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2 decision making
1.
Decision Making © 2011
Lew Hofmann
2.
Overview
• Break-Even Analysis • Preference Matrices • Payoff Tables (Decision Tables) • Decision Trees © 2011 Lew Hofmann
3.
Break-Even Analysis
• Break-even analysis is used to compare processes by finding the volume at which two different processes have equal total costs. • Break-even point is the volume at which total revenues equal total costs. • Variable costs (c) are costs that vary directly with the volume of output. (EG: material costs, labor, etc.) • Fixed costs (F) are those costs that remain constant with changes in output level. (EG: Insurance, rent, property taxes, etc.) © 2011 Lew Hofmann
4.
Break-Even Analysis
• Gives you a comparison of Revenues and Total Costs over a range of operations/output. • Assumes all changes are linear • Fixed Costs (F) are assumed to be level and constant as output changes. • Variable Costs (c) are assumed to change linearly with output. • Revenues are assumed to change linearly with output. • In reality, no changes are linear, but the technique can still be helpful. © 2011 Lew Hofmann
5.
Break-Even Graph
Total Revenues fi ts Pro Total Costs Dollars Break-Even Point s s Lo Fixed Costs Volume of Output (Q) © 2011 Lew Hofmann
6.
Break-Even Analysis
in the real world. • Fixed costs increase incrementally as output capacity increases. • As capacity increases, periodic expansion of plant and equipment is required, insurance cost and taxes increase… • Variable Cost increase is curvilinear as output production increases. • As you purchase greater quantities of materials, you usually get quantity discounts. • Revenue increase is curvilinear as output increases. • Quantity discounts are given to larger sales. © 2011 Lew Hofmann
7.
The Complications of
Non-linearity Dollars Variable Costs Fixed Costs Volume of Output (Q) © 2011 Lew Hofmann
8.
Break-Even Analysis
(You don’t need the formula for exams.) • Q is the volume in units • c is the variable cost per unit • F is the total fixed costs • p is the revenue per unit • cQ is the total variable cost. (Variable cost per unit x Volume) • Total cost = F + cQ (Fixed costs + total Variable costs) • Total revenue = pQ (Revenue per unit x Volume) • Break even is where Total Revenue = Total costs: pQ = F + cQ © 2011 Lew Hofmann
9.
Break-Even Analysis
can tell you… ...if a forecast sales volume is sufficient to make a profit, or at least cover your costs. ...how low your variable cost per unit must be to break even, given current product price and sales-volume forecast. ...what the fixed cost need to be to break even. ...how price levels affect the break-even volume. © 2011 Lew Hofmann
10.
Hospital Example
A hospital is considering a new procedure to be offered, billed at $200 per patient. The fixed cost (F) per year is… $100,000, with variable costs at $100 per patient. How many patients do they need to cover their costs? (I.E. what is the break-even level for this service?) Q = F / (p - c) = 100,000 / (200-100) = 1,000 patients Where Q = total # of patients; F = fixed costs; p = revenue per unit; c = variable costs per patient © 2011 Lew Hofmann
11.
Using Excel Solver
• Select the Break-Even solver model on the L-Drive (under my name) • Select MGT 360 © 2011 Lew Hofmann
12.
Using Excel Solver
cont. • Select Excel Solver Models • Select the Break-Even Analysis model. © 2011 Lew Hofmann
13.
Enabling the Macros
Mac PC © 2011 Lew Hofmann
14.
Running The Model
• You will get this screen whether you enable the macros or not, but your answer won’t be correct if you don’t enable them. © 2011 Lew Hofmann
15.
Using the Excel
Solver, enter the data requested in the yellow blocks, and the answer will appear in the green block, along with the chart. Total Revenue Total Costs © 2011 Lew Hofmann
16.
Hospital Example
(solved using graphical method) 40,000 – Quantity Total Annual Total Annual 30,000 – (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) Dollars 20,000 – 0 100,000 0 2000 300,000 400,000 10,000 – 0– | | | | 500 1000 1500 2000 Patients (Q) © 2011 Lew Hofmann
17.
Quantity
Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 40,000 – (2000, 40,000) 30,000 – Total annual revenues 20,000 – DOLLARS 10,000 – 0– | | | | 500 1000 1500 2000 Patients (Q) © 2011 Lew Hofmann
18.
Quantity
Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 40,000 – (2000, 40,000) 30,000 – Total annual revenues (2000, 30,000) 20,000 – Total annual costs DOLLARS 10,000 – 0– Fixed costs | | | | 500 1000 1500 2000 Patients (Q) © 2011 Lew Hofmann
19.
Quantity
Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 40,000 – (2000, 40,000) Profits 30,000 – Total annual revenues (2000, 30,000) 20,000 – Total annual costs DOLLARS Break-even quantity is 1000 patients 10,000 – 0– Loss Fixed costs | | | | 500 1000 1500 2000 Patients (Q) © 2011 Lew Hofmann
20.
Per-patient cost of
the procedure. Sensitivity Analysis pQ – (F + cQ) Total annual revenues 200(1500) ––[100,000 + 100(1500)] 40,000 = $5,000 profit Profits 30,000 – Total annual costs 20,000 – DOLLARS Forecast (Q) = 1,500 10,000 – 0– Loss Fixed costs | | | | 500 1000 1500 2000 Patients (Q) © 2011 Lew Hofmann
21.
Two Processes and
Make-or-Buy Decisions • Breakeven analysis can be used to choose between two different processes • Also can be used to decide between using an internal process or outsourcing that process service. • The solution finds the point at which the total costs of each of the two processes are equal. • A forecast of sales (volume level) is then applied to see which alternative (process) has the lowest cost for that volume. © 2011 Lew Hofmann
22.
Two-Process Example
• Process #1 fixed costs for making widgets is $12,000, and the variable cost is $1.50 per unit. • Process #2 fixed costs for making widgets is $2400 and the variable cost is $2.00 per unit. • If expected demand is 25,000 widgets, which process is less expensive? © 2011 Lew Hofmann
23.
Breakeven for
Two Processes For any volume above 19,200 units, Process #1 should be used. © 2011 Lew Hofmann
24.
Fm – Fb
Q= cb – cm Breakeven for 12,000 – 2,400 Q= Two Processes 2.0 – 1.5 Q = 19,200 © 2011 Lew Hofmann
25.
Preference Matrix
• An analysis that allows you to rate alternatives by quantifying tangible and/or intangible criteria. • Criteria are ranked and weighted for each alternative being evaluated. • Each score is weighted according to its perceived importance to you, with the total weights typically equaling 100. • Thus it measures your preference. • Alternative with highest sum of the weighted scores is the one you most prefer. © 2011 Lew Hofmann
26.
Using the
Preference Matrix (A hypothetical example) • Problem: Where to go to dinner. • Possible Criteria: • Price • Quality • Distance • Atmosphere • Type of food © 2011 Lew Hofmann
27.
Weighting the Criteria
Criteria Weight Price 4 Quality 1 Distance 3 Atmosphere 1 Type of food 1 These are the criteria I selected, and the weights are how important each criteria is relative to the other criteria. I used a scale of 1-10 (1 being 10% of the weight), but any scale can be used. © 2011 Lew Hofmann
28.
Evaluating
McDonalds Criteria Weight Eval. Score (w) (e) (w)(e) Price 4 10 40 Quality 1 2 2 Distance 3 8 24 Atmosphere 1 2 2 Type of food 1 5 5 73 For simplicity, the valuation scale should be the same as the one for the weights. Evaluations are subjective, and can be individual preference or group-consensus. The score of 73 is used to compare with the scores from other options. © 2011 Lew Hofmann
29.
Preference Matrix
(New product evaluation) Management decides that a product Threshold score = 800 evaluation must have a total score of at least 800 to be acceptable. Performance Weights Scores Weighted Scores Criterion (A ) (B ) (A x B ) Market potential Unit profit margin Operations compatibility Competitive advantage Investment requirement Project risk © 2011 Lew Hofmann
30.
Preference Matrix
Establishing the criteria weights Threshold score = 800 Performance Weights Scores Weighted Scores Criterion (A ) (B ) (A x B ) Market potential 30 In this example, Unit profit margin 20 the most weight Operations compatibility 20 is given to a Competitive advantage 15 product’s market Investment requirement 10 potential. Project risk 5 © 2011 Lew Hofmann
31.
Preference Matrix
Rating a product These are the ratings for one of Threshold score = 800 the products being considered. Performance Weight Score Weighted Score Criterion (A ) (B ) ( A x B) Market potential 30 8 Unit profit margin 20 10 Operations compatibility 20 6 Competitive advantage 15 10 Investment requirement 10 2 Project risk 5 4 © 2011 Lew Hofmann
32.
Preference Matrix
Threshold score = 800 Performance Weight Score Weighted Score Criterion (A ) (B ) (A x B ) Market potential 30 8 240 Unit profit margin 20 10 200 Operations compatibility 20 6 120 Competitive advantage 15 10 150 Investment requirement 10 2 20 Project risk 5 4 20 © 2011 Lew Hofmann Total weighted score = 750
33.
Preference Matrix
Score does not meet the Threshold score = 800 threshold and is rejected. Performance Weight Score Weighted Score Criterion (A ) (B ) ( A x B) Market potential 30 8 240 Unit profit margin 20 10 200 Operations compatibility 20 6 120 Competitive advantage 15 10 150 Investment requirement 10 2 20 Project risk 5 4 20 © 2011 Lew Hofmann Weighted score = 750
34.
© 2011 Lew
Hofmann
35.
Decision-Making
Terminology • Alternatives • Possible solutions or alternatives to a problem. • States of Nature (Chance Events) • Events effecting the outcome, but which the decision-maker cannot control. • EG: What the stock market is going to do. • Payoffs • Profits, losses, costs, etc. that result from implementing an alternative. © 2011 Lew Hofmann
36.
Decision-Making
Contexts • Certainty • Only one state of nature can occur. • You have complete knowledge about the outcome. (Break-even analysis is decision making under certainty.) • Risk • Two or more states of nature • You know the probabilities of their occurrence (Expected-value analysis is decision making under risk.) • Uncertainty • The number of states of nature may be unknown. • Probabilities of occurrence are unknown. (Payoff tables are a good example.) © 2011 Lew Hofmann
37.
A Continuum of
Awareness Decreasing Knowledge about the problem situation Certainty Risk Uncertainty Only 1 state More than one States of nature of nature state of nature may be unknown, with known or a least their probabilities probabilities are unknown. © 2011 Lew Hofmann
38.
Payoff Tables
Under Uncertainty States of Nature Bear Level Bull Market Market Market Alternatives Stock A 400 500 600 Stock B 200 400 1100 Stock C 100 500 900 With uncertainty, you don’t know the probabilities for the states of nature. © 2011 Lew Hofmann
39.
Payoff Tables
Under Uncertainty • Maximax • The optimist’s approach • Maximin • The pessimist’s approach • Minimax Regret • Another pessimistic approach © 2011 Lew Hofmann
40.
Maximax Approach
Pick the best of the best payoffs Bear Level Bull Market Market Market Stock A 400 500 600 Stock B 200 400 1100 Stock C 100 500 900 © 2011 Lew Hofmann
41.
Maximin Approach
Pick the Best of the Worst payoffs Bear Level Bull Market Market Market Stock A 400 500 600 Stock B 200 400 1100 Stock C 100 500 900 © 2011 Lew Hofmann
42.
Minimax Regret Approach
Minimizes the regret you would have from making the wrong choice. Bear Level Bull Market Market Market Stock A 400 500 600 0 0 500 Stock B 200 400 1100 200 100 0 Stock C 100 500 900 300 0 200 Determine the maximum regret, if any, you could have for each payoff. © 2011 Lew Hofmann
43.
Regret Matrix
Compute total regrets for each alternative and select the one with the smallest total regret. Bear Level Bull Market Market Market Stock A 0 0 500 500 Stock B 200 100 0 300 Stock C 300 0 200 500 Add across each row to get the total regret for each alternative. Pick the alternative that has the LEAST regret. © 2011 Lew Hofmann
44.
Expected Value Analysis
Decision Making Under Risk! Bear Level Bull Market Market Market Probabilities .2 .6 .2 Stock A 400 500 600 Stock B 200 400 1100 Stock C 100 500 900 © 2011 Lew Hofmann
45.
Expected Value Analysis
Computing Expected Values Bear Level Bull EV Market Market Market Probabilities .2 .6 .2 Stock A 400x.2 500x.6 600x.2 =80 =300 =120 500 Stock B 200x.2 400x.6 1100x.2 =40 =240 =220 500 Stock C 100x.2 500x.6 900x.2 =20 =300 =180 500 © 2011 Lew Hofmann
46.
Expected Value Analysis
using the Excel Solver Why does the solver model pick stock A? (All three have the same expected value!) © 2011 Lew Hofmann
47.
Probability Distributions
as a measure of risk. Probabilities B CA .6 .5 Probability distributions for .4 the alternatives .3 C B A A C B .2 .1 100 200 300 400 500 600 700 800 900 1000 1100 Expected Payoffs A B C © 2011 Lew Hofmann
48.
Standard Deviation
as a measure of risk The lower the standard deviation, the less likely it is that payoffs will deviate from the mean. Alternative Standard Deviation Stock A 63.25 Stock B 316.93 Stock C 252.98 © 2011 Lew Hofmann
49.
Coefficient of Variation
• Standard Deviation only works as a measure of risk when the expected values you obtain are relatively similar. • Coefficient of Variation must be used to measure risk when the expected values are widely different. © 2011 Lew Hofmann
50.
Using Coefficient of
Variation Standard Deviation Coefficient of Variation = Expected Value Expected Coeff. Of Std. Dev. Value Variation Stock A 63.25 500 0.1265 Stock B 316.93 500 0.63386 Stock C 252.98 500 0.50596 Since the expected values are the same in this example, there is no need to use Coefficient of Variation. © 2011 Lew Hofmann
51.
Using Coefficient of
Variation Expected Standard Coefficient R.O.I Value Deviation of Variation X 100 15% 23.5 .235 Y 100,000 15% 12,600 .126 Smaller coefficient of variation indicates less risk! In this example the Expected Values of the alternatives are widely different, so we need to use Coefficient of Variation to make our comparison. © 2011 Lew Hofmann
52.
MaxiMin Decision
(another example) Events (Uncertain Demand) Alternatives Low High Small facility 200 270 Large facility 160 800 Do nothing 0 0 1. Look at the payoffs for each alternative and identify the lowest payoff for each. 2. Choose the alternative that has the highest of these. (the maximum of the minimums) © 2011 Lew Hofmann
53.
MaxiMax Decision
Events (Uncertain Demand) Alternatives Low High Small facility 200 270 Large facility 160 800 Do nothing 0 0 1. Look at the payoffs for each alternative and identify the “highest” payoff for each. 2. Choose the alternative that has the highest of these. (the maximum of the maximums) © 2011 Lew Hofmann
54.
MiniMax Regret
Events (Uncertain Demand) Alternatives Low High Small facility 200 270 Large facility 160 800 Do nothing 0 0 Look at each payoff and ask yourself, “If I end up here, do I have any regrets?” Your regret, if any, is the difference between that payoff and the best choice you could have made with a different alternative, given the same state of nature (event). © 2011 Lew Hofmann
55.
MiniMax Regret
Events (Uncertain Demand) Alternatives Low High Small facility 200 270 Large facility 160 800 Do nothing 0 0 If you chose a small If you chose a large facility and facility and demand is demand is low, you regret you didn’t low, you have zero build a small facility. Your regret is regret. You could not 40, which is the difference between have done better with the 160 you got and the 200 you a different alternative. could have gotten. © 2011 Lew Hofmann
56.
MiniMax Regret
Events If you chose a small (Uncertain Demand) facility and demand is high, you forgo the Alternatives Low High higher payoff of 800, and thus have a Small facility 200 270 regret of 530. Large facility 160 800 Do nothing 0 0 Regret Matrix Events Building a large Alternatives Low High Total Regrets facility offers the Small facility 0 530 530 least regret. Large facility 40 0 40 Do nothing 200 800 1000 © 2011 Lew Hofmann
57.
Expected Value
Decision Making under Risk Multiply each payoff times the probability of occurrence its associated event. Events Alternatives Low High (0.4) (0.6) Small facility 200 270 200*0.4 + 270*0.6 = 242 Large facility 160 800 160*0.4 + 800*0.6 = 544 Do nothing 0 0 Select the alternative with the highest weighted payoff. © 2011 Lew Hofmann
58.
Decision Trees
• Decision Trees are schematic models of alternatives available along with their possible consequences. • They are used in sequential decision situations. • Decision points are represented by squares. • Event points (states of nature) are represented by circles. © 2011 Lew Hofmann
59.
Decision Trees
E1& Probability Payoff 1 E2& Probability Payoff 2 1 e ativ E3& Probability Payoff 3 rn Alte Alternative 3 Payoff 1 Alternative 4 1 2 Payoff 2 ty 1st Al bi li Alternative 5 decision te rn ba Possible Payoff 3 at Pro 2nd decision iv & e E1 2 E2& Probability = Event node Payoff 1 E3& Probability Payoff 2 = Decision node © 2011 Lew Hofmann
60.
.2
$400 x .2 = $80 Bear Market Level Market .6 $500 $500 x .6 = $300 Buy stock A .2 Bull Market $600 x .2 = $120 Bear Market .2 $200 x .2 = $40 Buy stock B Level Market .6 $500 $400 x .6 = $240 Bull Market .2 $1100 x .2 = $220 Bear Market .2 $100 x .2 = $20 Buy stock C Level Market .6 $500 x .6 = $300 $500 Bull Market .2 $900 x .2 = $180 © 2011 Lew Hofmann
61.
Decision Trees
•After drawing a decision tree, we solve it by working from right to left, starting with decisions furthest to the right, and calculating the expected payoff for each of its possible paths. • We pick the alternative for that decision that has the best expected payoff. •We “saw off,” or “prune,” the branches not chosen by marking two short lines through them. •The decision node’s expected payoff is the one associated with the single remaining branch. © 2011 Lew Hofmann
62.
Sample Problem
A retailer must decide whether to build a small or a large facility at a new location. Demand can either be low or high, with the probabilities estimated to be 0.4 and 0.6 respectively. If a small facility is built and demand is high, the manager may choose not to expand (payoff = $223,000) or expand (payoff = $270,000) However, if demand is low, there is no reason to expand. (payoff = $200,000) If a large facility is built and demand is low, the retailer can do nothing ($40,000) or stimulate demand by advertising. Advertising is estimated to have a 0.3 chance of a modest response ($20,000) and a 0.7 chance of a large response ($220,000). If a large facility is built and demand is high, the payoff is $800,000. © 2011 Lew Hofmann
63.
Drawing the Tree
A retailer must decide whether to build a small or a large facility at a new ty ci li location. l fa al Sm There are two choices: 1 Build a small facility or La build a large facility. rg e fa ci lit y © 2011 Lew Hofmann
64.
The “event” (state
of nature) in this example Drawing the Tree is demand. It can be either high or low. Low demand [0.4] $200 Hi gh ty d i li [0 em c .6 an Don’t expand l fa ] d al $223 Sm 2 Expand $270 1 La rg Demand can either be small or large, with the e fa probabilities estimated to be 0.4 and 0.6 respectively. ci lit y If a small facility is built and demand is high, the manager may choose not to expand (payoff = $223,000) or expand (payoff = $270,000) However, if demand is low, there is no reason to expand. (payoff = $200,000) © 2011 Lew Hofmann
65.
If a large
facility is built and demand is low, the retailer can do nothing ($40,000) or stimulate demand by advertising. Advertising is estimated to have a Completed Drawing 0.3 chance of a modest response This is the completed tree. ($20,000) and a 0.7 chance of a Low demand [0.4] Now we start pruning it large response ($220,000). $200 from the right. We will begin with decision #3. Hi gh ty d i li [0 em fa c .6 an ] Don’t expand The state of nature for l d al $223 the 3rd decision is the Sm 2 possible response to the Expand advertising $270 Do nothing 1 La $40 rg Advertise e d Modest response [0.3] fa an 3 $20 ci m lit y de 4] w 0. Lo [ Sizable response [0.7] $220 If a large facility is built and demand is high, the High demand [0.6] $800 payoff is $800,000. © 2011 Lew Hofmann
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Solving Decision #3
Low demand [0.4] $200 Hi gh ty d i li [0 em c .6 an Don’t expand l fa ] d al $223 Sm 2 Expand $270 Do nothing 1 0.3 x $20 = $6 La $40 rg Advertise e d Modest response [0.3] fa an 3 $20 ci m lit y de 4] w 0. The 40% probability Lo [ Sizable response [0.7] of low demand is $6 + $154 = $160 $220 not yet considered 0.7 x $220 = $154 since it is the same for both advertising High demand [0.6] © 2011of nature. states Lew Hofmann $800
67.
Solving Decision #3
Low demand [0.4] $200 Hi gh We eliminate the “do ty d ili [0 em nothing” option since it has a ac .6 an ] Don’t expand lf d lower payoff than does al $223 Sm advertising. 2 Expand $270 Do nothing 1 La $40 rg Advertise e d Modest response [0.3] fa an 3 $20 ci m lit y de 4] w 0. $160 Lo [ Sizable response [0.7] $160 $220 High demand [0.6] © 2011 Lew Hofmann $800
68.
Here there is
no state of nature involved with expanding or not expanding. Solving Decision #2 They are simply choices if we end up with high demand. Low demand [0.4] $200 Hi gh ty d i li [0 em Expanding has a c .6 an Don’t expand l fa ] d higher expected al $223 Sm value than not 2 Expand expanding. $270 Do nothing $270 1 La $40 rg Advertise e d Modest response [0.3] fa an 3 $20 ci m lit y de 4] w 0. $160 Lo [ Sizable response [0.7] $160 $220 High demand [0.6] © 2011 Lew Hofmann $800
69.
Low demand expected
value of $80 is added to the high demand expected value of $162 Solving Decision #1 Low demand [0.4] $200 x 0.4 = $80 $242 Hi gh ci li ty d [0 em .6 an Don’t expand $242 l fa ] d al $223 Sm 2 Expand $270 $270 x 0.6 = $162 Do nothing 1 La $40 rg Advertise e d Modest response [0.3] fa an 3 $20 ci m lit y de 4] . $160 Low [0 Sizable response [0.7] $160 $220 High demand [0.6] © 2011 Lew Hofmann $800
70.
Solving Decision #1
Low demand [0.4] $200 The expected value of $242 high demand for the large Hi facility ($480) is added to gh the expected value of low ty d i li [0 em demand for the large c .6 an Don’t expand l fa ] d facility ($64). al $223 Sm 2 Expand $270 Do nothing $270 1 La $40 rg Advertise e d Modest response [0.3] fa an 3 $20 ci m lit y de 4] . $160 Lo w [0 Sizable response [0.7] 0.4 x $160 = $64 $160 $220 $544 High demand [0.6] © 2011 Lew Hofmann $800 x 0.6 = $480
71.
Solving Decision #1
Low demand [0.4] $200 The expected value of Hi building a small facility gh ty d can now be compared to ili $242 [0 em c .6 an Don’t expand the expected value of l fa ] d al $223 building a large facility. Sm 2 Expand $270 Do nothing $270 1 La $40 rg Advertise e d Modest response [0.3] fa an 3 $20 $544 ci lit y m de 4] . ow [0 $160 L Sizable response [0.7] $160 $220 $544 High demand [0.6] $800 © 2011 Lew Hofmann
72.
Advantages of
Decision Trees • Gives structure to a problem situation • Visual representation of the options • Forces management to consider each alternative and compare them • Optimum courses of action are apparent. • The only technique for dealing with multiple (sequential) decisions. © 2011 Lew Hofmann
73.
Disadvantages of
Decision Trees • Many problems are too complex for visual display • Complex trees are only computational • Subject to estimation errors (As with any probabilistic decision tool) • Only as good as the data used. (True with any model.) © 2011 Lew Hofmann
74.
Homework Assignment #1
Six problems: Due in class next week this time. 1. Breakeven 2. Two Processes Recommend using the Excel Solver for the above problems. 3. Preference Matrix 4. Payoff Table 5. Decision-Tree problem #1 (a,b) 6. Decision-Tree problem #2 (a,b) Do these manually. On the exam you will not have the use of the computer program for analyzing preference matrices, payoff tables or decision trees. Doing these problems on the computer may NOT adequately prepare you for doing the problems on the exams. © 2011 Lew Hofmann
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1. Break Even
Analysis Mary Williams, owner of Williams Products, is evaluating whether to introduce a new product line. After thinking through the production process and the costs of raw materials and equipment, she estimates the variable costs of each unit produced and sold to be $6 and the fixed costs per year at $60,000. (Solver won’t provide answers to b, c, or d.) a.If the selling price is set at $18 each, how many units must be produced and sold for Williams to break even? b.Williams forecasts sales of 10,000 units for the first year if the selling price is $14 each. What would be the total contribution to profits from this new product during the first year? c.If the selling price is set at $12.50, forecast sales is 15,000 units. Which pricing strategy ($14 or $12.50) would result in the greater total contribution to profits? d.What other considerations would be crucial to the final decision about making and marketing the new product? © 2011 Lew Hofmann
76.
2. Two Processes
Use Excel Solver Gabriel Manufacturing must implement a manufacturing process that reduces the amount of toxic by-products. Two processes have been identified that provide the same level of toxic by-product reduction. The first process would incur $300,000 of fixed costs and $600 per unit of variable costs. The second process has fixed costs of $120,000 and variable costs of $900 per unit. a.What is the break-even quantity beyond which the first process is more attractive? b.What is the difference in total cost if the quantity produced is 800 units? (You can either estimate this from the solver solution graph, or use the formula given in slide #21.) © 2011 Lew Hofmann
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3. Preference Matrix
You can use the Solver software or do it on a spreadsheet. Axel Express, Inc. collected the following information on two possible locations for a new warehouse (1 = poor, 10 = excellent). a. Which location, A or B, should be chosen on the basis of the total weighted score? b. If the factors were weighted equally, would the choice change? © 2011 Lew Hofmann
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4. Payoff Table
You can use the Solver software or do it on a spreadsheet, but you will need to know how to solve it manually on the test. Build-Rite Construction has received favorable publicity from guest appearances on a public TV home improvement program. Public TV programming decisions seem to be unpredictable, so Build-Rite cannot estimate the probability of continued benefits from its relationship with the show. Demand for home improvements next year may be either low or high. But they must decide now whether to hire more employees, do nothing, or develop subcontracts with other home improvement contractors. Build-Rite has developed the following payoff table. Alternative Low Moderate High Hire ($250,000) $100,000 $625,000 Subcontract $100,000 $150,000 $415,000 Do Nothing $ 50,000 $ 80,000 $300,000 Which alternative is best, according to each of the following criteria? a. Maximin © 2011 Lew Hofmann b. Maximax c. Minimax regret
79.
5. Decision Tree
#1 Do this manually (no computer). A manager is trying to decide whether to buy one machine or two. If only one is purchased, and demand proves to be excessive, the second machine can be purchased later. Some sales will be lost, however, because the lead time for producing this type of machine is six months. In addition, the cost per machine will be lower if both are purchased at the same time. The probability of low demand is estimated to be 0.20. The after-tax net present value of the benefits from purchasing the two machines together is $90,000 if demand is low, and $180,000 if demand is high. If one machine is purchased and demand is low, the net present value is $120,000. If demand is high, the manager has three options. Doing nothing has a net present value of $120,000; subcontracting, $160,000; and buying the second machine, $140,000. a.Draw a decision tree for this problem. b.How many machines should the company buy initially, and what is the expected payoff for this alternative? © 2011 Lew Hofmann
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6. Decision Tree
Problem #2 Do this manually (no computer). A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being 0.25, 0.40, and 0.35 respectively. A small facility is expected to earn an after-tax, net-present value of $18,000 if demand is low, and $75,000 if demand is medium or high. Expanding a small facility to medium size after demand is established as medium or high will only yield an after-tax net profit of $60,000. Expanding it to a large facility if demand is high, nets $125,000. Initially building a medium-sized facility and not expanding it would result in a $25,000 loss if demand is low, but net $140,000 in medium demand and $150,000 in high demand. Expanding to a large facility at that point would only net $145,000. Building a large facility will net $220,000 if demand is high; $125,000 if demand is medium, and is expected to lose $60,000 if demand is low. a.Draw an analyze a decision tree for this problem. b.What should management do to achieve the highest expected payoff? © 2011 Lew Hofmann
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