Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation

Подождите немного. Документ загружается.

Engineering Economics 737

d - -- (9-18)

The various components of a plant such as equipment, buildings, and

improvements are characterized by projected lifetimes. During this

period, each item depreciates from its initial investment cost, CFC, to a

salvage value, S, over the period of n years of its projected lifetime. At

the end of any particular year, k, the depreciated value or book value,

Vk, is:

Vk -- CFC -- Z

(9-19)

where Dj is the annual depreciation charge for year j. Substituting Equa-

tion 9-17 into Equation 9-19 gives

Vk -- CFC -- Z (CvC --

S)dj

= CFC -- (CFc -- S)Z dj

(9-20)

For the straight line depreciation procedure,

k k 1

Zdj-Zd-kd--

I 1 n

(9-21)

and

V k - CFc (CFc -- S) (9-22)

Double Declining Balance (DDB) Depreciation

Equipment and complete plants depreciate and lose value more rap-

idly in the early stages of life. The depreciation based upon the declin-

ing book value balance can be expressed as:

Dj- dj.Vj_, (9-23)

The rate of depreciation, dj, is the same for each year, j; however, the

depreciation charges decrease each year because the book value

decreases each year. For a declining balance method, the depreciation

738 Fortran Programs for Chemical Process Design

rate of decline is up to twice, but no more than twice the straight line

rate. This is given by:

dj - d -- (9-24)

Capitalized Cost

The capitalized cost, C K, of a piece of equipment of a fixed capital

cost, Cvc, having a finite life of n years and an annual interest rate, i, is

defined by

(C K - Cvc)(1 + i) ~ : C K - S

(9-25)

where S = salvage or scrap value

C K is in excess of CFc by an amount, which, when compounded at an

annual interest rate, i, for n years, will have a future worth of C K less

the salvage or scrap value, S. If the renewal cost of the equipment and

the interest rate are constants at (CFc- S) and i, then CK is the amount

of the capital required to replace the equipment in perpetuity.

Rearranging Equation 9-25 gives

{ s ]E 1

CK -- Cvc- (l+i-------~ (l+i) ~-1 (9-26)

C K = (CFc- S.fd)f K (9-27)

where fd = discount factor

fK = the capitalized cost factor = (1

+ i)n/[(1

+ i) ~- 1]

The Average Rate Of Return (ARR)

The average rate of return (ARR) method averages out the cash flow

over the life of the project. This is defined by

ARR average cash flow

- x 100 (9-28)

original investment

The higher the percentage value of the ARR, the better the profitability

of the project.

Engineering Economics 739

Present Value Ratio (Present Worth Ratio)

A commonly used profitability index in conjunction with the NPV

method shows how closely a project has met the criterion of economic

performance. This index is known as the present value ratio (PVR) or

present worth ratio (PWR), and is defined as

Present present value of all positive cash flows

value present value of all negative cash flows (9-29)

The present value ratio (PVR) gives an indication of how much the

project makes relative to the investment. A ratio of 1.0 shows that the

income just matches the expected income from capital invested for a

given interest rate. A ratio of less than 1.0 indicates that the income

does not come up to the minimum expectations. A ratio of more than

1.0 means that the project exceeds the minimum expectations.

Profitability

A project is profitable if its earnings are greater than the cost of capi-

tal. In addition, the larger the additional earnings, the more profitable

the venture, and the greater the justification for putting the capital at

risk. Therefore, a profitability estimate attempts to quantify the risk taken.

The methods used to assess profitability are:

1. return on investment (ROI)

2. payback period (PB)

3. net present value (NPV)

4. discounted cash flow rate of return (DCFRR)

5. net return rate (NRR)

6. equivalent maximum investment period (EMIP)

7. interest recovery period (IRP)

8. rate of return on depreciated investment

9. rate of return on average investment

10. capitalized cost

11. average rate of return (ARR)

12. present value ratio (PVR)

Abrams [11] has listed other methods for assessing a project's

profitability.

740

Fortran Programs for Chemical Process Design

Economic Analysis

Computer programs have been developed to estimate the net

present value (NPV), present value ratio (PVR), net return rate (NRR),

average rate of return (ARR), payback period (PBP) and discounted

cash flow rate of return (DCFRR). These analyses are done for a given

cash flow over the operating life of a project. These programs can be

incorporated as subroutines into larger programs, if required. In addi-

tion, a detailed computer program has been developed to review an eco-

nomic project using Kirkpatrick's [ 12] input data. These data are defined

as follows:

Annual Revenue,

$. The money received (sales minus the cost of

sales) for one-year production from the plant. This is assumed as being

constant for life of the project.

Annual Operating Cost,

$. The cost of raw materials, labor, utili-

ties, administration, insurance, and royalties, etc., but does not include

debt service payments.

Depreciating Base,

$. The capitalized cost of the facility and less

non-depreciable items, such as land and inventory. No salvage is sub-

tracted because double declining balance depreciation is used.

Project

Life, Years. The length of time for which the facility is to be

operated. It is also the term of the loan and the depreciation time.

Initial Loan,

$. The capitalized cost minus owner equity.

Payments/Year.

The number of payments on the loan per year:

1-annually, 2-biannually, 4-quarterly, and 12-monthly.

Periodic Interest Rate.

The annual interest rate divided by the

payments per year. For a 10 percent annual interest rate and monthly

repayments, this is 0.10/12.

Investment Tax Credit,

$. The percentage of the initial investment

allowed as a tax credit in the year the investment is made.

Tax

Rate.

The percentage tax that must be paid on the project's pre-

tax income. This rate is assumed to remain constant during the life of

the project.

Debt Service/Period, $. The amount of each loan payment, that is:

Engineering Economics

741

I Annual interest ]

(Loan) Payments per year

1-II+

/ye r, xPayments /

Annual interest /

year

Payments per year

The Salvage Value (or Scrap

Value). The projected salvage value

of equipment at the end of the project lifetime is that portion of the fixed

capital that cannot be depreciated.

Land Value. Land is not considered depreciable. It can be used

indefinitely for succeeding projects on a specific site, or it can be sold.

Working capital. The capital invested in various necessary invento-

ried items, which are completely recoverable at any time.

The calculations for every year of the project life are:

1. Calculate the depreciation as double declining (that is, twice the

depreciation based divided by project life), and subtract it from

the depreciation base.

2. Calculate the yearly interest and principal of the debt service

payments.

3. Subtract from the revenue, the operating cost, annual deprecia-

tion, and interest.

4. Subtract from positive pre-tax income, until no negative pre-tax

income remains, if the pre-tax income is negative or has been

negative in a prior year.

5. Calculate the income tax due at the given rate, and apply the

investment tax credit against the income tax due until the credit

is exhausted, if after Step 4, the pre-tax income is still positive.

6. Deduct the income tax remaining after Step 5 from the pre-tax

income, leaving the after-tax income.

7. Add the after-tax income to the depreciation for the year, yield-

ing the cash flow.

8. Determine the loan balance at the end of the year.

9. Determine the amount of unused depreciation after the last year

of the project's life. Because double declining depreciation does

not totally exhaust the depreciation account, the unused

depreciaton should be added to the cash flow of the last year as

salvage value recovered at the termination of the project under

consideration.

742

Fortran Programs for Chemical Process Design

1 0. Calculate the net present value, NPV, for a known discount rate.

11. Determine the present value ratio, PVR.

1 2. Calculate the net return rate, NRR.

13. Calculate the average rate of return, ARR.

14. Estimate the payback period, PBP.

For a given discount rate, calculate the discount factor during the

operating life of the project. Multiply the discount factor by the cash

flow and obtain the net present value and the net return rate. Valle-Riesta

[8] has listed alternative methods of calculating cash flow, as shown in

Table 9-6.

Methods 1 and 2 in Table 9-6 give identical results.

Table 9-6

Method of Computing Cash Flow from Project

Method 1

1. Cost of Manufacture

(COM) includes depreciation

2. General expenses

3. Total operating expense

(3) = (1) + (2)

4. Total sales

5. Profit before taxes

6. Income taxes

(6) = 1/2 (5)

7. Profit after tax

(7) = (5) - (6) = 1/2 (5)

8. Depreciation

9. Continuous cash flow from project

(9)=(7)+(8)

Method 2

1. Cost of Manufacture

(COM) includes depreciation

2. Depreciation

3. COM less depreciation

(3)+(1)-(2)

4. General expenses

5. Out of pocket expenditure

6. Total sales

7. Cash flow before taxes

(7)=(6)-(5)

8. Profit before taxes

(8) = (7) - (2)

9. Income tax

(9) = 1/2 (8)

10. Profit after tax

(10) = (8) - (9) = 1/2 (8)

11. Continuous cash flow from project

(11)=(10)+(2)

Source: Valle-Riesta [81

Engineering Economics

743

Cash flows into a project can be time-dependent, in which the cash

flows occur in a continuous process rather than on a one-time basis.

Figure 9-4 illustrates a continuous cash flow diagram. Continuous cash

flows into the project are from sales revenues, and cash flows out are

for out-of-pocket expenses. The difference between the incoming and

outgoing cash flow is the net cash flow generated by the project. The

combined net cash flow generated by all the company's projects is re-

duced by the income tax payment to yield the net continuous cash flow.

Expressing the definition of profit with the continuous cash flow results

in the following:

Profit before taxes - continuous cash flow- depreciation before taxes

Profit after taxes - continuous cash flow - depreciation after taxes

Cash flow in (from sales)

Project

Cash flow out

(out-of-pocket cash expenses)

Net cash flow generated by project

V..Net cash flow from other projects

,.,

Income tax

Cash flow (after taxes ) to corporation

Corporation

Figure 9-4. A continuous cash flow diagram. Source: Valle-Riestra [8].

744

Fortran Programs for Chemical Process Design

It is useful to keep in mind that:

Cash flow ~: profit

Allen [9] has provided a systematic procedure for assessing investment

proposals for new plant and equipment, exploiting new technology,

and replacing uneconomic, inefficient, and obsolete plants, process,

and equipment.

Inflation

A decrease in the average purchasing value of currency is referred to

as inflation. An inflation rate of 15 percent, for example, means that the

average cost of goods and services will increase 15 percent in one year.

The result is that commencing construction one year early will reduce

the amount of money expended by 15 percent. Since the 1980s, infla-

tion has been considered in most economic project evaluations.

When inflation is used in economic evaluations, all items except

interest on a loan and depreciation are considered to increase in value at

the same rate as inflation. Generally, interest is set at the time a loan is

negotiated and does not change with inflation. In addition, depreciation

depends on the method (for example, straight line or double declining

balance) used and the capital charges incurred before start-up are not

affected by the inflation rate after start-up. Determining the profitabil-

ity of a project (for example, NPV), the interest rate is assumed to be

greater than the inflation rate. Money may be lost on the project while

the net present value indicates the opposite, if the inflation rate is greater

than the interest rate. There are cases in which the interest rate is set at

the expected inflation rate plus a real expected interest rate. The real

expected interest rate is the interest rate that is used to calculate the net

present value when there is no inflation. Alternatively, the present value

is calculated using the inflation rate as the interest rate, the net present

value is then determined using the real expected interest rate.

CAPITAL COST ESTIMATION

Capital cost estimation is an essential part of investment appraisal.

Many types of capital cost estimates are made, ranging from the order

of magnitude to detailed estimates requiring the collection of accurate

technical data. The American Association of Cost Engineers defined

five types of cost estimates as follows:

Engineering Economics 745

Order-of-magnitude estimate (ratio estimate).

Approximate method

based on cost data for previous similar types of plant. Probable error

within 10 to 50 percent.

Study estimate (factored estimate).

Better than order-of-magnitude

but requires knowledge of major items of equipment. Used for feasibil-

ity surveys. Probable error up to 30 percent.

Preliminary estimate (budget authorization estimate).

detailed information required than for study estimate. Probable error up

to 20 percent.

Definitive estimate (project control estimate).

Based on consider-

able data obtained before preparing completed drawings and specifica-

tions. Probable error within 10 percent.

Detailed estimate (firm or contractor's estimate).

Requires com-

pleted drawings and specifications. Probable error within 10 percent.

Process plant designs start from preliminary designs based on

approximate technical data, calculations, and cost data to final designs

that require detailed and accurate data, calculations, and quotations. Cost

estimates of a proposed plant are continuously carried out during the

development of a process from the laboratory to construction.

The total capital cost, CTc, of a project consists of the fixed capital

cost, CFc, plus the working capital, Cwc, plus the cost of land and any

other non-depreciable assets, C L. This is given by

CTc = CFc + Cwc + C L (9-30)

The fixed capital cost, CFc, is the capital required to provide all the

depreciable facilities. CFc may be divided into two classes known as the

battery limits and auxiliary facilities. The boundary of battery limits

includes all manufacturing and processing equipment. The auxiliary

facilities are the storage areas, administration offices, utilities and other

essential and non-essential supporting facilities.

Equipment Cost Estimations By Capacity Ratio Exponents

It is often necessary to calculate the cost of a piece of equipment

when there are no available cost data for the particular size of capacity.

If the cost of a piece of equipment or plant size or capacity, Q~, is C~, the

cost C2 of a similar piece of equipment or plant size or capacity,

Q2, can

be calculated from the equation

746

Fortran Programs for Chemical Process Design

/ / n'

C2 - Cl -~1

(9-31)

where

the value, m, depends on the type of equipment or plant. The value of

the index, m, is generally taken as 0.6 [13], the well known six-tenths

rule. This value can be used to get a rough estimate of the capital cost, if

there are insufficient data to calculate the index for the particular size of

equipment required. Table 9-7 lists values of m for various types of

equipment. Cost indexes should be used to bring the cost data to a

desired year. A cost index is a value for a given point in time showing

the cost at that time relative to a certain base time. If the cost at some

time in the past is known, the equipment cost at the present time can be

determined from the equation

Present c~ - previ~ c~ present index )previous index

(9-32)

Cost indexes are used to give a general estimate, but no index can

account for all the factors. Many different types of cost indexes are

Table 9-7

Typical Exponents for Equipment Cost vs Capacity

Equipment Exponent (m)

Reciprocating compressor

Turboblowers compressor

Electric motors

Evaporators

Heat exchangers

Piping

Pumps

Rectangular tanks

Spherical tanks

Towers, constant diameter

Towers, constant height

0.75

0.5

0.8

0.5

0.65 to 0.95

0.7 to 0.9

0.5

0.7

1.0

Source: Institution of Chemical Engineers [15].