Chapter 11: Quantitative Techniques Flashcards
What is high/low analysis
analysing semi-variable costs into fixed/ variable elements based on historic info of costs at different levels
What are the steps for high/low analysis?
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
What is the formula for variable cost/ unit
(cost at high level- cost at low level)/ (high level activity- low level activity)
What are the advantages of high/low analysis?
1) simple to calculate
2) easy to understand & use
What are the disadvantages of high/low analysis?
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
What is wright’s law
as cumulative output doubles, the cumulative average time per unit fall to a fixed% (aka learning rate) of the previous average time
What is the learning curve?
mathematical expression that as complex & labour intensive procedures are repeated, unit labour times decrease
What are limitations of the learning curve model?
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
Steps to complete the cumulative average (increase units)
Step 1: calc cumulative average time for target production
Step 2: calc total cumulative time
Step 3: Time to make X units more
If output double what method do we use?
If we need to find an intermediate amount what method do we use?
Doubles= tabular approach
Intermediate= algebraic approach
What is the formula for the algebraic approach?
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
What algebraic formula can be used if we have a specific number of times the number of units has doubled?
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
How does the learning effect apply to pricing decisions
prices will be set too high if based on the cost of making the first few units
How does the learning effect apply to work scheduling
Less labour per unit will be required as more are made
management implications e.g redundancy
How does the learning effect apply to product viability
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
How does the learning effect apply to standard setting
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
How does the learning effect apply to budgeting
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
How does a steady rate affect the learning curve
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
What is the experience curve
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
What is linear regression
uses formula to estimate the linear relationship between variables (models dependence of variables)
Shown as an equation and then graphically
What is regression analysis
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
What are the 2 relationships of linear regression
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
Limitation of regression analysis
Based on sample data
If we select a different sample output is likely to be different so need a stable relationship between variables
What is interpolation
Value of x is within the range of our original data
safer than extrapolation
What is extrapolation
Value of x is outside the range of our original data
What are the limitations of simple linear regression?
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
What is the equation to cost adjust
Index level to which cost will be adjusted/ actual index level of costs
What is correlation
establishing how strong a relationship is
What is the boundary for a strong correlation
> 0.8 or r<-0.8
What is the co-efficient of determination
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)
What are the limitations of correlation
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
What are time series analysis
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
4 main components of a time series graph
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.
What 2 models deal with seasonal variations?
1) Additive model
2) Multiplicative model
What is the additive model
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
What is the multiplicative model
Used when seasonal variations are given as a %
Multiply the trend figures by seasonal variation % and add or deduct from trend
What are the advantages of time series analysis
identifies seasonal variations
can be non linear
accurate
What are the disadvantages of time series analysis
complicated
seasons may change
based on historical data
less useful LT
What are the problems of using time series analysis
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
