cash flow (DCF) after-tax return on equity is achieved with defined leverage, interest rate, depreciation method, tax rate, and project life. The production cost of the synthetic fuel is usually presented as a uniform cost consisting of the sum of the annual levelized carrying charge plus annual feedstock and operating costs. The levelized carrying charge is the uniform annual charge which, when discounted over the life of the project at the weighted cost of capital3 to the base investment year, equals the inital investment plus the present value of tax payments.

In the case of regulated utility financing, published computations frequently provide an average cost of production over the life of the project. This consists of the average annual capital-related cost (average earnings on rate base plus average depreciation and income tax) plus annual feedstock and other operating costs. If V1 is the inital rate base which depreciates linearly over the book life, nb, and r is the expected “fair rate of return”, then:

Average annual earnings on rate base = rV1(nb+1nb)

Annual hook depreciation =  V1nb

If special tax incentives are ignored, and the total rate base is assumed to be tax depreciable, and tax depreciation is taken equal to book depreciation, then:

(1)Average annual income tax = T(r−id)(1−T) V1(nb+12nb)

Where T=incremental tax rate

d=debt fraction

i=interest on debt

Therefore, the average annual capital-related production cost equals:

V1[1nb + (r + T(r−id)(1−T))(nb+12nb)]

It should be noted that the average capital-related production cost calculated as above is an arithmetic average which does not account for the time value of money. Furthermore, feedstock and other operating costs are expressed in terms of a base year with no consideration of escalation rates and the time value of money.

As an alternative to the arithmetic average production cost, one can compute a levelized production cost (which is equal to the levelized revenue requirement for a regulated utility) which consists of a levelized carrying charge plus levelized feedstock and other operating costs. This technique is commonly used for the comparison of alternative electric utility generation options.4. It consists of computing a constant annual charge which has a present value equal to the sum of present value of capital-related costs and the present value of operating costs. For a regulated utility, with tax simplifications as before, the book value at the beginning of year t is5:

Vt = V1(1 − (t−1)nb)

and earnings in year t are:

rV1(1 − (t−1)nb)

After-tax return on equity in year t, which equals earnings less interest on deht, is:

(r − id)V1(1 − (t−1)nb)

and the income tax in year t is:

T(r−id)(1−T)V1(1 − (t−1)nb)

Therefore, the capital-related production cost in year t, equals:

V1nb + rV1(1 − (t−1)nb) + T(r−id)(1-T) V1(1-(t−1)nb)

which is equivalent to:

(2)V1[1nb + (r − T(r−id)(1−T) ) + (1 − (t−1)nb)]

The expression 1 − (t−1)nb, when summed from t=1 through t=nb, is equivalent to unity less a uniform gradient of slope 1nb. The uniform series which is equivalent (i.e., has the same present value) to the uniform gradient at a discount factor r, is:6

1nb(1r − nb(1+r)nb − 1)

Therefore, the levelized capital-related production cost (or carrying charge) equals:

(3)V1[1nb + (r + T(r−id)(1−T))] [1 − 1nbr + 1(1+r)nb−1]

It is instructive to compare the arithmetic average and levelized capital-related costs from Expressions (l) and (3), respectively. If one assumed, for the typical utility-owned synthetic fuel facility that:

nb= 20 years

i = 9.00 %

d = 60%

r = 11.40% (which implies a 15% return on equity)

T = 48%

then Expression (1) yields an arithmetic average cost of $13.89 per year, and Expression (3) yields a levelized cost of $16.72 per year, both for an initial rate base of $100. The divergence between the two will increase as the expected life of the project and the discount rate increase.

Though published analyses usually distinguish between the computational methods used to determine capital-related costs with industrial as opposed to utility financing, there is no real difference other than in input assumptions on the degree of leverage, return on equity, and tax treatment. For example, if one hypothetically assumes that an industrial facility requires the same DCF return of ll.40% and the same leverage, depreciation, and tax rate as assumed above for a utility, then:

Capital recovery factor7= 0.1289

The capital recovery factor represents the uniform payment which has a present value of unity when discounted over twenty years to the beginning of the first year at 11.40%. In addition to capital recovery, taxes have to be paid. The uniform tax payment equals T/(1−T) times the uniform after-tax return on equity:

Uniform tax payment = 4852×6011.4 (0.1289 − 0.05)                                              = 0.0383

Therefore, the uniform annual capital recovery factor plus tax payment equals 0.1672 per dollar of initial investment, as before.

The effect of the degree of leverage will, of course, be significant. If the incremental capital structure for the industrial enterprise is assumed to be 70% equity and 30% debt, while other assumptions remain the same, then:

Weighted incremental cost of capital=13.20%Capital recovery factor=0.1441

Uniform tax payment=4852×10.5013.20(0.1320 − 0.05)=0.0602

Therefore, the uniform annual capital recovery factor plus tax payments has increased from 0.1672 to 0.2043 per dollar of initial investment as the fraction of debt in the incremental capital structure has declined from 60% to 30%.

For purposes of illustration, the above computations were based on a number of simplifying assumptions. Published computations8 may account for accelerated depreciation, investment tax credit, local taxes and insurance, and the return of working capital at the end of the project life. Account may also be taken of the fact that construction outlays occur over a span of time rather than at a point in time.

Since the purpose of most published computations is to develop a price for synthetic fuels, feedstock and other operating costs are added to the uniform capital-related costs to obtain an overall uniform production cost. Since this cost is usually presented in terms of dollars in a specified year, feedstock and other operating costs are included in dollars for that year.

The methods described above for computing the costs of synthetic fuels have two major drawbacks: internal inconsistency and unsuitability for comparison with oil and natural gas prices. The internal inconsistency lies in the way inflation is handled. The incremental cost of capital used in the computations includes an allowance for expected inflation. For example, the 9% cost of debt assumed in the above examples probably consists of about 3% real interest and 6% inflation. It is incorrect to allow for inflation in computing capital-related costs while ignoring it in computing operating costs. Computations should either be made on a completely inflation-free basis or inflation should be allowed for in all costs.

To illustrate the error that can be introduced by ignoring the escalation of operating costs, consider the following data for a hypothetical utility-owned coal-based synthetic natural gas (SNG) facility:

Capital investment in base year = $1.5 billion

Annual production9 of SNG = 82 trillion BTU

Operating costs in base year = $150 million

General inflation rate = 6% per year

Cost of debt = 9% per year

Cost of equity = 15% per year

Fraction of debt in incremental capital = 60% per year

Escalation of operating costs = 6% per year

Project Life = 20 years

Depreciation: straight over 20 years

Income tax rate = 48%

The levelized carrying charge is 16.72% as calculated before. Therefore the annual capital-related production cost is (0.1672) × ($1.5 billion) which equals approximately $251 million. The levelized value of operating costs is the base year operating cost times the following factor:10

0.114(1.11420 − 1.0620)(0.114 − 0.06)(1.11420 − 1) = 1.5031

The levelized production cost is therefore $251 million plus ($150 million) × (1.5031) which equals approximately $476 million per year. This is equivalent to a levelized unit cost of SNG of $5.80 per million BTU [(476 × 106) ÷ (82 × 106)].

It would be incorrect to state that the constant cost of producing SNG in terms of base year dollars is $251 million plus $150 million which is equivalent to $4.89 per million BTU. It is true that operating costs in the base year are $150 million, but the $251 million need not necessarily represent capital-related production costs in the base year. The $251 million is merely a convenient way of representing what the present value of capital-related charges over the life of the project will be when discounted at the incremental weighted cost of capital. There are an infinite number of different series of capital charges which can yield the same discount factor. There is no a priori reason why a levelized carrying charge is the best representation of the economic costs incurred in the base year as a result of the investment made.

An alternative approach to computing the levelized production cost in terms of base year dollars is to perform the computation on an inflation-free basis. In this case, the cost of debt and the weighted cost of capital must be represented on an inflation-free basis, as follows:

i = 1.091.06 − 1 = 2.830%r = 1.1141.06 − 1 = 5.094%

If these values are used in Expression (3), the levelized charge becomes 9.99%. Therefore, the annual capital-related production cost is (0.0999) ($1.5 billion) which equals approximately $150 million. The levelized overall production cost is therefore $150 million plus $150 million which equals $300 million or $3.66 per million BTU of SNG. Though this approach is consistent in that both capital-related and operating costs are in terms of base year dollars, it is still necessary to question the economic meaning of the cost of gas that has been computed. The validity of the levelized carrying charge must still be proven.

In some published studies,11 the cost of synthetic fuel is computed, not just for the base year, but also for specified years in the future. This is done by assuming different start-up dates for the facility and computing the corresponding uniform capital-related production costs. In addition, for each start-up date the cost of the product is computed in the base year and later years by adding escalating operating costs and dividing by the production rate. As an example of this technique, consider the hypothetical SNG facility discussed earlier. The levelized carrying charge was computed at 16.72 % for a weighted cost of capital of 11.4% which was assumed to allow for an expected rate of inflation of 6 %. The base year investment was $1.5 billion and base year operating costs were $150 million. The resulting base year cost of SNG was $4.89 per million BTU. Now, if it is assumed that both investment and operating costs are escalating at 6 % per year, then one can compute the unit costs of gas shown in Table 1 for three different start-up dates.

Table 1. Illustrative SNG Production Costs with Different Facility Start-Up Dates and Uniform Capital-Related Costs (Current $ Per Million BTU)

Start-Up Date (beginning of year)Year051004.89−−55.516.54−106.347.378.76157.448.489.87

This type of an analysis has been used in published studies on the basis for indicating in what year a synthetic fuel would become competitive with imported oil or with natural gas. For example, if one assumes that the incremental price of distillate oil or natural gas in year 0 is $3.60 per million BTU and that it is escalating on a real price basis at 4% per year, then the escalation rate in current dollars will be 10.24% assuming a 6 % inflation rate. The prices will therefore be as follows in year 0 through 15:

Year051015Price, $/million BTU3.605.869.5415.54

Based on these numbers, the typical conclusion of such studies would be that investments will not be made in such SNG facilities until sometime between year 5 and year 10, unless subsidization occurs. The validity of this conclusion depends upon the validity of Table 1. Inspection of this table shows that the cost, and therefore the price, of gas is different in the same year depending upon the start-up date of the facility. This result might seem to be counter-intuitive. The operating characteristics of all three facilities are identical in each year with the same operating costs. The operating characteristics of all three facilities are identical in each year, with the same gas production rate and the same operating costs. The investment cost in all three facilities are identical in terms of real dollars. The only difference between the three facilities is the date at which they must be replaced. However, replacement cost will be the same in real dollar terms whenever it occurs if one assumes continuation of the same rate of escalation of investment. Intuitively, one might suggest that the price of gas should be the same in the same year irrespective of start-up date. The question, then, is whether there is such a solution which will also yield a return equal to the incremental cost of capital for each of the start-up dates. This question is answered below.

8.2.6 Cash Flow Generation

To arrive at a current year cash generation figure, book income is adjusted for the noncash expenses by adding back the depreciation and deferred taxes.

This brief discussion of deferred taxes is simplified because any one project or asset could involve several differences between financial reporting and tax reporting. A few examples of timing differences include:

Financial ReportingTaxUsing straight-line depreciation method.Using an accelerated depreciation method.Capitalizing intangible drilling and development costs (IDCs) when incurred and expensed.Expensing 70% of IDC when incurred and amortizing the remaining 30% over 60 months.Expensing geological and geophysical costs when incurred.Capitalizing geological and geophysical costs, then amortizing such costs over production.Capitalizing interest expense as part of a project construction cost, to be depreciated over the life of the asset.Expensing interest expense when incurred.

2.4 Objective function and assumptions

The objective function used for this optimization problem is maximization of the NPV and given in Eq. (1)

(1)NPV=∑n=020NCFn1+rn,

where NCFn is non-discounted cash flow for the year n, and r is the discount rate. Various assumptions considered in techno-economic analysis include: 20 years project life, 10% discount rate, straight line depreciation method over 7 years, 30% tax rate, and two-year construction time. The chemical composition of Saccharina japonica reported by Roesijadi et al. (2010) was used in the simulation. An efficiency of 0.35 g VFA/g of dry biomass is considered in AD. The selling prices of products such as ethanol, heavier alcohols, DDS, and microalgae considered in this study to calculate process revenue were 0.72 $/kg, 1.13 $/kg, 0.13$/kg, and 0.5 $/kg, respectively. Likewise, costs of raw materials such as brown algae, MTBE, cooling H2O, chilled H2O, H2, LP steam, and electricity were 68 $/t, 1100 $/t, 0.013 $/t, 1 $/t, 1.5 $/t, 12.68 $/t, and 0.0622 $/kWh, respectively.

7.1.4 Depreciation

Any facility has a finite lifetime; therefore provisions must be taken for the replacements of equipment and buildings that, after a specific time, will not be economically useful to operate or to use. Equipment and buildings will depreciate its value with time until it is sold at the estimated resale value of its useful life (salvage value). Thus depreciation is the process of putting aside a specific amount for equipment and building replacement at the end of their useful lifetime. Depreciation is considered an expense, and it will reduce the profits to be reported, and consequently, it will reduce the taxes to be paid.

There are several depreciation methods; however, at the end of the asset lifetime, the total tax related to depreciation is the same. These depreciation methods are straight line (SL), sum-of-the-year digits (SYD), double declining balance (DDB), and the modified accelerated cost recovery (MACR).

The straight-line depreciation method assumes that the asset is depreciated at a constant rate for the number of years (n) of tax life. It allows a constant annual deduction where it is assumed that P is the initial asset value and Q is its salvage value:

(7.6)D=P−Qn

Under this method the book value (B) of an item at any given year (j) will be the initial value minus the depreciation up to that time:

(7.7)B=P−jnP−Q

In current practice, there is a faster depreciation in the early years; this happens because, as the times go by, the wear and tear of the assets are cumulative, and at the final stages, the differences are small. SYD and DDB are types of faster depreciation methods; they use different distributions to represent this depreciation.

In the SYD method the depreciation for the year n1 is given as follows:

(7.8)D=n−n1+1nn+12P−Q

The second declination method is a variation of the SYD method, such as the following:

(7.9)D=2n1−2nn−1P

As an example, an asset that has a 15 years lifetime has an initial cost of $20,000, and its salvage value is $2000; Table 7.2 and Fig. 7.1 show the difference between the three methods of depreciation here considered. In this example the last depreciation in the DDB method needs to be adjusted to end with the maximum deducted taxation; in any case the total deduction cannot be larger than the difference between the asset price and its salvage value.

Table 7.2. Depreciation methods.

Straight lineSum-of-the-year digitsDouble declining balanceYearDepreciationFractionDepreciationFractionDepreciationFraction112000.06722500.1252666.6660.148212000.06721000.1172311.1110.128312000.06719500.1082002.9620.111412000.06718000.1001735.9010.096512000.06716500.0921504.4470.084612000.06715000.0831303.8540.072712000.06713500.0751130.0070.063812000.06712000.067979.3390.054912000.06710500.058848.7610.0471012000.0679000.050735.5920.0411112000.0677500.042637.5130.0351212000.0676000.033552.5120.0311312000.0674500.025478.8430.0271412000.0673000.017414.9970.0231512000.0671500.008697.4860.039Total18,000118,000118,0001

3.2 Economic evaluation of multi-stage membrane processes

Economic analysis of the flowsheet was carried out only for the case that produced > 90% He purity with 99% recovery. Techno-economic analysis (TEA) reported here incorporates capital cost estimates with relatively high contingency factors, reflecting a higher risk investment of first-of-a-kind (FOAK) facility. Aspen Process Economic Analyzer (APEA) v.10 was used to develop a conceptual process model for calculating the purchased cost of equipment (PCE) from equipment sizing and costing data. The economic model considered 35% company tax rate, 10% internal rate of return (IRR), and 15% project contingency. The total project capital cost was considered to depreciate, via straight-line depreciation method, over the 10 years of the economic life of the facilities. Membrane module cost considered $50/m2 for all stages during capital investment and replacement cost considered $10/m2 with 5 years membrane lifetime. This skid cost includes the cost of membrane modules, module housings, connecting valves, supporting structure, and instrumentation. The economic model was used to calculate minimum helium production price to reach a breakeven point for a 10% internal rate of return (IRR) for all selected design concepts of helium upgrading plant (i.e. > 90% purity). The Economic evaluation was undertaken using an NPV (Net Present Value) method based on the amount of helium produced (thousand cubic feet, MSCF). The NPV calculation does not include high-pressure final compression of helium product to meet transport pressure specification.

Table 4 shows the results of NPV value, IRR and helium production price ($/ thousand cubic feet) for selected flowsheets of upgraded helium (> 90% purity). It is seen that concept-C-2 have maximum NPV of $ 2.122 billion at 14 bar feed pressure with minimum helium production price $ 7.72/MSCF. Membrane process design concept-C-1 and concept-A-1 can produce helium with the second ($8.89/MSCF) and third ($9.04/MSCF) most low price from natural gas where 1% He feed concentration respectively, which is much lower than current US crude helium (50-70%) auction price $119.31/MSCF (2018). Overall, a combination of high permeability membrane in the initial stage and high selective membrane in the last stage shows low cost-optimal and efficient process.

Table 4. Helium production price ($/thousand cubic feet) from natural gas with IRR, NPV value for different design concepts.

Membrane process conceptsFeed pressure (bar)PurityRecoveryTotal Power (kW)Total Area (m2)US. $/MS C FIRRNPV (US.$ billions)Concept-A- 125> 90%99%4575.81.23E + 059.04118.89%2.107Concept-B25> 90%99%4396.69.81E + 0520.1664.55%1.984Concept-C-113> 90%99%3127.71.93E + 058.89115.87%2.109Concept-C-214> 90%99%3413.59.54E + 047.72130.00%2.122Concept-D13> 90%99%2972.41.46E + 0625.453.94%1.927

Which depreciation method is used at least according to the GAAP?

Which method of depreciation is accepted by GAAP?

Which of the following depreciation methods is the least used according to GAAP quizlet?

Does GAAP prefer straight