IENG 217 Cost Estimating for Engineers Break Even & Sensitivity

Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. Your boss asks you to figure out if it should be done.

Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram ,000 25,000 i = 15%

Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram ,000 25,000 NPW = (P/A,15,5) = -16,196 i = 15%

Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram ,000 25,000 NPW = (P/A,15,5) = -16,196 i = 15%

Motivation Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market ,000 40,000

Motivation Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market ,000 40,000 NPW = (P/A,15,5) = 34,086

Motivation Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market ,000 40,000 NPW = (P/A,15,5) = 34,086

Motivation Tell your boss, new numbers indicate a go. Boss indicates that perhaps he was a bit hasty. Sales have fallen a bit below marketing forecast, perhaps a 32,000 savings would be more appropriate ,000 32,000

Motivation Tell your boss, new numbers indicate a go. Boss indicates that perhaps he was a bit hasty. Sales have fallen a bit below marketing forecast, perhaps a 32,000 savings would be more appropriate ,000 32,000 NPW = (P/A,15,5) = 7,269

Motivation Tell your boss, new numbers indicate a go. Boss indicates that perhaps he was a bit hasty. Sales have fallen a bit below marketing forecast, perhaps a 32,000 savings would be more appropriate ,000 32,000 NPW = (P/A,15,5) = 7,269

Motivation Tell your boss, new numbers indicate a go. Boss leans back in his chair and says, you know....

Motivation Tell your boss, new numbers indicate a go. Boss leans back in his chair and says, you know.... I’ll do anything, just tell me what numbers you want to use!

Motivation ,000 A NPW = A(P/A,15,5) > 0

Motivation ,000 A NPW = A(P/A,15,5) > 0 A > 100(A/P,15,5) > 29,830

A < 29,830 A > 29,830 Motivation ,000 A

Fixed vs Variable u Fixed - do not vary with production general admin., taxes, rent, depreciation u Variable - costs vary in proportion to the quantity of output material, direct labor, material handling

Fixed vs Variable u Fixed - do not vary with production general admin., taxes, rent, depreciation u Variable - costs vary in proportion to the quantity of output material, direct labor, material handling TC(x) = FC + VC(x)

Fixed vs Variable TC(x) = FC + VC(x) FC TC VC

Break Even Profit = R(x) - FC - VC(x) FC TC R

Break-Even Analysis SiteFixed Cost/YrVariable Cost A=Austin $20,000 $50 S= Sioux Falls60, D=Denver80,00030 TC = FC + VC * X

Break-Even (cont) Break-Even Analysis 0 50, , , , , ,0001,5002,0002,5003,0003,5004,000 Volume Total Cost Austin S. Falls Denver

Example u Company produces crude oil from a field where the basis of decision is the number of barrels produced. Two methods for production are: u automated tank battery u manually operated tank battery

Example u Automated tank battery u annual depreciation = $3,200 u annual maintenance = $5,200 u Other fixed & variable costs

Automated Tank Battery TC(x) = ( , ,200) X

Example u Manual Tank Battery u annual depreciation = $2,000 u annual maintenance = $7,500 u other costs

Manual Tank Battery TC(x) = (2, , ) X

BreakEven TC A (x) = TC M (x)

BreakEven TC A (x) = TC M (x) 9, x = 9, x

BreakEven TC A (x) = TC M (x) 9, x = 9, x x = 476

BreakEven TC A (x) = TC M (x) 9, x = 9, x x = 476 x * = 145,000

Example

Average vs Marginal Cost x xTC xAC )( )(  x xTC xMC    )( )(

Example u Cost of running an automobile is TC(x) = $ x where $950 covers annual depreciation and maintenance and x is the number of miles driven per year

Example )( )(  xx xTC xAC 20.0 ).0950()( )(        x x x xTC xMC

Example Average vs Marginal Cost (Automobile) ,00020,00030,000 Miles per year cost Average Marginal

Marginal Returns

Example u Small firm sells garden chemicals. x = number of tons sold per year SP(x) = selling price per ton (to sell x tons) = $( x) TR(x) = total revenue at x tons = $( x) x TC(x) = total production cost for x tons = $(8, x)

Example TP(x) = total profit at x tons = TR(x) - TX(x) = (800x - 0.8x 2 ) - (8, x) = -0.8x x - 8,000 Compute a.x at which revenue is maximized b.marginal revenue at max revenue c.x at which profit is maximized d.average profit at max profit

Example TR(x) = -0.8x x a.max R tonsx x x xx x xTR ) 8.0( 0 )( 2       

Example TR(x) = -0.8x x b.Marginal Revenue MR(500) = -1.6(500) = $0

Example TP(x) = -0.8x x - 8,000 c.max profit )000,84008.( 0 )( 2        x x x xx x xTP

Example TP(x) = -0.8x x - 8,000 c.average profit tonAP xx x xx x /168$)250( /000, , )( 2    

Break-Even Analysis SiteFixed Cost/YrVariable Cost A=Austin $20,000 $50 S= Sioux Falls60, D=Denver80,00030 TC = FC + VC * X

Break-Even (cont) Break-Even Analysis 0 50, , , , , ,0001,5002,0002,5003,0003,5004,000 Volume Total Cost Austin S. Falls Denver

Class Problem A firm is considering a new product line and the following data have been recorded: Sales price$ 15 / unit Cost of Capital$300,000 Overhead$ 50,000 / yr. Oper/maint.$ 50 / hr. Material Cost$ 5 / unit Production 50 hrs / 1,000 units Planning Horizon 5 yrs. MARR 15% Compute the break even point.

Class Problem

Profit Margin = Sale Price - Material - Labor/Oper. = $ $50 / hr = $ 7.50 / unit 50 hrs 1000 units

Class Problem Profit Margin = Sale Price - Material - Labor/Oper. = $ $25 / hr = $ 7.50 / unit 50 hrs 1000 units , X 50,000

Class Problem Profit Margin = Sale Price - Material - Labor/Oper. = $ $25 / hr = $ 7.50 / unit 50 hrs 1000 units , X 50, ,000(A/P,15,5) + 50,000 = 7.5X 139,495 = 7.5X X = 18,600

Suppose we consider the following cash flow diagram: NPW = (P/A,15,5) = $ 17,325 Sensitivity ,000 35,000 i = 15%

Suppose we don’t know A=35,000 exactly but believe we can estimate it within some percentage error of + X. Sensitivity ,000 35,000(1+X) i = 15%

Then, EUAW = -100(A/P,15,5) + 35(1+X) > 0 35(1+X) > 100(.2983) X > Sensitivity ,000 35,000(1+X) i = 15%

Sensitivity (cont.) NPV vs. Errors in A (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50, Error X NPV

Now suppose we believe that the initial investment might be off by some amount X. Sensitivity (A o ) ,000(1+X) 35,000 i = 15%

Sensitivity (A o ) NPV vs Initial Cost Errors (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50, Error X NPV

Sensitivity (A & A o ) NPV vs Errors (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50, Error X NPV Errors in initial cost Errors in Annual receipts

Now suppose we believe that the planning horizon might be shorter or longer than we expected. Sensitivity (PH) ,000 35,000 i = 15%

Sensitivity (PH) NPV vs Planning Horizon (30,000) (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50, NPV PH

Sensitivity (Ind. Changes) NPV vs Errors (20,000) (10,000) 0 10,000 20,000 30,000 40,000 50, Error X NPV Errors in initial cost Errors in Annual receipts n=3 n=7 Planning Horizon MARR

Multivariable Sensitivity Suppose our net revenue is composed of $50,000 in annual revenues which have an error of X and $20,000 in annual maint. costs which might have an error of Y (i=15%) ,000 50,000(1+X) 20,000(1+Y)

Multivariable Sensitivity Suppose our net revenue is compose of $50,000 in annual revenues which have an error of X and $20,000 in annual maint. costs which might have an error of Y (i=15%) ,000 50,000(1+X) 20,000(1+Y) You Solve It!!!

Multivariable Sensitivity

EUAW = -100(A/P,15,5) + 50(1+X) - 20(1+Y) > 0 50(1+X) - 20(1+Y) > ,000 50,000(1+X) 20,000(1+Y)

Multivariable Sensitivity EUAW = -100(A/P,15,5) + 50(1+X) - 20(1+Y) > 0 50(1+X) - 20(1+Y) > X - 20Y > X > 0.4Y ,000 50,000(1+X) 20,000(1+Y)

Multivariable Sensitivity Unfavorable Favorable + 10%

Mutually Exclusive Alt. Suppose we work for an entity in which the MARR is not specifically stated and there is some uncertainty as to which value to use. Suppose also we have the following cash flows for 3 mutually exclusive alternatives. tA 1t A 2t A 3t 0(50,000)(75,000)(100,000) 118,000 25,000 32, ,000 25,000 32, ,000 25,000 32, ,000 25,000 32, ,000 25,000 32,000

Mutually Exclusive Alt. tA 1t A 2t A 3t 0(50,000)(75,000)(100,000) 118,000 25,000 32, ,000 25,000 32, ,000 25,000 32, ,000 25,000 32, ,000 25,000 32,000 MARR =NPV 1 NPV 2 NPV 3 4.0%30,133 36,296 42, %25,823 30,309 34, %21,869 24,818 27, %18,234 19,770 21, %14,886 15,119 15, %11,795 10,827 9, %8,937 6,857 4, %6,289 3, %3,831 (235)(4,300)

Mutually Exclusive Alt. NPV vs. MARR (10,000) 0 10,000 20,000 30,000 40,000 50, %5.0%10.0%15.0%20.0% MARR NPV NPV1 NPV2 NPV3