Lecture 33 :
Economics Economics of Chemical Plants ± Cost Estimation Estimation
The purpose of building chemical processes is to make money ± Smith R, Chemical Chemical Process Design Design & Integration Integration 2005. An
acceptable plant design must present a process that is capable of operating under conditions which will yield a profit ± Plant Design Design and Economics Economics for Chemical Chemical Engineers, Engineers, Peters M & Timmerhaus Timmerhaus K., 1991 Energy In
Raw Materials + Other Feeds
CHEMICAL PROCESS
Products + Wastes
Energy Out
Industry needs to make money to survive !!!
After a flowsheet flowsheet and a preliminary technical package have been prepared, prepared, the next step is to conduct the economic analysis to ensure the venture is a profitable one. This analysis could be done in stages.
Stages of Process Design
Stages of Economics Economic s Analysis
Chemical Route Selection
Economic Potential 1 : Revenue Revenue ± Raw Materi Material al
Conceptual Design (Material & Energy Balance after process optimisation)
Economic Potential 2 : Revenu Revenue e ± Raw Mate Materia riall - Utiliti Utilities es
Detail Equipment Design
Economic Economic Potentia Potentiall 3 - n : Revenu Revenue e ± Raw Mate Materia riall ± Utiliti Utilities es ± Equipme Equipment nt Cost Cost
Site Design
Overall Economics incorporating Economic Potential Potential 3 - n, Site cost and Operatin Operating g Cost.
If at any stage, the analysis results in losses, there are 3 options to consider; 1. 2. 3.
Terminate the project Look for better process alternatives Increase the product price
Method for Cost Estimation of Capital Investments. The total investment required for a new design can be divided into 5 parts; Battery Li Limit mits In Investmen ment Manufacturing Manufacturing area of the process plus the building and structure str ucture to house it
Utility Investment Utility plant including onsite power generation, steam generation and distribution, process & cooling water, effluent treatment, refrigeration, compressed air and inert gas supply.
Off site Investment Auxilliary buildings buildings eg. offices, roads, railroads, fire protection system, system, communication communication system, waste disposal, storage, plant vehicles, loading and weighing devices.
Engineering Fees Fees paid to consultants/contractors, survey fees & property cost.
Working Capital Raw materials materials cost for start up, operation & inventories, transportation, transportation, payroll and current current account
1. Batt Batter ery y Limits Limits Inve Invest stmen mentt The battery limit investment covers the purchase of individual plant items and their installations to form a working process. Equipment costs may be obtained from vendors or published cost date. Care should be taken to ensure that t he cost is based on delivered cost.
The cost of specific item depends on size, materials of construction, design pressure and temperature. temperature. Normally the cost data is presented in the form ;
«Q» C E ! C B ¬ ¼ Q B ½
M
The cost estimate then needs to be brought up to date using cost indexes.
C 1 C 2
CE ± estimate cost for equipment equipment with capacity Q CB ± known known base base cost for for equipment with capacity QB
!
IND EX 1 IND EX 2
C1 ± Equipment Equipment cost in Year 1 C2 ± Equipment Equipment cost in Year 2 INDEX 1 - cost index in year 1
M - consta constant nt depe dependi nding ng on equipment type.
INDEX INDEX 2 - cost index index in year year 2
Typically used indices to enable the cost projection into a different year are ;
Chemical Engineering (CE) Indexes : 1957-59 = 100, Jan 2000 = 435.8 Marshall and Swift : 1926 = 100 The CE index is particularly useful and available for equipment covering heat exchangers, pipes, valves & fittings, Process Instruments, Pumps & compressors, Electrical equipments, structural support & miscellanous. Highly recommended for cost estimation calculation. Published in Chemical Engineering magazine
Engineering News ± Record Construction Index shows the variation in labour rates and material costs for industrial construction.
Nelson Farrar Indexes (for refinery) Published in Oil and Gas Journal.
Information on the various cost indexes up to the year 1990 from 1975 is available in ³Plant Design and Economics for Chemical Engineers ± 5th Edition´ by Peters and Timmerhaus 2004 pg 238.
The capital cost estimates for equipment has to also take into consideration of different materials and operating conditions. This is done through the use of correction factor.
Material of construction ( f m) Has a significant influence on the capital cost calculation. Typical factors used for pressure vessel : Carbon Steel ± 1, Low Grade Stainless Steel ± 2.1, High Grade Stainless Steel ± 3.2, Nickel ± 5.4 & Titanium ± 7.7
Operational Pressure ( f P ) Higher pressure also influences the capital cost through the thickness of the material used. Typical factors used for equipment pressure: 0.01 bar abs ± 2, 0.1 bar abs ± 1.3, 0.5 to 7 bar absolute ± 1.0, 50 bar abs ± 1.5 & 100 bar abs ± 1.9
Operational Temperature ( f T ) Higher temperature influences the capital cost through the reduced allowable stress for the materials. Typical factors used for equipment temperature: 0 ± 100 C ± 1, 300 C ± 1.6 & 500 C ± 2.1 Data taken from Chemical Process Design & Integration, Smith R 2005
Taken into consideration of the factors; M
C E
«Q» C B ¬ ¼ f m f P f T Q B ½
In the event of cost data for the particular size or capacity designed for a plant not available, the sixth-tenths factor rule could be used to estimate the cost for the equipment.
The equation takes the form; Cost of equipment size a = (cost of equipment size b) . X0.6
where X represents the factor for scale up or scale down between the equipment with size a against the equipment with size b. The exponent factor of 0.6 is a simplification. The more realistic approximation value for the factor is given in the next page. Eg.
the purchased cost of a 0.2 m3 glass lined jacket reactor was $10,000 in 1991. Estimate the purchased cost of similar reactor of 1.2 m3 size in 1996. The Chem Eng Plant Cost index is 361 in 1991 and is 382 in 1996. Given
Cost of reactor in 1996 = ($10,000) (382 / 361) . (1.2 / 0.2) 0.54 = $ 27,850 The exponent factor is available in the table shown in next page.
In addition to the purchased cost of the equipment, investment is required to install the equipments which include;
Cost of installation Piping & valves Control systems Foundation Structures Insulation Fire proofing Electrical Painting Contingency The total cost of the installed battery limits equipment will normally be 2 to 4 times the purchased cost of the equipments. Lang
H J, Cost Relationship in Preliminary Cost Estimation, Chem Eng 54 : 117 (1947) Hand W E, From Flowsheet to Cost Estimates, Petrol Refiner ,37, 331 (1958)
2. Utility Investment The cost of utilities in considered from their sources within the site to the battery limits of the chemical process served. 3. Off-site Investment The cost of utilities and off-sites (sometime referred to as services together) ranges typically from 20 to 40 % of the total installed cost of the battery lim it plant. The larger plant site will have a larger fraction and vice versa. Baumann
HC, Estimating Cost for Process Auxilliaries. Chem Eng Prog, 51 : 45
4. Working Capital The cost that has to be paid to make the process into productive operation. For an estimate, the following could be taken; 30 % of annual sales 15 % of total capital investment
The total capital cost of the process, services and working capital can be obtained by applying multiplying factors or installation factors to the purchased cost of the individual items of equipment
C F ! § f i C E ,i i Fixed capital cost for complete System
Installation factor for equipment i
Cost of equipment i
Data on typical factors for capital cost based on delivered equipment cost could be found in ;
Chemical Process Design & Integration, Smith R, pg 21 (2005) Plant Design & Economics for Chemical Engineers 5th Ed., Peters & Timmerhaus, pg 251 (2004) For the two types of processes namely solid and liquid, the percentage of total capital investment when compared to the total cost based on on-site delivery equipment cost are;
Solid Processing Fluid Processing
Smith R 440 % 580 %
Peters & Timmerhaus 455% 569 %
Example of Factors for Capital Cost . Item
Fluid Processing Plant
Solid Processing Plant
Direct Costs Purchased Equipment Delivered
100
100
Equipment Installation
40
50
Piping Installed
70
20
Instrument. & Control
20
10
Electrical
10
10
Utilities
50
20
Off sites
20
20
Building (including services)
20
30
Site Preparation
10
10
340
270
100
80
40
30
480
380
70
60
580
440
Total
Capital Cost (Installed)
Indirect
Costs
Design Eng & Construction Contingency Total
Fixed Capital
Working Capital
Total Capital Investment/cost
Example; Prepare a study estimate of the fixed capital investment for a solid fluid processing plant if the delivered equipment cost is $100,000. Use the cost factor outlined in the Table shown earlier. The process has a high degree of automatic controls and mainly outdoor operation.
Method for Revenue Estimation. The revenue generated by plant operation could be estimated from the sale of the product / byproducts produced by the plant. Annual sales revenue = production capacity X price per production unit In conducting an economic analysis of a process, the engineer must establish production rates, as a fraction or percentage of the design capacity for each year of process operation. It is common to use 50% for the first year of operation due to the uncertainty of the plant commissioning and start up. From then on, the full capacity can be used for the revenue calculation. As for the plant operation time, taking into account of the plant downtime normally of about 10-20%, it is typical to use 300 to 330 days per year for operation time. Product prices are best determine by a market study.
Total Product Cost Estimation. The total product cost comprised of all the cost for operating the plant, selling the products, recovering the capital investment and contributing to corporate functions such as management and research and development. They can be divided into 2 categories; i. Manufacturing costs Variable production cost ± raw materials (incl. transportation), labour directly applied to the manufacturing operation, utilities, plant maintenance, operating supplies, laboratory supplies, royalty, catalyst and solvents. Only applies when the plant is under operation. Fixed charges ± depreciation, property taxes, insurance, loan interest and rent. Applies independent of plant operation. Plant Overhead Cost ± hospital and medical services, general plant maintenance and overhead, safety services, payroll overhead and benefits, warehouse and storage facilities etc.
ii. General Expenses Administrative costs ± expenses connected with executive and administrative activities. Can be estimated as 15 ± 20 % of operating labour. Distribution and Marketing Costs ± expenses incurred in the process of distributing and selling the products. Eg. sales offices expenses, marketing & advertising, technical support etc. The range used for many chemical plant is 2 ± 20% fo total product cost with the higher figure applies to new or specialised product while the lower figure applies to large volume products. Research and Development Costs ± expenses for undertaking the R&D work which could be estimated at 5% of total product cost.
Conclusion. In this lecture, we have look at how estimation can be made for cost and revenue which are important for economic analysis for chemical process plant. Next we will be looking at the economic analysis which involve the cash flow and the elements that have impact on it.
Lecture 3434-35 : Economics
of Chemical Plants ± Some Fundamental Economics
In doing the analysis of the cash flow of a chemical plant project, a number of economics fundamentals have to be understood.
Profit & Cash Flow. Gross Profit : It is defined as the product sales revenue minus the total product cost. Gross Profit = Sales Product Cost depreciation (in the respective operation year) Net Profit : It is the net earnings after income tax. Net Profit = [Sales Product Cost depreciation (in the respective operation year) ] (1- tax rate) Cash Flow: It is the net profit earned plus the depreciation for the respective years of operation. Cash Flow = [Sales Product Cost depreciation (in the respective operation year) ] (1- tax rate) + depreciation (in the respective operation year)
The cash flow is useful when performing the economic analysis for the venture overall where the pay back, return on investment or NPV are used.
Example Given the annual production cost of a plant operating at 70% capacity is $280,000. The sum of annual fixed charges, overhead cost and general expenses is $200,000 and does not change with production rate. Total annual sales is $560,000 and product sells at $4/kg. i. What is the breakeven point in kgs of product sell per year? ii. Determine the gross annual profit and net annual profit at 100 percent capacity if the income tax rate is 35% of gross profit. i. The breakeven point is when total annual sales is equal to total annual product cost.
Direct Production Cost / kg = Variable production cost / kg of products produced = $280,000 / ($560,000 / $4/kg) = $ 2 per kg product. Let Y = products produced / yr. Kg product required for breakeven (Y) = Annual fixed charges + ($2 x Y) = Sale Price x Y Kg product required for breakeven (Y) = $200,000 + ($2 x Y) = $4 x Y Kg product required for breakeven (Y) = 100,000 Actual plant capacity = [Annual Sales / Cost per kg product ] / 0.7 (capacity) = 200,00 kg per yr. Therefore in order to break even the plant has to operate at least at 50% capacity in order to break even
Example Given the annual production cost of a plant operating at 70% capacity is $280,000. The sum of annual fixed charges, overhead cost and general expenses is $200,000 and does not change with production rate. Total annual sales is $560,000 and product sells at $4/kg. i. What is the breakeven point in kgs of product sell per year? ii. Determine the gross annual profit and net annual profit at 100 percent capacity if the income tax rate is 35% of gross profit. ii. The gross annual profit and net annual profit at 100% capacity.
Gross Annual profit = Total sales - Total annual cost = ($4 x 200,000) - ( 200,000 + $2 x 200,000) = $ 200,000 Net Annual profit = Gross Profit ( 1 ± income tax rate) = $200,000 - ( 1 ± 0.35 ) = $ 130,000
Interest Rate. Interest rate is the cost of borrowing money or the earnings on money loaned.
Simple Interest : In economic terminology, the amount of capital on which interest is paid is designated as the principal, and rate of interest is defined as the amount of interest earned by a unit of principal in a unit of time (normally a year). If an interest rate of 4% is given over a year to a capital of RM1000, then over 4 years;
Interest
= Interest rate X No. of Years X Principal = 0.04 X 4 years X 1000 = RM 160
Compound Interest : Interest, like all negotiable capital, has a time value. Compound interest takes into account of this by stipulating that interest is due regularly at the end of each interest period. If payment is not made, the amount due is added to the principal, and the interest is charged on this converted principal during the following time unit. Therefore, the total amount of principal plus compound interest (S) due after N interest periods is; S = Principal (1 + i )N
Annuities. An annuity is a series of equal payments occurring at equal time intervals. Payment of this type can be used to
pay off a debt, accumulate a desired amount of capital or receive a lump sum of capital that is due in periodic installments as in some life insurance plans. The common type of annuity involves payments which occur at the end of each interest period. By definition, the amount of the annuity (S) is the sum of all accumulated amounts from each payment (R);
S = R (1+i)N-1 + R (1+i)N-2 + R (1+i)N-3 + . + R (1+i) + R S = R (1 + i )N - 1
i interest rate
i Present worth of an annuity (P) is defined as the principal which would have to be invested at the present time at compound interest rate i to yield a total amount at the end of the annuity term equal to the amount of the annuity.
P = R (1 + i )N - 1 i (1 + i )N
Cost of Capital There are several sources for raising capital such as loans, bonds, stocks or corporate funds. The corporate funds, primarily from undistributed profits and depreciation accumulations are usually a major source of capital for established businesses. Borrowed funds are often used to supply all or part of corporate investments. In the preliminary design of a project, either of the 2 methods below is assumed;
1. No interest are included in calculation assuming that the capital comes from internal funds 2. Interest is charged on the total capital investment. As the design proceed to the final stages, the actual sources of new capital should be considered. The role of
interest rate in the economic analysis has to be clearly understood. The effect on Income Tax. Interest on loans and bonds can be considered as costs when determining the income tax. If annual income tax rate is 35%, for every $1 spent for interest on loans or bonds has a true cost after tax of only $ 0.65 . Normally, new businesses rely on external financing while successful/established businesses rely on mostly their internal funds.
Loan Payment. To calculate the payment amount for the loan, the following formula can be used, N « j 1 » P 0 ¬1 i § 1 i ¼ 1 ½ L ! N
j 1 1 i § 1
L ± payment amount per period, P 0 ± Loan Principal, N ± No. of installments period i ± interest rate, j ± the month of payment
Example : Present the spreadsheet for the following case: A loan of $100,000 at a nominal interest rate of 10% per year is made for a repayment period of 10 years. Determine the constant payment per month, the interest and principal paid each month and the remaining unpaid principal at the end of each month. The equation required to calculate: Constant payment
N « j 1 » P 0 ¬1 i § 1 i ¼ 1 ½ L ! N
§ 1 i
j 1
1
Interest paid
Principal paid
j ± month of payment m ± month of principal payment
I j ! i P j 1
« p j ! i ¬ P 0
j 1
§ m !1
j 1
Remaining unpaid principal
p j 1 ! P 0 § pm m !1
»
pm ¼
½
Example : Present the spreadsheet for the following case: A loan of $100,000 at a nominal interest rate of 10% per year is made for a repayment period of 10 years. Determine the constant payment per month, the interest and principal paid each month and the remaining unpaid principal at the end of each month.
Time Value of Money Money can be used to earn money by investment eg savings account, bonds or projects. Therefore, an initial amount of money that is invested increases in value with time. The effect is known as the time value of money. The earning power of money can be included in the analysis of business profitability. The calculation for time value of money has been discussed earlier under interest. S = Principal (1 + i )N
Compounding factor
where S will be the future worth of money at the time period calculated. Reciprocally, the time value for money could be calculated backward using the equation S = Principal (1 + i ) -N
Discounting factor
Therefore, the present worth of money could be calculated from a given future worth of money.
Minimum Acceptable Rate of Return (M ARR) A commonly used profitability standard. It is defined as the rate of earning that must be achieved by an
investment in order for it to be acceptable to the investor. It is expressed as fraction per year or percentage per year.
Normally the rate taken as the M ARR is based on the highest rate of earning on safe investment such as corporate bonds, government bonds and loans. Most of the time the rate is added with few more percentage to reflect risk on the investment put into the process plant. In simple term, it can be calculated based on the annual net profit divided by the total capital investment. Investment
type
Level of Risk
MARR recommended (%)
1.
Safe Corporate Investment
Safe
4-8
2.
New capacity with established corporate market position
Low
8-16
3.
New product entering into established market or new process technology
Medium
16-24
4.
New product or process in a new application
High
24-32
5.
Everything new, high R&D and marketing effort
Very High
32-48+
Income Tax. There are several form of tax that needs to be accounted for in performing the economic analysis. Taxable Income Tax that is paid based on gross earning / revenue after deducting all expenses (total product cost). Dividends to shareholders or loan repayments are not counted in the gross earning which means that they are not tax exempted. Capital Gain Tax Tax that is levied on profits made from the sale of capital assets such as land, buildings or equipments. For depreciable asset, the profit for selling the asset is calculated by the sale value minus the cost of selling, cost of acquisition less the amount of depreciation that has already been charged. Non Income Taxes Tax which include property and excise taxes. Tax of this type are referred to as direct since they must be paid directly by particular business and cannot be passed on as such to the consumer. Property taxes are normally charged on annual basis and the amount vary to within 1-4 percent of the assessed valuation. Excise taxes include charges for import custom duties, transfer of stacks and bonds etc.
Fixed Charges Fixed charges could be included in the total product cost i.e., there are tax exempted. They include the depreciation, property taxes and insurance.
Depreciation. Concept of depreciation is based on the fact that asset deteriorate with time thus its value as well. In general, all property with a limited useful life of more than a year that is used in a trade or business, or held for the production of income, is depreciable. Depreciation is a charge to the revenues resulting from an investment in real property and it allows for recovery of the investment through tax deductions. Amortization is an alternate word used but it refers to more restricted meaning in tax policy. Other useful terms : Current Value the value of the asset in its condition at the time of valuation. Book Value the difference between the original cost of a property and all the depreciation charged up to a time. These are important as they are included in the values of all assets of corporation. Salvage value the net amount of money obtainable from the sale of used property over and above any charges involved in removal and sale. The term implies that the property can be of further service. However, if the property could no longer be used, i t can be sold for material recovery and the income obtained is termed as Scrap Value. Service Life - the period over which the use of a property is economically feasible. Recovery Period - the period over which depreciation is charged as established under the tax codes.
M ethod for Calculating Depreciation. Depreciation resulted in a reduction in income tax payable in the years in which it is charged. The total amount of depreciation that can be charged is fixed and equal to the investment in depreciable property. Because of the time value of money, it is in the interest of the tax payer to depreciate property as rapidly as possible to allow for tax savings to be gained earlier. Straight Line method The property value is assumed to decrease linearly with time over the recovery period.
d !
V n
V ± Asset/Property Value, n ± the no. of years for recovery period
Modified Accelerated Cost Recovery System (MACRS) Used for most income tax purposes. M ethod is based on the classical double declining balance method but with no salvage or scrap value allowed. The method allows a depreciation charge in each year of the recovery period that is twice the average rate of recovery on the remaining undepreciated balance for the full recovery period. Eg calculation assume a 5 year recover period. 1st year : d = 2 x (1 / recovery period) = 2 x (1/5) = 40% 2nd year: d = 2 x (1-0.4) / 5 = 24 % 3rd year : d = 2 x (1 0.4 - 0.24) / 5 = 14.4 % 4th year : d = 2 x (1 -0.4 0.24 0.144) = 8.64 % 5th year : d = 2 x (1 0.4 0.24 0.144 0.0864) / 5 = 5.18 %
Prop erty Taxes. As exp lained ear lier wher e t he ta x is impos ed o n t he va lue o f t he prop erty . The ca lculat io n o f t he prop erty va lue ta kes into a cco unt o f t he depr eciat io n.
Ins ura nce. The a nnua l ins ura nce costs f or or dinary industr ia l pro jects ar e appro ximat ely 1 p er cent o f t he fixed cap ita l invest ment . I t is importa nt to ens ur e t he eco no mic op erat io n o f t he p la nt is prot ect ed a ga inst emer gencies or unf or es een develop ments . Ins ura nce ar e ta ken due to lega l r espo ns ibility to prot ect t he bus iness prop erty a nd emp loy ees a ga inst a ccidents , p la nt ha zar ds , t hef t et c. Also , pro duct lia bility ins ura nce need to be ta ken to prot ect t he corporat io n f ro m lia bility s uit by custo mers a ffect ed by t he pro duct t hro ugh unf or es een cir cumsta nces .
Conclusion In this lecture, we have covered the elements that have impact on the cash flow. The next lecture will touch on the cash flow analysis.
Lecture 36 :
Economics of Chemical Plants ± Cash Flow/Profitability Analysis
After the chemical plant has been commissioned and is producing product , the revenue earned must pay for both fixed cost and variable costs. A profitability analysis has to be conducted to assess the potential of the venture.
Cash Flow analysis is a good tool to evaluate the profitability of the venture. Show the cumulative cash flow standing of the venture with respect to time. Indicate the breakeven point (time required to recover all capital investments) Return at the end of the plant life
Cumulative Cash Flow
Time of Project Execution
In performing the profitability analysis based on the cash flow (projected), a number of quantitative measures or indices have been proposed. There are methods which do not take into account the time value of money which are;
Pay back Period / Time The time taken by the project to recover all the capital investments made break even The shorter the payback time, the more attractive the project is. R efers
to the manufacturing and non manufacturing related fixed capital investment.
PBP = Fixed Capital Investment (F) Annual Cash Flow
As the cash flow usually changes from year to year, taking the average will result in
PBP
V A x 1 N ( A j )
N
R efers
to the manufacturing and non manufacturing related fixed capital investment.
§ j 1
Average Annual Cash Flow
In performing the profitability analysis based on the cash flow (projected), a number of quantitative measures or indices have been proposed. There are methods which do not take into account the time value of money which are;
Incorporating the minimum acceptable rate of return (m ar ); The term V + A x is approximately equal to 0.85 X Total Capital Investment (taking working capital as 15%) and, The Average Annual Cash flow is equal to Average of Net Annual Profit (N p,ave) plus Average of Annual Depreciation (d j,ave) The equation for Pay Back Period becomes ;
P B P !
0.85 F mar F 0.85
F N
!
0.85 0.85 mar N
In performing the profitability analysis based on the cash flow (projected), a number of quantitative measures or indices have been proposed. There are methods which do not take into account the time value of money which are;
Return on Investment (ROI) Defined as the ratio of profit to investment. The most commonly used to reflect profit and investment are annual net profit and Total Capital Investment (F) measured every year. ROI = Net Profit / Total Capital Investment (F) Net profit is not constant from year to year. Therefore, the average ROI over the entire project period could be used instead. N
RO I
Evaluation Period
1 N
§ ( N
p , j
j 1 ¡
F
)
S um of annual net
profit
In performing the profitability analysis based on the cash flow (projected), a number of quantitative measures or indices have been proposed. There are methods which do not take into account the time value of money which are;
Net Return Defined as the amount of cash flow over and above that is required to meet the minimum acceptable rate of return and recover the total capital investment. The quantity is calculated by subtracting the total amount earned at the minimum acceptable rate of return plus the total capital investment from the total cash flow. N
Rn
N
j b
j b
§ N
p , j d j rec j § F j M ar . N § F j
j 1 ¢
S um
N
of Annual net profit + depreciation + recovery from sales of property
¢
¢
N ± no. of period for the assessment -b ± the year in which investment is made
Min. acceptable rate of return T otal Capital Investment
M ARR/Mar minimum acceptable rate of return is defined as the rate of earning that must be achieved by an investment in order for it to be acceptable to the investor.
Example.
N
ROI !
1
§ ( N
p , j
)
j !1
N Total I nvestment
Evaluation Period
S um of annual net
profit
PBP
0.85 F mar F 0.85
F N
0.85 0.85
mar
N
N
Rn
N
j b
j b
§ N
p , j d j rec j § F j M ar . N § F j
j 1 £
S um
N
of Annual net profit + depreciation + recovery from sales of property
£
£
Min. acceptable rate of return T otal Capital Investment
N ± no. of period for the assessment -b ± the year in which investment is made
However there are methods which takes into account of time value of money Net Present Worth (NPW) is defined as the total of the present worth of all cash flows minus the present worth of all capital investments.. N
NPW ! § PWF c f , j ?( s j coj d j )(1 * ) rec j d j A j !1
Present worth factor calculated based on an interest rate for the cash flow in year j
Cash flow during the evaluation period (sales ± total cost ± depreciation)
Recovery
from property sales
* income
N
§ PWF
v , j
tax rate
F j
j ! b
T otal Investment Present worth in year j factor for investment made in year j
Discounted Cash Flow Rate of Return (DCFRR) Defined as the return obtained from an investment in which all investments and cash flows are discounted. It is determined by setting the Net Present Worth equal to zero and solving for the discount rate that satisfies the resulting relation. N
NPW ! § PWF c f , j ?( s j coj d j )(1 * ) rec j d j A j !1
Present worth factor calculated based on an interest rate for the cash flow in year j
Cash flow during the evaluation period (sales ± total cost ± depreciation) * income
Recovery
from property sales
tax rate
N
PWF § !
v , j
F j ! 0
j b
T otal Investment Present worth in year j factor for investment made in year j
When the NPW is zero, the minimum acceptable rate of return (Mar) used to calculate the NPW will be the DCFRR. Since the discount rate appears in numerous exponents, it is generally impossible to solve the equation analytically and iterative solution is required.
