MONEY TIME RELATIONSHIPS

TYPE OF COSTS(Cost Concepts)

TYPE OF COSTS

Cost Terminology:When dealing with economic analysis/ engineering economic studies, it is important to use consistent definitions for cost terms. Otherwise, confusion and misunderstanding of the end results can take place.

Definition of Common Cost Terms:Fixed Costs: Are those costs which remain unaffected by changes in level of activity (volume of production). Fixed costs tend to remain constant over a specific range of operations. When large changes occur, like plant expansion or shut down is involved, fixed costs will be effected. Typical fixed cost are: insurance and taxes on facilities, general management and administrative salaries, interest cost on borrowed money, etc.

Definition of Common Cost Terms:

Variable Costs: Are those associated with an operation which vary in total with the quantity of out put/ activity level. For example: The cost of material and labour used in a product or service are variable costs because they vary in total with the number of out put units (cost per unit item staying the same).

Recurring Costs:Describes various types of expenditures. Recurring costs are those that are repetitive and occur when an organization produces similar goods or services on a continuing basis. Fixed and variable costs can also be recurring in nature.

Non-recurring Costs: Are those that are not repetitive.Cost of developing or establishing a capability/ capacity to operate. One time cost of land and factory built on it.

Definition of Common Cost Terms:

5.Direct Costs: Direct costs are those that can be reasonably measured and allocated to a specific output or work activity.Labour and material cost directly associated with a product or service activity are direct costs. e.g. material needed to make a pair of chairs would be direct cost.

Indirect Costs:Indirect costs are those are difficult to attribute or to allocate to a specific output or work activity.Generally refers to types of costs that take too much effort to allocate to a specific activity.Generally such costs are allocated through selected formula, e.g. proportional to direct labour hours, direct labour costs, etc.Cost of common tools, general supplies, equipment maintenance, etc. are treated as indirect costs.

Definition of Common Cost Terms:

Overheads:Consist of plant operating costs that are not direct labour or indirect material costs.Indirect costs and overheads costs terms can be used interchangeably.Examples of overheads include electricity, general repairs, property taxes, and supervision.Allocation of overheads among products and services use methods like proportional to direct labour costs, direct labour hours, direct material costs, or machine hours, etc. Standard Costs:Standard costs are representative costs per unit of output that is determined/ established in advance of actual production.Developed from direct labour hours, materials, etcStandard costs play an important role in cost control and other management functions ,i.e. measuring performance, preparing bids, etc.

Definition of Common Cost Terms:

Cash Cost versus Book Cost:A cost that involves payment of cash is called a cash cost (results in cash flow)A cost that does not involve a cash transaction, and is reflected in the accounting record/ system is a non cash cost. It is often referred to as a book cost, i.e. depreciation cost.Sunk Cost:A sunk cost is one that has occurred in the past and has no relevance tothe future costs/revenues related to an alternate course of action.

Opportunity Cost:An opportunity cost is incurred because of the use of limited resources, such that the opportunity to use those resources to monetary advantage in an alternative use is forgone.Thus it is the cost of the rejected (forgone) opportunity.Is hidden or implied.

Definition of Common Cost Terms:

Incremental Costs or Incremental Revenue:It is the additional cost, or revenue, that results from increasing the output of a system by one or more units.Incremental cost are generally associated with go/ no-go decisions that involve a limited change in output or activity level.

TIME VALUE OF MONEYCASH FLOW DIAGRAMS

CAPITAL VS TIME VALUE:The term CAPITAL refers to WEALTH in the form of MONEY or PROPERTY that can be used to produce more wealth.Majority of economic studies involve commitment of capital for extended periods of time, so the EFFECT OF TIME MUST BE CONSIDERED, i.e.It is a recognized fact that A RUPEE TODAY IS WORTH MORE THAN A RUPEE ONE OR MORE YEARS FROM NOW, because of the interest (or profit) it can or will earn during the period.THEREFORE, MONEY HAS A TIME VALUE.TIME VALUE OF MONEY PRINCIPLES ARE VERY IMPORTANT FOR THE PROPER EVALUATION OF ENGINEERING PROJECTS OF A COMPANY.

CAPITAL:Capital may be classified into the following two basic categories:

EQUITY CAPITAL: Is that owned by the individuals who have invested their money or property in a business project or venture in the hope of receiving a Profit.DEBT CAPITAL: Also called borrowed capital. Is obtained from lenders for investment. In return, lenders receive interest from the borrowers.

WHETHER BORROWED OR EQUITY CAPITAL, THE PROJECT OR VENTURE MUST POVIDE A RETURN SUFFICIENT TO BE FINANCIALLY ATTRACTIVE TO SUPPLIERS OF MONEY OR PROPERTY.

CONCEPT OF EQUIVALENCEHow can alternate financial proposals be compared when payments take place at different time intervals and interest rates are involved over extended periods of time?We must compare the alternative options or proposals BY REDUCING THEM TO AN EQUIVALENT BASIS.i.e. By taking into consideration:Interest rateAmount of money involvedTiming of monetary receipts/ expensesManner in which he interest or profit on invested capital is paid and the initial capital recovered.ECONOMIC EQUIVALENCE is established when we are indifferent between a future payment, or series of future payments and a present sum of money.

INTEREST CONCEPTS:SIMPLE INTEREST:When the total INTEREST earned is linearly proportional to :Initial amount of the loan (principal amount)Interest rateNumber of interest periods (time)The interest is said to be SIMPLE INTEREST.The total interest, I, earned or paid can be computed by the formula: I = (P) (N) (i) where: P = principal amount = 1000 I = (1000) (3) (10%) N = no of years = 3 = 300 I = interest rate = 10%

The total amount paid at the end of N interest periods = P + I = 1300Simple interest is not used frequently in modern commercial practice.

INTEREST CONCEPTS:COMPOUND INTEREST:When the interest charge for any interest period is based on the remaining principal amount plus any accumulated interest charges at the beginning of that period, the interest is said to be COMPOUND INTEREST. Period Amount at beginning Interest Amount Amount owed at end of period of period 1 1000 100 1100 2 1100 110 1210 3 1210 121 1331

The difference (1331-1300) is due to the effect of compounding, which is the calculation of interest on previously earned interest.This difference would be much greater for larger amounts of money, higher interest rates or greater number of years.COMPOUND INTEREST is much more common in practice than simple Interest. { Calculated as F = P (1 + I )}

COMPOUND INTEREST:

The following notation is used in formulas for compound interest calculations:

i = effective interest rate per interest periodN = number of compounding periods P = present sum of moneyF = future sum of moneyA = end of period cash flows in a uniform series for a specific number of periods, staring at the end of the first period.

CASH FLOW DIAGRAM:Useful for situations in which the analyst needs to clarify or visualize what is involved when flow of money occurs at various times:

Beginning of End of F = Rs. 11,713 year 1 year 101234 = NP = 8000i = 10% per yearThe cash flow diagram employs several conventions/rules:

Horizontal line is a TIME SCALE, time progressing from L to R. The period (e.g. year, quarter, month) labels can be applied to time intervals.

Arrows signify cash flows, and are placed at the end of the period. DOWN WARD ARROWS = Expenses, -ve cash flow or cash outflows. UPWARD ARROWS = Receipts, +ve cash flows or cash inflows.

Cash flow diagram is dependent on the point of view. Direction of arrows would be different for lenders/ borrowers.

INTEREST FORMULAS RELATING PRESENT AND FUTURE VALUES OF A SINGLE CASH FLOW F = future equivalent value (find) 0 1 2 3 4 N-2 N-1 N (N = no of interest P = present value periods) Finding F when P is given: P is invested at i % interest rate . The amount P will grow: (a) At end of one period: F = P + Pi = P(1+i) (b) At end of two periods: F = P ( 1+ i) + (P(1+i) i ) F = P (1+i) + Pi + P i = P( 1+2i+i) = P (1 + i) (c) Similarly, at end of three periods: F = P(1+i)

Therefore at the end of N periods, it will be : F = P (1 + i ) Also: F = P (F/P, i, N), F/P =To find F given P

The quantity ( 1 + i) is called the SINGLE PAYMENT COMPOUND AMOUNT FACTOR

INTEREST FORMULAS RELATING PRESENT AND FUTURE VALUES OF A SINGLE CASH FLOW F = future 0 (find) 1 2 3 4 N-2 N-1 N (No of interest P = present equivalent periods) Finding P when F is given:

F is future amount at i % interest rate , at N years. Therefore, at time 0 (present): P = F (1 + i ) Also: P = F (P/F, i, N) P/F =To find P given F

The quantity ( 1 + i) is called the SINGLE PAYMENT PRESENT WORTH FACTOR

INTEREST FORMULAS RELATING TO A UNIFORM SERIES (ANNUITY) TO ITS PRESENT AND FUTURE EQUIVALENT VALUES A = uniform amounts (given) 0 (find) 1 2 3 4 N-2 N-1 N (No of interest P = present equivalent periods) F = future equivalentThe above figure shows:Cash flow diagram involving a series of uniform (equal) receipts, each of amount A, occurring at the end of each period, for N periods, with interest rate i % per period.Such a series is also called an ANNUITY.A occurs at end of each period.Thus: (a) P (present equivalent value) occurs one interest period before first A (b) F (future equivalent) occurs at the same as last A, and N periods after P (c) A (annual equivalent amount) occurs at end of period 1 through N.

INTEREST FORMULAS RELATING TO A UNIFORM SERIES (ANNUITY) TO ITS PRESENT AND FUTURE EQUIVALENT VALUES FINDING F GIVEN A: A = uniform amounts (given) 0 (find) 1 2 3 4 N-2 N-1 N (No of interest P = present equivalent periods) F = future equivalentCash flow A occurs at end of each period of N at i% interest rate per period.F (future equivalent) at the end of N periods is obtained by summing up the F at each cash flow:F = A (F/P, i, N-1) + A (F/P, i, N-2) + A (F/P, i, N-3) +.. A (F/P, i, 1) + A (F/P, i, 0) = A { (1+i) + (1+i) + (1+i) + (1+i) + (1+i) } Summing up of the N terms of a geometric sequence, we get: F = A ( 1 + i ) - 1 UNIFORM SERIES COMPOUND AMOUNT FACTOR i F = A ( F/A, i , N )

INTEREST FORMULAS RELATING TO A UNIFORM SERIES (ANNUITY) TO ITS PRESENT AND FUTURE EQUIVALENT VALUES FINDING P GIVEN A: A = uniform amounts (given) 0 (find) 1 2 3 4 N-2 N-1 N (No of interest P = present equivalent periods) F = future equivalent We know that F = P ( 1 + i )

Therefore: P ( 1 + i ) = A ( 1 + i ) - 1 i Re-arranging, we get: UNIFORM SERIES PRESENT P = A ( 1 + i ) - 1 WORTH FACTOR i ( 1 + i ) P = A ( P/A, i, N )

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