Business & CommercialAwareness

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Lecture 6: Decision Making 2 Quantitative

j.a.g.willard@herts.ac.uk

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Learning outcomes• To understand the role played by quantitative

techniques in decision making

• To understand a range of quantitative decision making techniques commonly used in business

• To be able to use the simpler quantitative techniques which will support decision making

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The role of quantitative decisions

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strategicMany complex factorsNon-numerical relationshipsJudgment and experience needed

operationalSmaller decision scope

Good approx. by numerical modelsAssumptions require qualitative input

tacticalMix depends on decision

ALL decisions are a mix of quantitative and qualitative factorsIn general the more that decisions deal with the whole business . . . . . . . the greater the input from the qualitative factorsScenario analysis and financial models have wide strategic usePoor decisions often result from inappropriate mix of the 2 types

How are quantitative tools used?

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Collect data

Check data

Select Model

Use Model

Check Output

Reality Check

Input to Decision

In many business decisions the quantitative input has errors

The check boxes (in dark grey) are essential to ensure the quality of the

decision

Quantitative decision tools

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Modelling Tool

Application

Break-even analysis Identifies at what point an investment project would move from loss to profit, for instance what volume, price, product mix are required

Pay-off Period Identifies when investment projects would move into profit ie: when up front investment and the ongoing costs are paid back from income

Cost-benefit Identifies whether an investment project will make a loss or a profit. This can be over the whole lifetime of the investment or over a specified number of years. Some businesses require an investment to return an overall profit over the first X years or they will not invest

Moving averages A forecasting tool which can be used to generate estimates of future business values (eg sales, income). It averages these quantities over the past N months/quarters/years and gives a smoothed forecast

Linear regression A simple but powerful method to forecast a business quantity which is increasing or decreasing over time – also called trend analysis

MCDA

(Multiple Criteria Decision Analysis)

The Solution Matrix is an example. It is a pseudo quantitative tool which allows selection of the best alternative when considering qualitative factors and quantitative factors which cannot be aggregated (eg labour availability, proximity to customers, greenness)

Financia

lForecastin

gMulti

Factor

See weekly reading for descriptions of a wider range of numerical tools commonly used in business

XProduct Y

INVESTMENT (£m)

Product ZW

W

V

V

X

Break-even or Switchover Analysis

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This technique is used if you need to determine a switchover decision point

• Imagine 2 investment options, Product Y and Z• For each, the more we invest the more profit we create• If we can only invest in one, which one? - and how much do we invest?

• Plot the profit against the cost of investment for each product option• Where the 2 lines cross (W-W) is where it becomes better to invest in Product Y• Otherwise invest in Z. But if you invest less than V-V you make a loss• If you have the available funds invest up to X in Product Y

Pay-off period

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This very simple technique is used if you need to determine when you start to make a cumulative profit on an investment

•Tabulate cost, income and net position on a monthly, quarterly or yearly basis•Where the cumulative net position goes positive is the pay-off period•This is important to a business as it is the point at which they will no longer lose money from an investment•Business environments are volatile and can quickly reduce investment viability•The sooner pay-off occurs, the lower the risk

In £k Year 1 Year 2 Year 3 Year 4

Cost 745 797 995 984

Income 600 780 1,134 1,160

Net -145 -17 +139 +176

Cum Net -145 -162 -23 +153

Pay-off does not occur until Year 4This is a risky investment

-1000

0

1000

2000

3000

4000

Year 1 Year 2 Year 3 Year 4

Cost-Benefit

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This accounting based technique is used to determine whether an investment will be profitable. It can also be used to vary key inputs to look at the sensitivity of the profit to possible future changes

•List all the costs and all the incomes

•Separate these into sub-categories – but not too finely divided

•Identify the spend per time period – eg monthly, quarterly, yearly

•Tabulate, calculate the totals and compare cost and income total

Enhancements

Ratios2 important ratios

Cost/Income: Total cost Total Income

Must be < 100% or no profits

Profit margin:100% - cost/income% of sales which are profitCan be calculated overall or as a marginal value for one sales unit

What-if analysisBuild your cost-benefit using a spreadsheetEnter the key variables in cellsChange these variablesThe sensitivity of the investment to changes in key variables can be determined eg:Price, market share, manufacturing cost, raw material costs etc

Time value of moneyMoney value reduces over time£1 today buys less in 1 yearDriven by inflation & interest rateReduce money figures by x% (x is the discount rate)In Year 2 reduce by another x%In Year Z it will = value/(1+x)Z

Cost-Benefit example

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Costs (£k) Year 1 Year 2 Year 3 Year 4

Manufacturing 400 500 640 660

Advertising 150 100 120 90

Warehousing 50 50 75 75

Retail costs 15 10 12 9

Overheads 130 137 148 150

TOTAL COSTS (£k) 745 797 995 984

Sales volume (k) 100 130 180 200

Price(£) £6.00 £6.00 £6.30 £5.80

TOTAL INCOME (£k) 600 780 1,134 1,160

PROFIT (£k) -145 -17 +139 +176

Cost/Income Years 1-4 = 3521/3674 = 96%. In Year 4 = 984/1160 = 85%Profit margin in Year 1 = -145/600 = -24%. In Year 4 = 176/1160 = 15%

Total =£3,521k

Total =£3,674k

Forecasting

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Business decisions are future orientated. They involve the allocation of resources (time, money, people) to generate an improved performance.

It is not possible to know what will happen in the future, so businesses estimate the key variables – prices, interest rates, sales, competitor activity

•This is called Time Series Forecasting

•It can be fairly accurate given: good data + the right method

•But do not forecast too many months ahead as environments change

There are 4 basic types of Time Series Forecast

stationary trend seasonal cyclical

to be studied on the module refer to reading list – if interested

Moving average forecasting

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USE: If the business variable is changing up and down randomly

RESTRICTIONS: Variability should be constant over time

Time periods must be of equal length – month/quarter/year

No trend, seasonal activity or cyclical pattern

HOW IT WORKS: Choose a number of time periods over which to average

This should usually be in the range 2-6

Collect historical data covering this number of periods

Calculate the average of these pieces of data

This is the moving average forecast for the future

When you get the next real piece of data do it again

This is a revised forecast replacing the one last you calculated

Update your forecast each time you have a new piece of data

THE OPTIMUM: Try all averaging over all numbers of periods between 2 and 6

Add the errors (forgetting any minus signs)

The best is the one with the lowest average error

Moving averages – example

what is the price forecast for Year 5?

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Average over 2 years: (6.30 + 5.80) / 2 = £6.050Average over 3 years: (6.00 + 6.30 + 5.80) / 3 = £6.033Average over 4 years: (6.00 + 6.00 + 6.30 + 5.80) / 4 = £6.025

Not much difference, any of them will be okay

But maybe the price in year 4 is the best guide as it is the most recent price This is really the Moving Average over 1 period – called a Naïve Forecast

Year 1 Year 2 Year 3 Year 4

Sales volume (k) 100 130 180 200

Price(£) £6.00 £6.00 £6.30 £5.80

Check restrictions: Price varies randomly, variability not increasing

Trend forecasts by linear regression

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USE: If the business variable is changing steadily over time

RESTRICTIONS: Variability should be constant over time

Time periods must be of equal length – month/quarter/year

A seasonal activity or cyclical pattern is okay but this must be

modelled separately and the impact added into the trend forecast

HOW IT WORKS: To be accurate you need an Excel spreadsheet

Plot a line or scatter graph of your business data

Right click on the data plot line

Select “Add Trendline” and then the “Display equation on Chart” box

Your graph shows the equation of the forecast line, eg:

y = 0.75x + 45 or in a more general format y = Ax + B

To forecast into the future substitute the value of the time period for x

EG: in the above equation, in time period 7 y = 0.75 x 7 + 45 = 50.25

THE OPTIMUM: Excel has done this for you automatically

Linear regression – example

what is the sales volume forecast for Year 5?

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Year 1 Year 2 Year 3 Year 4

Sales volume (k) 100 130 180 200

Price(£) £6.00 £6.00 £6.30 £5.80

Check restrictions: Volume is increasing steadily, variability not increasing

From Excel the equation is y = 35x + 65or: Sales = 35 time + 65

in Year 5: Sales = 35 x 5 + 65 = 240 (in thousands)

Multiple criteria decision analysis

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USE: Where there are several quantitative decision variables which

cannot be added together as they have different units

eg: costs (£), market share (%), distance from supplier (km)

Or where decision variables are qualitative but can be scored out of 10

Or both of the above

HOW IT WORKS: This is the methodology of the Solution Matrix used to evaluate ideas

It will also be seen again when we look at Risk Evaluation

• Identify the decision criteria

• Weight their importance to the decision, relative to each other

• Score each investment option out of 10: good = 10 poor = 1

• Multiply the scores by the weights for each option and add them

• The investment option with the highest score is the best one

The scores and weights can be allocated by group decision, by

averaging the scores of several decision makers or as the

least preferred method, by one person – though this is subject to bias

MCDA - example

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Criterion Investment 1 Investment 2 Investment 3

Cost £10m £12m £15m

Income £25m £27m £32m

Labour Availability Within 10 miles No skilled labour Within 20 miles

Pay-off period 3 years 3.5 years 4 years

Environmental impact

Significant Low initially but becoming significant

Limited

Three investment options have been short-listed. The key criteria have been selected by a panel of decision makers. How each of the investment options performs against these criteria is tabulated below.

Which is the best investment option?

MCDA - solution

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Criteria Weight Investment A Investment B Investment C

Score Utility Score Utility Score Utility

Cost 10 8 80 7 70 5 50

Income 9 6 54 7 63 8 72

Labour 5 8 40 2 10 4 20

Pay-off period 6 7 42 5 30 4 24

Environment 4 4 16 5 20 9 36

TOTAL 232 193 202

• The weights and scores for the options are determined by the decision panel• This is best done if each member assesses the score against each criterion• These are averaged to give the results – saving a lot of debate• Weights or scores with large differences are discussed and agreed• Above, Investment A is the best . . . .

. . . . but if labour supply & cost worsened the decision may be marginal

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In this lecture we have learned:•Where quantitative decisions are needed in business•The process used to obtain quantitative decision inputs•The range of commonly used quantitative decision tools•How to use some of the simpler but common tools:

• Break-even analysis

• Pay-off period

• Cost-benefit analysis

• Forecasting by moving averages and linear regression

• Multi-criteria decision analysis for:

• numerical criteria which cannot be added together

• subjectively assessed qualitative criteria

Summary