Chapter 11: Quantitative Techniques

Question 1

What is high/low analysis

Answer 1

analysing semi-variable costs into fixed/ variable elements based on historic info of costs at different levels

Question 2

What are the steps for high/low analysis?

Answer 2

Step 1: select the highest & lowest activity level

Step 2: find variable cost/ unit

Step 3: Find the fixed cost (use either high or low activity)

Step 4: Use the VC and FC to forecast total cost for a specified level of activity

Question 3

What is the formula for variable cost/ unit

Answer 3

(cost at high level- cost at low level)/ (high level activity- low level activity)

Question 4

What are the advantages of high/low analysis?

Answer 4

1) simple to calculate
2) easy to understand & use

Question 5

What are the disadvantages of high/low analysis?

Answer 5

1) assumes activity is only factor affecting cost
2) assumes historical costs are reliable for future prediction
3) uses only 2 values- results could be distorted due to random variations in these values

Question 6

What is wright’s law

Answer 6

as cumulative output doubles, the cumulative average time per unit fall to a fixed% (aka learning rate) of the previous average time

Question 7

What is the learning curve?

Answer 7

mathematical expression that as complex & labour intensive procedures are repeated, unit labour times decrease

Question 8

What are limitations of the learning curve model?

Answer 8

1) Process is labour intensive- modern manufacturing = capital intensive (machines) so labour effect can’t apply if speeds limit production time

2) Product is new- now products have short lives so new products are introduced on a regular basis - more probable that there’s a learning effect

3) Product is complex- more likely learning curve will be significant so longer to reach a steady state/ plateau

4) Production is repetitive (no breaks) -JIT is multi-skilled/ multi tasked workers so some benefits of a single tasked environment can be lost. Producing in small batches to meet customer demand = loss of learning effect

Question 9

Steps to complete the cumulative average (increase units)

Answer 9

Step 1: calc cumulative average time for target production

Step 2: calc total cumulative time

Step 3: Time to make X units more

Question 10

If output double what method do we use?
If we need to find an intermediate amount what method do we use?

Answer 10

Doubles= tabular approach
Intermediate= algebraic approach

Question 11

What is the formula for the algebraic approach?

Answer 11

Y= a * X^b

X= cumulative number of units
Y= cumulative average time per unit to produce x units
A= time required to produce the first unit of output
B= index of learning = log r/ log 2 where r= learning rate expressed as a decimal

Question 12

What algebraic formula can be used if we have a specific number of times the number of units has doubled?

Answer 12

Y = a * r^n

Y= cumulative average time per unit to produce X units
A= time required to produce the first unit of output
n= number of times the units have doubled since the first unit was produced
R= learning rate expressed as a decimal

Question 13

How does the learning effect apply to pricing decisions

Answer 13

prices will be set too high if based on the cost of making the first few units

Question 14

How does the learning effect apply to work scheduling

Answer 14

Less labour per unit will be required as more are made
management implications e.g redundancy

Question 15

How does the learning effect apply to product viability

Answer 15

viability may change depending on a learning effect
e.g could make a loss on intial units but overtime the labour cost per unit can decrease to make a profit with higher volumes

Question 16

How does the learning effect apply to standard setting

Answer 16

if there’s a learning effect but it’s ignored the standard cost can be too high
Learning effects can make standard setting difficult
Ignoring a learning effect can lead to calculating planning & operating variances

Question 17

How does the learning effect apply to budgeting

Answer 17

need to take the effect into account
if labour effect is taken into account to reduce labour budget but working capital may be required sooner than expected

Question 18

How does a steady rate affect the learning curve

Answer 18

Only good for a certain range of products
Machine efficiency can restrict further improvements or can be a go-slow arrangement

Once steady state is reached - direct labour hours won’t reduce further = basis for budget

Question 19

What is the experience curve

Answer 19

Extends the learning curve beyond direct labour
Relates directly to cost
Shows how total cost per unit declines as output increases

Total cost= all OH so cost reduction via substitution, factory size, tech etc will be reflected

Question 20

What is linear regression

Answer 20

uses formula to estimate the linear relationship between variables (models dependence of variables)

Shown as an equation and then graphically

Question 21

What is regression analysis

Answer 21

Estimates the line of best fit in data

Minimises the sum of the squares of deviations of the line from the observed data (aka leadt squares method)

Make forecasts when a linear relationship between variables is assumed & historical data is available for analysis

Question 22

What are the 2 relationships of linear regression

Answer 22

1) Time series & trend line - x= time, y= sales, production volume or cost

2) Total cost ( FC & VC) - alternative to high/low method but more accurate (based on more items of historical data)
X= volume of activity
Y= total cost
A= amount of FC
B= Variable cost per unit of activity

Question 23

Limitation of regression analysis

Answer 23

Based on sample data
If we select a different sample output is likely to be different so need a stable relationship between variables

Question 24

What is interpolation

Answer 24

Value of x is within the range of our original data
safer than extrapolation

Question 25

What is extrapolation

Answer 25

Value of x is outside the range of our original data

Question 26

What are the limitations of simple linear regression?

Answer 26

1) Assumes a linear relationship
2) Only measures 2 variables - dependent variables is normally impacted by several independent variables
3) Shouldn’t be used for extrapolation- unreliable
4) Assumes historical trends continue into future - sudden market changes not immediately reflected - use experience, intuition & judgement to amend forecasts
5) interpolated predictions only reliable if there’s a sig correlation
6) Inflation- need to adjust historic forecast

Question 27

What is the equation to cost adjust

Answer 27

Index level to which cost will be adjusted/ actual index level of costs

Question 28

What is correlation

Answer 28

establishing how strong a relationship is

Question 29

What is the boundary for a strong correlation

Answer 29

> 0.8 or r<-0.8

Question 30

What is the co-efficient of determination

Answer 30

proportion of total variation in the y variable that is explained by the regression equation
Between 0 to 1

e.g if it’s a function of machine hours at 0.8 then 80% of total variation is from machine hours and 20 % is something else (error term)

Question 31

What are the limitations of correlation

Answer 31

1) Misleading- it’s based on just a sample not whole population. Could be random sampling errors

2) correlation and causality = different. Because they’re correlated doesn’t mean it caused it

3) r= 0 could miss detecting an obvious relationship if it’s not a linear one

Question 32

What are time series analysis

Answer 32

based on historical data
Assumptions on past patterns e.g seasonality to forecast future data points
Curvier

Set of values which vary over time using regular time intervals
Breaks down into components easier to extrapolate

Question 33

4 main components of a time series graph

Answer 33

1) Basic trend (T) (LT)- general direction of graph over a long interval of time once ST variations have been smoothed out

2) Cyclical variations (c) (medium term) - don’t necessarily follow similar patterns. Recur at time periods of more than 1year e.g boom, decline, recession, recovery

3) Random variations (R) (ST)- sporadic motions from odd events e.g pandemics, floods & strikes. Unpredictable. Can be isolated & removed

4) seasonal variations (S) (ST) - identical (almost) patterns at successive periods e.g christmas and sales.

Question 34

What 2 models deal with seasonal variations?

Answer 34

1) Additive model
2) Multiplicative model

Question 35

What is the additive model

Answer 35

express variations in absolute terms with above/below average figures being pos or neg

Actual data= T+s+c+r
In short term C - negligible in ST) and R can be ignored- unpredictable

Seasonal variation = original time series figure- trend

Question 36

What is the multiplicative model

Answer 36

Used when seasonal variations are given as a %
Multiply the trend figures by seasonal variation % and add or deduct from trend

Question 37

What are the advantages of time series analysis

Answer 37

identifies seasonal variations
can be non linear
accurate

Question 38

What are the disadvantages of time series analysis

Answer 38

complicated
seasons may change
based on historical data
less useful LT

Question 39

What are the problems of using time series analysis

Answer 39

Extrapolation - past doesn’t necessarily reflect future
seasonal adjustments based on historic figures - past doesn’t reflect future -if there’s large variations/ residual = less reliable