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Sessions 9 & 10 - Basic Cost Concepts & Engineering
Economy
Why The Need To Manage Costs?
Money is the most liquid of resources, and like a liquid it can slip away very easily. It is
often said that if the money is available, any other resources can be obtained. This may be
a simplification, but it shows how important money is. Money is used for many purposes,
including capital and cost expenditure.
All economic analyses deal with costs. They are concerned with money being spent, how
it can be spent in the most economical way, and how as well as when it will be recovered
out of income.
Cost Terms
Terms Explanations
First Cost or Initial
Cost
The initial cost of capitalized asset, including purchase price,
transportation, installation and other related initial expenditure
incurred (such as training) to ready the asset for use.
Does not occur again once an activity is initiated.
Operation &
Maintenance Costs
Include labour costs for operating and maintenance personnel,
operating and maintenance supply costs, fuel and power costs, costs
of repair and spare parts, insurance, tax and other overheads.
These costs can be substantial, often exceeding the first cost in total
amount, though the timing of occurrence differs substantially.
These costs occur over time until the structure, system or
equipment is retired from service.
Fixed Cost or
Overhead Cost
Remains a constant charge on the business and contains all those
cost items which do not change with a change in production, e.g.,
depreciation, insurance & rental.
Variable Costs or
Direct Costs or
Incremental Costs
or Marginal Costs
Costs which vary in some relationship to the level of operational
activity. Their total amount goes up or down with the volume of
production. However, their costs per individual unit of production
remain almost constant.
Those costs, which can be identified as part of the cost of the
finished product. Consist of direct material & direct labour costs.
Variable costs are “incremental” in that each additional unit of
CIE 210 PS Notes Sessions 9 & 10 – Basic Cost Concepts & Engg Econ 06/11/10 WCH 1
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production causes an added increment of cost.
Direct material cost The cost of material which can be identified with the finished
product. The material goes into the product and the quantity used
varies directly with volume.
Direct labour cost The cost of wages which can be traced directly to the final product
cost. This includes the wages of machine operators & those directly
involved in the manufacture of goods & services.
Indirect costs Those costs which cannot be directly identified with the finished
product. Classified as manufacturing expenses or overheads.
Consist of indirect material & indirect labour costs & other
manufacturing expenses.
Indirect material
cost
Materials whose usage does not depend on the volume produced.
Indirect materials include lubricants used to grease machines,
coolants and the cost of timber pallets in the warehouse. Such costs
are shared by all production units but cannot be measured directly
against individual items (a kind of overhead).
Indirect labour cost Includes the wages of supervisors, cleaners and security staff who
are not directly involved with the physical production of goods and
services. The cost of idle time due to delays, overtime premiums &
the provision of sick leave and holiday pay are also regarded as
indirect costs.
Other
manufacturing
expenses
All other indirect items fall within this area. Include heating &
lighting (electricity), plant depreciation, rent & insurance.
Life-cycle Cost The cost for the entire life-cycle of a product, and includes
feasibility, design, construction, operation and disposal costs.
The direct material, direct labour & manufacturing overheads are input costs to the
production system & initially represent the value of work-in-process.
As completed products emerge from the production system, costs are transferred out of
WIP inventory & placed in the finished goods inventory until they are sold. The cost of
goods sold can then be matched against sales to find the gross profit.
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Capital Investment Vs Operating Expense
The distinction between the above depends on the expected service life & the first cost.
Generally, items with long service lives & high first costs are treated as investments – they are
capitalized & increase the asset of the company. A capitalised item is depreciated over a
number of operating periods which coincide with the expected service life of the item. It is
tagged with an asset number & is physically counted during annual stock-taking or physical
inventory exercise.
Generally, the first cost of an equipment or plant includes the purchase price, transportation
cost, government taxes & duties and cost of installation.
Profit Selling or
Purchase
PriceGeneral
overheads &
Administrative
costs
Total
Costs
Operations
overheads (or
indirect costs)
Total
Operation
Cost
Direct labour
costs
Prime
cost
Direct material
costs
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Engineering Economy
In industrial engineering, it is often necessary to compare among alternative designs,
procedures, plans and methods. Since the available alternative courses of action involve
different amounts of investment and different operating costs and benefits, the inevitable
question is “Will it pay?” The method of solution requires us to express each alternative in
some common form and then choose the best, taking both the monetary and intangible factors
into account.
It answers one of 2 questions:
(1) Which of the choices considered is best from a financial point of view? (i.e., which
equipment offers the required service at lowest cost?), or
(2) What is the expected return on investment (ROI) in using this equipment? (i.e., if I
were to purchase this equipment, would I make a satisfactory return for the money
invested?).
In most computations, a minimum attractive rate of return (MARR) is used. This is the
smallest interest rate, or rate of return, at which one is willing to invest money. It represents
the interest rate a company expects to make on its investments.
Interest Rate
The interest rate is the rent charged on the money lent for a defined period of time.
Simple Interest
Under simple interest, the interest owed upon repayment of a loan is proportional to the
length of time the principal sum has been borrowed.
Compound Interest
Whenever the interest charged for any interest period is based on the remaining principal
amount plus any accumulated interest charged up to the beginning of that period, the
interest is said to be compounded. [Put simply, the interest earned is added to the
principal, and the total (principal + interest) is carried forward to the following period to
continue to earn interest.]
Compound interest is much more common in practice than simple interest, and the
interest obtained due to the effect of compounding is higher than that obtained from
simple interest calculation. The difference would be much greater for a larger amount of
money, a higher interest rate, or a greater number of interest periods.
Consider the following variables in an engineering economy problem:
CIE 210 PS Notes Sessions 9 & 10 – Basic Cost Concepts & Engg Econ 06/11/10 WCH 4
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P = present value (or principal sum);
F = future value;
I = interest owed;
i = interest rate (in decimals) per year;
n= no. of interest periods
To calculate simple interest,
I = Pin, or F = P (1 + in).
To calculate compound interest,
F = P (1+ i) n
, or P = F / (1+ i) n
.
Another variable commonly used is the uniform annual amount A, which represents a
constant value, A, occurring at the end of each interest period over a continuous number
of interest periods.
Time Value Of Money
As money can earn a certain interest through its investment for a period of time, a dollar
received at some future date is not worth as much as a dollar in hand at present. The
relationship between interest and time leads to the concept of the time value of money.
[The concept of time value of money is related directly to the concept of opportunity cost.
If instead of receiving a certain sum right now, and you had to wait until the end of a
whole year for it, you would have lost the interest that you could have earned.]
The Future Value of Present Money
F = P (1+ i) n
,
The Present Value of Future Money
P = F / (1+ i) n
or F (1+ i) – n
.
Both present value and future value represent sums of money at points in time. The only
requirement is that present value precedes future value in time.
Functional Notation
(1+ i)n
is also given the factor notation: (F/P, i %, n) and 1 / (1+ i)n
given the notation
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(P/F, i %, n), where the top letter of the ratio is the sum of money you want to find, given
the bottom sum, i is the interest rate, and n the number of periods.
Interpreting The Functional Notation
F = P (F/P, i %, n) means “the calculated amount, F, at the point in time it occurs (i.e., n
periods from when P occurs), is equivalent to the known value of P at the point in time it
occurs, for the given interest rate, i %.” Tables of different values of i and n are available
for engineering economy calculations.
Economic Equivalence
In engineering economy, 2 things are said to be equivalent when they have the same
effect. When 2 or more alternatives are to be compared, their relative merits are often not
directly apparent from a simple statement of their future receipts and disbursements. To
compare, these amounts must first be placed on an equivalent basis, for example, at the
same point in time. When interest is earned, monetary amounts can be directly added only
if they occur at the same point in time.
The factors involved in the equivalence of sums of money are:
- the amounts of the sums;
- the times of occurrence of the sums; and
- the interest rate.
In the interest formulas, P occurs at the start of an interest period, and F and A payments
occur at the end of interest periods.
Depreciation
A fixed or physical asset decreases in value because of the reduction in usefulness with
the passage of time, usually over its expected service life. The process by which it loses
its value is called ‘depreciation’.
Regardless of the reason for a decrease in value of an asset, the depreciation should be
taken into account in engineering economy studies because of favourable income tax
allowances. Taxes are paid on net income less depreciation for the year, thus lowering the
taxes paid. [It is an operation cost, affecting the profitability of a company.]
Depreciation is usually charged once a year, in keeping with the end-of-year convention.
Book Value
The book value of an asset is the acquisition cost of an asset less its accumulated
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depreciation charges. It represents the current worth of an asset as indicated in the books
of accounts.
Straight-line (SL) Depreciation
The book value of the asset decreases linearly with time, because the same depreciation
charge is made each year. The yearly depreciation is determined by dividing the first cost
minus its salvage value by the life of the asset.
D t = (P – V) / n
where:
t = year,
D t = annual depreciation charge,
P = first cost,
V = salvage value, and
n = expected depreciable life or recovery period.
Since the asset is depreciated by the same amount each year,
Book value after t years, BV t = P – D t.
Cash Flow Diagrams
A cash flow diagram is a means of visualizing and simplifying the flow of receipts and
disbursements for the acquisition and operation of items in an enterprise.
The horizontal line is a time scale with progression of time moving from left to right, with the
interest periods or years written below the intervals of time. It is marked off in equal
increments, one per period, up to the duration of the project.
The arrows represent cash flows. Arrows may go in opposing directions as cash flows may
represent either costs or incomes. Costs, expenditures, payments and disbursements (negative
cash flows or cash outflows) will be shown as downward pointing arrows. Benefits, revenues,
incomes or receipts (positive cash flows or cash inflows) are shown as upward pointing
arrows. Arrow lengths are approximately proportional to the magnitude of the cash flow.
The “end-of-year” convention is used, where all disbursements and receipts (i.e., cash flows)
are assumed to take place at the end of the year in which they occur.
Expenses incurred before time = 0 are sunk costs and are not relevant to the problem.
However, salvage value is income, so it is drawn as positive.
The net cash flow is the arithmetic sum of receipts (+) and disbursements (–) that occur at the
same point in time.
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It is important to draw the cash flow diagram for any proposal as it does not only give us a
pictorial view of the cash flows, it also allows us to write the cash flow equation (with
functional notations) more easily.
A = $14,667/- F = $44,560/-
+
1 2 3 4 5 years
–
P = $123,545/-
E.g., NPW = – $123,545 + $14,667 (P/A, i %, 5) + $44,560 (P/F, i %, 5)
Once we know the interest rate, it is a matter of checking the interest factor tables, substitute
the factors into the equation, and calculate the NPW.
Procedure in Decision-Making
1) Define alternatives clearly and determine the differences in consequences;
2) Quantify these differences in terms of money;
3) Apply evaluation criteria to the quantifiable monetary figures to provide a basis
for objective decision making.
4) Consider other non-quantifiable factors before a final decision is made.
The no. of initial alternatives may be large but analysis of 6 major factors – cost, volume,
human resource constraints, technology, quality & reliability – typically reduces the large
number to only a few.
[Note: One alternative often ignored is to do nothing & maintain existing conditions.
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Basic Methods for Making Engineering Economy Studies
All engineering economy studies of capital projects should be made so as to include
consideration of the return that a given project will or should produce. As the patterns of
capital investment, revenue or saving flows and cost flows can be quite different in various
projects, there is no single method for making engineering economy studies that is ideal for all
cases.
There are 4 commonly used methods for comparing the relative financial merits of competing
alternatives in engineering economy problems:
(1) Break-even Analysis method;
(2) Payback Period method;
(3) Net Present Worth (NPW) method; and
(4) Internal Rate of Return (IRR) method.
The alternative selected will be that which offers the shortest payback period, the most return,
or is of the lowest cost, for the same investment.
Or, we can determine the Rate of Return by solving for i * and choosing the alternative
offering the greatest rate of return, irreducible considerations being equal.
Other methods are discussed in the IED module “Engineering Economy”.
Break-even Analysis
In this “Break-even” analysis, the relationship among cost, volume and profit are put
together graphically. It shows how much sales volume in units or dollar sales a company
needs to have in order to break even financially. The break-even point is that point of
activity (sales volume) where total revenues and total expenses are equal. It is the point of
zero profit or zero loss. In order to calculate break-even points, it is necessary to
determine fixed and variable costs for various sales volume.
At a level above this, total revenue is greater than total costs, and a profit is made. Below
this level of activity, total revenue is less than total costs and a loss is incurred. Decisions
pertaining to how many and how much to sell and the varying of the costs to achieve
certain maximized-profit position or minimized-loss position can be determined.
The formula for calculating the break-even quantity is given by:
SP x Q = FC + VC x Q,
Break-even Quantity, Q = FC / (SP – VC),
where SP is the unit selling price, VC is the unit variable cost, and FC the fixed costs
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(overheads).
The term (SP – VC) is called ‘contribution’. It is the amount by which the selling price
per unit exceeds the variable cost per unit (or total revenues exceed total variable costs).
Contribution margin is the excess of sales over variable expenses.
Assumptions:
1) All costs can be classified as either fixed or variable and these two costs remain
unchanged during the period involved;
2) Selling price remains constant regardless of volume.
We are considering only the quantitative aspects of this analysis. Non-quantitative aspects
are just as important, and have to be considered, but this cannot be done in an entirely
quantitative context.
The break-even quantity may be solved from the equation:
Sales = Variable Expenses + Fixed Expenses + Net Income.
Alternatively,
Break-even (units) = Fixed Expenses + Desired Net Income
Contribution Margin per unit
[It is more useful to talk about a break-even region, rather than a break-even point,
because as all costs can only be estimates and are never known precisely, changes in the
cost or revenue estimates will change the calculated break-even value. The term ‘point’
also gives a misleading impression of accuracy.]
Payback Period Method
This method is concerned primarily with the period of time required to recover an investment.
This is useful when there are different rates of investment and annual cash flow spread over
the period. The payback period is obtained when the cumulative cash flow curve intersects the
x-axis. The alternative that returns the initial investment in the shortest time period is
preferred.
Mathematically, payback period = net investment / net annual cash flow after taxes.
The merit of an investment may be judged by comparing the pay-back period with the
estimated life of the equipment.
This is the most popular method in general use. However, it will provide the wrong answer as
this method does not consider:
- the returns after payback (i.e., the economic life & the salvage value);
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- the time value of money during the economic life of the equipment.
The Net Present Worth (NPW) Method
The concept of PW discounts the future cash flows arising from an investment at a
predetermined standard rate of interest. This gives the present value which is then compared to
the amount being invested. To be realistically profitable, the NPW must be greater than the
sum invested. The rate considered is usually the cost of capital or MARR.
The criterion is that as long as the net present worth of the cash flows is equal to or greater
than zero, the project is economically justified.
However, there must be a common analysis period when comparing alternatives. It is incorrect
to compare the NPW of Pump A, say, which is expected to last 6 years, with the NPW of
Pump B, expected to last 12 years. In this example, the assumption would be that Pump A will
be replaced by another identical Pump A at the end of 6 years. This gives a common analysis
period of 12 years.
In situations like this, restructure the problem so there is a common analysis period. This is
easy when the different lives of the alternatives have a practical least common multiple. When
this is not the case, some assumptions must be made to select a suitable common analysis
period. Or, just don’t use the NPW method.
Internal Rate of Return (IRR) Method
Also known as the Return on Investment (ROI) method. It answers the question “If I make this
investment, will there be a sufficient return (i.e., interest) on the money invested?”
For any set of disbursements-receipts relationships, there is some rate of return that will
exactly reduce the worth of the investment to zero at the end of the time period. The computed
interest or profit rate, i *, which will fulfill this condition, is the internal rate of return.
To determine the ROI for an investment, derive the mathematical expression for the present
worth by bringing all the cash flows to the present. This expression will be in terms of the
appropriate functional notations as the interest rate is unknown. The interest rate, i *, that
reduces the expression to zero is found by trial and error (including interpolation), and uses the
discount factors for the appropriate number of years at different rates of interest.
Other things being equal, the preferred alternative is the one with the highest IRR.
As a rule, the IRR must be able to cover the sum of savings interest rate (if the principal is
deposited in a bank to earn interest) and business risk, to make the investment proposal
attractive.
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The IRR is the interest (profit) rate earned by all capital that is invested in the project each
year.
Need to Invest?
Sometimes when an unsatisfactory condition is under review and an investment in fixed asset
is proposed to correct this condition, no thought is given to possible methods of improving the
conditions without a substantial investment.
For example, new machinery may be proposed to reduce high labour costs on a certain
operation. However, work simplification methods based on motion study may provide an
alternative way to reduce these costs
Or, new equipment may be proposed to reduce product quality rejects. Yet, it could be possible
that the same result might be obtained through the use of statistical quality control techniques.
CIE 210 PS Notes Sessions 9 & 10 – Basic Cost Concepts & Engg Econ 06/11/10 WCH 12
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