Definition: ENGINEERING ECONOMY is a discipline concerned with the systematic evaluation of the costs and benefits of the proposed business projects and ventures. Its objective is to choose which among the alternative course of action will give the maximum benefit at the least cost. Engineering Economy, Economy, therefore therefor e involves the application of definite laws of Economics, theories of investment and business practices to engineering problems involving cost. It also involves the study of cost features and other financial data and their applications in the field of engineering as basis for decision.
Definition: ENGINEERING ECONOMY is a discipline concerned with the systematic evaluation of the costs and benefits of the proposed business projects and ventures. Its objective is to choose which among the alternative course of action will give the maximum benefit at the least cost. Engineering Economy, Economy, therefore therefor e involves the application of definite laws of Economics, theories of investment and business practices to engineering problems involving cost. It also involves the study of cost features and other financial data and their applications in the field of engineering as basis for decision.
COST CONCEPTS DEMAND – is the quantity of a certain commodity that is bought at a certain
price at a given place and time.
SUPPLY – – is the quantity of a certain commodity that is offered for sale at a
certain price at a given place and time.
FIXED COST – – are costs that do not vary in proportion to the quantity of
output.
VARIA B LE COST – – are costs that vary in i n proportion to quantity of output. BREA K EVEN EVE N POINT POI NT – – is the level of production at which revenue is exactly
equal to total costs
Elements of Cost: 1) Materials a) Direct Materials are those which are used in the finished product itself. b) Indirect Materials are those materials used in production but which do not go into the finished product. 2) Labor a) Direct Labor is the actual work applied directly to the manufacture of the product b) Indirect Labor is the work necessary for the operation of the factory, but which cannot be identified with one particular process or product
3) Overhead Expenses Expenses which cannot be allocated to direct materials or direct labir. PRIME COST = Direct Materials Cost + Direct Labor Cost PRODUCTION COST = Direct Materials Cost + Direct Labor Cost + Overhead Cost Or PRODUCTION COST = Prime Cost + Overhead Cost
L AW OF SUPPLY
The supply of the commodity varies directly as the price of the commodity, though not proportionately p r i c e
Supply
L A W O F D EM A N D
The demand for a commodity varies inversely as the price of the commodity, though not proportionately p r i c e
LAW OF DEMAND AND SUPPLY
Under conditions of perfect competition, the price at which any given product will be supplied and purchased is the price that will result in the supply and the demand being equal. p r i c e
Quantity
The relationship between price and demand can be expressed as a line p r i c e
p = a - bD
Demand (D)
Where a is the intercept on the price (p)axis and –b is the slope.
TOTAL REVENUE – VOLUME RELATIONSHIP T O T A L
R e v e n u e
Peak point – represents the Maximum revenue
Demand that maximizes Total Revenue
TR pD TR (a bD) D or
D'
Volume (D)
COST - VOLUME RELATIONSHIP Total Cost
TC TVC TFC TC vcD TFC
C o s t
Variable Cost
Fixed Cost
Volume (D)
COMBINATION OF COST - VOLUME & REVENUE VOLUME RELATIONSHIP C o s t
or
R e v e n u e
Represents the Maximum Profit Total Cost
Demand that maximizes Total Profit D*
Volume (D)
*
D
a vc 2b
Formulas: Price: p Total Revenue:
a
bD
TR pD TR (a bD) D or TR aD bD2
Total Cost : TC TVC TFC
TC vcD TFC
Profit: P TR TC P pD (vcD TFC ) P (a bD) D vcD TFC P bD2 (a vc) D TFC
a D 2b
Demand that maximizes Revenue
Demand that maximizes Profit (Optimum Profit)
*
D
a vc 2b
Break even points: Profit = 0 P TR TC P pD (vcD TFC ) P (a bD) D vcD TFC P bD2 (a vc) D TFC
0 bD2 (a vc) D TFC
D
'
(a vc)
(a vc) 2 4(b)(TFC ) 2(b)
COST CONCEPTS
I.
B:
Price is not constant
Break even point: C O S T
R e or v e n u e
TFC D p vc '
D'
TFC p vc
Break Even Point where TR=TC
Examples: 1. A company produces circuit boards to update the outdated computer equipment. The fixed cost is $42,000 per month and the variable cost is $53 per circuit board. The selling price per unit is p = $150 – 0.02D. Maximum output of the plant is 4000 units per month. (a) Determine the optimum value for this product. (b) What is the maximum profit per month? (c) At what volumes does break-even occur? (d) What is the company’s range of profitable demand?
Examples 2. A large semiconductor plant has approximately 95% of sales due to a single circuit design. The plant can therefore be considered to produce 3,000,000 printed circuit boards (PCBs) per year. Presently, the plant is operating at 60% of capacity. The selling price of the PCB is p = $19.25 – (10- 6 )D, and the variable cost per PCB is $15.75. At zero output, the plants annual fixed costs are $1,000,000 and are approximately constant up to the maximum production quantity per year. a. What is the present expected annual profit or loss (60% capacity)? b. What t h e p e r c e n t a g e of production capacity that will result in optimal operation? What is the maximum profit or minimum loss at this optimal volume?
Examples: 3. A manufacturing company leases for $100,000 per year a
building that houses its manufacturing facilities. In addition, the machinery in the building is being paid for installments of $20,000 per year. Each unit of product produced costs $15 in labor and $10 in materials and can be sold for $40. a.How many units per year must be sold for the company to break even? b. If 10,000 units per year are sold, what is the annual profit? c. If the selling price is lowered to $35 per unit, how many
4.A company produces and sells a consumer product and thus far has been able to control the volume of the product by varying the selling price. The company is seeking to maximize its net profit. It has been concluded that the relationship between price and demand, per month, is approximately D = 500 5 p, where p is the price per unit in dollars. The fixed cost is $1,000 per month, and the variable cost is $20 per unit. Obtain the answer mathematically to the following questions: a. What is demand that will maximize revenue per month and the maximum revenue b. What is the optimal number of units that should be produced and sold per month? c. What is the maximum profit per month?
5. A plant operation has fixed cost of $2,000,000 per year, and its output capacity is 100,000 electrical appliances per year. The variable cost is $40 per unit, and the product sells for $90 per unit. a) What is the annual break even volume of this product? b) Compare annual profit when the plant is operating at 90% capacity with the plant operation at 100% capacity. Assume that the first 90% of capacity output is sold at $90 per unit and that the remaining 10% of production is sold at $70 per unit.
Examples 6.
A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately D = 780 – 10p units. The fixed cost is $800 per month, and the variable cost is $30 per unit produced. What number of units should be produced per month and sold to maximize net profit? What is the maximum profit per month? Determine the range of profitable demand.
Examples: 7. The annual fixed costs for a plant are P100,000 and the variable costs are P140,000 at 70%utilization of available capacity with net sales of P280,000. What is the break even point in units of production if the selling price per unit is P40.
8. Suppose we know that p=1,000 – D/5, where p = price in dollars and D = annual demand. The total cost per year can be approximated by $1,000 + 2D 2 . a. Determine the value of D that maximizes profit. b. Show that in part(a) profit has been maximized rather than minimized.
Answer: (a) p = 1,000 - 0.2D
TC = 1,000 + 2D2 Profit
= Total Revenue - Total Cost = (1,000 - 0.2D)D - (1,000 + 2D2) = 1,000D - 2.2D2 - 1,000 d Profit d D
D* (b)
D*.
= 227.27 units per year
d 2 (Profit) d D
= 1,000 - 4.4 D* = 0
2
= - 4.4 < 0
Since the second derivative is negative, profit has been maximized at
6. The fixed cost for a steam line per meter of pipe is
$450X + $50 per year. The cost for loss of heat from the pipe per meter is $4.8/X 1/2 per year. Here X represents the thickness of insulation in meters and X is a continuous design variable. a. What is the optimum thickness of the insulation? b. How do you know that your answer in (a) minimizes total cost per year?
Answer: (a) Total Annual Cost (TAC) = Fixed cost + Cost of Heat Loss
= 450X + 50 +
4.80 X1/ 2
2.40 d (TAC) = 0 = 450 - 3/2 d X X
X (b)
3/2
2.40 = = 0.00533 450 X* = 0.0305 meters for X > 0.
3.6 d 2 (TAC) = > 0 2 5/ 2 X d X Since the second derivative is positive, X* = 0.0305 meters is a minimum cost thickness. (c) The cost of the extra insulation (a directly varying cost) is being traded-off against the
value of reduction in lost heat (an indirectly varying cost).
7. A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $40D. The fixed cost that can be allocated to the production of fireworks is negligible. The price changed per unit will be determined by the equation p=$180-(5)D, where D represents demand in units sold per week. a. What is the optimum number of units the defense contractor should produce in order to maximize profit per week? b. What is the profit if the optimum number of units are produced?
(a) Total Revenue = p D
= (180 – 5D)D = 180D – 5D2 Total Cost = (40D)D = 40D2 Total Profit = -5D2 + 180D – 40D2 d (Profit) d D
= - 10D + 180 – 80D = 0;
90D = 180; D* 2 units/week d 2 (Profit) d D2
(b)
= -90 < 0
maximum profit
Total Profit = -5(22) + 180(2) – 40(22) = -20 + 360 – 160 = $180 / week
Seatwork: 1. A company has determined that the price and that
monthly demand of one of its products are related by the equation D (400 p)
The associated fixed costs are $1,125/month, and the variable costs are $100/unit. a. What is the optimal number of units to maximize revenue and the maximum revenue? b. What is the optimal number of units that should be produced and sold each month to maximize profit?
2. A plant operation has fixed cost of $2,000,000 per year, and its output capacity is 100,000 electrical appliances per year. The variable cost is $40 per unit, and the product sells for $90 per unit. a) What is the annual break even volume of this product? b) Compare annual profit when the plant is operating at 90% capacity with the plant operation at 100% capacity. Assume that the first 90% of capacity output is sold at $90 per unit and that the remaining 10% of production is sold at $70 per unit.
3. A manufacturer is currently selling 1000 decorative lamps a month to the retailers at a price of P800 per lamp. Its estimates that for each P50 increase in the price will sell 20 fewer lamps each month. The manufacturer’s cost consists of a fixed overhead of P300,000/ month plus P300 per lamp for labor and materials. a. Set up the total cost function b. Set up the demand function c. Find the Break Even points d. Find the volume that will maximize profit e. What is the maximum profit? f. What is the volume of sales that will maximize your sales revenue?
4. Bragg & Stratton Company manufactures a specialized motor for chain saws. The company expects to manufacture and sell 30,000 motors in year 2001. It can manufacture an additional 10,000 motors without adding new machinery and equipment. Its projected total costs for the 30,000 units are as follows: Direct Materials $150,000 Direct Labor 100,000 Manufacturing Overhead: Variable Portion 100,000 Fixed Portion 80,000 Selling and Administrative costs: Variable Portion 180,000 Fixed Portion 70,000 The selling price for the motor is $80. a. What is the total manufacturing cost per unit if 300,000 motors are produced? b. What is the total manufacturing cost per unit if 40,000 motors are produced?
FE 1. Total Revenue (TR) = pD = (88.5 – 0.08D0.75)D
= 88.5D – 0.08D1.75 = 88.5 – 0.08(1.75)D0.75
d (TR) d D
D0.75 =
D=
88.5 (0.08)(1.75)
(0.08)(1.75) 88.5
1/0.75 =
5,425 units per year
Total Profit (TP) = TR – TC = 88.5D – 0.08D1.75 – (40,000 + 40D) = 48.5D – 0.08D1.75 d (TP) = 48.5 – 0.08(1.75)D0.75 = 0 d D 48.5 0.75 D = (0.08)(1.75)
FC = [$350,000 - 0.1($350,000)](12) = $3,780,000 per year (10% decrease)
(c)
vc = [$0.50 + 0.1 ($0.50)] = $0.55 per unit of sales (10% increase) $3,780,000 D = = $8,400,000 per year $1 - $0.55
Thus, no change occurred in the original breakeven point.
2-20
(a) D =
CF $2,000,000 = = 40,000 units per year p - cv ($90 - $40) / unit
(b) Profit(Loss) = Total Revenue - Total Cost
(90% Capacity) = 90,000 ($90) - [$2,000,000 + 90,000 ($40)] = $2,500,000 per year (100% Capacity) = [90,000($90) + 10,000($70)] [$2,000,000 + 100,000($40)] = $2,800,000 per year
BREAK – EVEN ANALYSIS, TWO ALTERNATIVES Industry is faced with certain situations where two or more alternatives can be considered. When the cost for two alternatives is affected by a common decision variable, there may exist a value of the variable for which the two alternatives will incur equal cost. This value is known as the break-even cost. Below this cost, one method will be more economical, and above this cost, the other will prove to be better economically. TCA TCB Total Cost
D’ TCA = TCB
Volume (D)
Examples 1. Two manufacturing methods are being considered. Method A has a fixed cost of P5,000 and a variable cost of P50. Method B has a fixed cost of P2500 and a variable cost of 150. For what production volume would one prefer (a) Method A, and (b) Method B?
