Study Unit 2 - CMAPrepCourse

Part 1
Study Unit 8
Budgeting Concepts & Forecasting
Techniques
Ronald Schmidt, CMA, CFM
Patti Burnett, CMA
SU 8.1 - Correlation and regression
• Forecasting Methods
– Qualitative – Manager’s experience and intuition
• Can you think of some methods
– Quantitative – Mathematical models and graphs
• Regression
• Trend analysis
• ?????
SU 8.1 - Correlation and regression
• Correlation Analysis
– Foundation of any quantitative method of
forecasting
– Strength of the linear relationship between two
variables
– Value ranges from 1 to -1
– The more a straight line the greater correlation (r)
SU 8.1 - Correlation and regression
• Qualitative methods:
forecast based on
manager’s experience and
knowledge
• Quantitative methods use
mathematical models
– Correlation analysis: strength
of a linear relationship
between 2 variables 
coefficient of correlation (r)
– r = [ -1 ; +1]
SU 8.1 - Correlation and regression
• Coefficient of determination (r2)
– Also coefficient of correlation squared
– Is a measure of how good fit between the two
variables
– Total variation in the dependent variable that is
accounted for by the independent variables
Statistic Definitions
(to know and remember)
• Correlation coefficient may refer to:
– Pearson product-moment correlation coefficient, also known as r, R, or
Pearson's r, a measure of the strength and direction of the linear relationship
between two variables that is defined as the (sample) covariance of the
variables divided by the product of their (sample) standard deviations.
• Related concepts:
– Correlation and dependence, a broad class of statistical relationships between
two or more random variables or observed data values
– Goodness of fit, any of several measures that measure how well a statistical
model fits observations by summarizing the discrepancy between observed
values and the values expected under the model in question
– Coefficient of determination, a measure of the proportion of variability in a
data set that is accounted for by a statistical model; often called R2; equal in a
single-variable linear regression to the square of Pearson's product-moment
correlation coefficient.
Statistic Definitions
(to know and remember)
• Coefficient of determination (r^2)
This is a measure of how good the fit between 2
variables is
– Regression Analysis : y = a + bx
•
•
•
•
y = dependent variable
a = the y intercept
b = slope of the regression line
x = independent variable
 RELEVANT RANGE
SU 8.1 - Question 1
Jura Corporation is developing standards for the
next year. Currently XZ-26, one of the material
components, is being purchased for $36.45 per
unit. It is expected that the component’s cost
will increase by approximately 10% next year
and the price could range from $38.75 to $44.18
per unit, depending on the quantity purchased.
The appropriate standard for XZ-26 for next year
should be set at the
A.
B.
Current actual cost plus the forecasted 10% price
increase.
Lowest purchase price in the anticipated range to keep
pressure on purchasing to always buy in the lowest price
range.
C.
Highest price in the anticipated range to ensure that
there are only favorable purchase price variances.
D.
Price agreed upon by the purchasing manager and the
appropriate level of company management.
SU 8.1 - Question 1 Answer
Correct Answer: D
Standard prices are designed for internal performance measurement. Standards
should be attainable, but not so easily as to not provide motivation. Management
should decide its objectives and set a standard that will achieve that objective when
the standard is met. For example, the lowest price might not be selected if the
company is using a JIT system, for which the primary objective is the minimization of
inventories.
Incorrect Answers:
A: The actual cost could be more or less depending in the quantity purchased.
B: The lowest price may not always be in the company’s best interests if the
quantity required to obtain the lowest price would lead to much higher carrying costs.
C: Standards should be set tightly enough to provide motivation to purchasing
management.
SU 8.1 - Question 2
Lake Corporation manufactures specialty
components for the electronics industry in a
highly labor intensive environment. Arc
Electronics has asked Lake to bid on a
component that Lake made for Arc last month.
The previous order was for 80 units and
required 120 hours of direct labor to
manufacture. Arc would now like 240 additional
components. Lake experiences an 80% learning
curve on all of its jobs. The number of direct
labor hours needed for Lake to complete the
240 additional components is
A.
B.
C.
D.
360.0
187.2
307.2
256.0
SU 8.1 - Question 2 Answer
Correct Answer: B
One common assumption made in a learning curve
model is that the cumulative average time per unit is
reduced by a certain percentage each time production
doubles. An 80% learning curve results in the following
performance for the lots shown:
Units
80
160
320
Cumulative
Average Hours
1.5 hours (120 ÷ 80)
1.2 hours (1.5 × .8)
.96 hours (1.2 × .8)
Thus, to produce 320 units, total production time will
be 307.2 hours (320 × .96). The total time for the last
240 units will be 187.2 hours (307.2 – 120). Incorrect
Answers: A: Assuming no learning curve effect results
in 360 hours. C: The total time for completing 320
units is 307.2 hours. D: The figure of 256 hours is a
nonsense answer.
SU 8.2 -Learning curve analysis
• Increased rate at which people perform
tasks as they gain experience
• % of reduced time to complete a task for
each doubling of cumulative production
• 2 methods:
- cumulative average-time learning
model
- incremental unit-time learning model
SU 8.2 - Question 1
The average labor cost per unit for the first batch
produced by a new process is $120. The
cumulative average labor cost after the second
batch is $72 per product. Using a batch size of 100
and assuming the learning curve continues, the
total labor cost of four batches will be
A.
B.
C.
D.
$4,320
$10,368
$2,592
$17,280
SU 8.2 - Question 1 Answer
A. The cost of the items in the fourth batch equals $4,320.
B. The amount of $10,368 is based on the assumption that the cumulative average
unit labor cost is reduced by the learning curve percentage with each batch, not each
doubling of output.
C. The amount of $2,592 represents the labor cost of 100 units at the unit rate
expected after another doubling of production to eight batches.
D. *Correct Answer* The learning curve reflects the increased rate at which people
perform tasks as they gain experience. The time required to perform a given task
becomes progressively shorter. Ordinarily, the curve is expressed in a percentage of
reduced time to complete a task for each doubling of cumulative production. One
common assumption in a learning curve model is that the cumulative average time
(and labor cost) per unit is reduced by a certain percentage each time production
doubles. Given a $120 cost per unit for the first 100 units and a $72 cost per unit when
cumulative production doubled to 200 units, the learning curve percentage must be
60% ($72 ÷ $120). If production is again doubled to 400 units (four batches), the
average unit labor cost should be $43.20 ($72 × 60%). Hence, total labor cost for 400
units is estimated to be $17,280 (400 units × $43.20).
SU 8.2 - Question 2
A particular manufacturing job is subject to an
estimated 80% learning curve. The first unit
required 50 labor hours to complete. What is
the cumulative average time per unit after
eight units are completed?
A.
B.
C.
D.
20.0 hours.
25.6 hours.
32.0 hours.
40.0 hours.
SU 8.2 - Question 2 Answer
A. The figure of 20.0 hours assumes three successive reductions of 10 hours [50
– (50 × 80%)] each.
B. *Correct Answer* The learning curve reflects the increased rate at which
people perform tasks as they gain experience. The time required to perform a
given task becomes progressively shorter. Ordinarily, the curve is expressed in a
percentage of reduced time to complete a task for each doubling of cumulative
production. One common assumption in a learning curve model is that the
cumulative average time (and labor cost) per unit is reduced by a certain
percentage each time production doubles. Thus, an 80% learning curve indicates
that a doubling of production will reduce the cumulative average unit
completion time by 20%. For example, if the first unit required 50 hours to
complete, the average completion time after two units will be 40 hours (50
hours × 80%). If production is again doubled (to four units), the average
completion time will be 32 hours (40 hours × 80%). When production is doubled
again to eight units, the cumulative average completion time will be 25.6 hours
(32 hours × 80%).
C. The average completion time after four units have been produced is 32 hours.
D. The average time after two units have been produced is 40 hours.
SU 8.3 -Time-series analysis
• Projects future trends based on past experience
– Secular trend: long-term change
– Seasonal variations
– Cyclical fluctuations: variations with level of activity
tied to the business cycle
– Irregular or random variables: unexpected
happenings (weather, strikes, fires…)
Techniques:
- Simple moving average
- Weighted moving average
- Exponential smoothing (3 steps)
SU 8.3 - Question 1
A forecasting technique that is a combination of the last forecast and the last observed
value is called
A
Delphi.
B
Least squares.
C
Regression.
D
Exponential smoothing.
SU 8.3 - Question 1 Answer
Correct Answer: D
Exponential smoothing is a widespread
technique for making projections because it
requires less data be kept on hand than the
moving average methods. The technique
involves weighting the actual result for the
previous period by a smoothing factor,
weighting the forecast for the previous period
by the smoothing factor’s complement, and
combining the two.
SU 8.3 - Question 2
Sales of big-screen televisions have grown steadily during the past 5 years. A dealer
predicted that the demand for February would be 148 televisions. Actual demand in
February was 158 televisions. If the smoothing constant (α) is 0.3, the demand
forecast for March, using the exponential smoothing model, will be
A
148 televisions.
B
151 televisions.
C
155 televisions.
D
158 televisions.
SU 8.3 - Question 2 Answer
Correct Answer: B
Exponential smoothing is a widespread technique for
making projections because it requires less data be kept
on hand than the moving average methods.
Mathematically, a forecast is arrived at with exponential
smoothing according to the following formula:
Forecast
=
(Smoothing factor ×
Previous month result) +
(Smoothing factor
complement × Previous
month forecast)
=
(0.3 × 158) + (0.7 × 148)
=
47.4 + 103.6
=
151
SU 8.3 - Question 3
The four components of time series data are secular trend, cyclical variation,
seasonality, and random variation. The seasonality in the data can be removed by
A
Multiplying the data by a seasonality
factor.
B
Ignoring it.
C
Taking the weighted average over four
time periods.
D
Subtracting a seasonality factor from the
data.
SU 8.3 - Question 3 Answer
Correct Answer: C
Time series analysis relies on past experience.
Changes in the value of a variable may have several
possible components including secular trends,
cyclical variation, seasonality, and random variation.
Seasonal variations are common in many
businesses. A variety of methods exist for including
seasonal variations in a forecasting model, but most
methods use a seasonal index. Alternatively,
seasonal variations can be removed from data by
using a weighted average of several time periods
instead of data from individual periods.
SU 8.4 - Expected value
• Possible outcomes of a probability distribution
• Highest expected monetary value
– Decision alternative
– State of nature = future event
– Payoff = financial result of combination (decision &
state of nature)
Work on the example to understand method
Expected value forces managers to evaluate decisions
in a more organized manner
Perfect information (EVPI)
SU 8.4 - Question 1
The probabilities shown in the table
below represent the estimate of sales for
a new product.
Sales (Units)
Probability
0-200
15%
201-400
45%
401-600
25%
601-800
15%
SU 8.4 - Question 1 (cont.)
What is the probability of selling between 201 and 600 units of the product?
What is the probability of selling
between 201 and 600 units of the
product?
A.
B.
C.
D.
0%
11.25%
70%
25%
SU 8.4 - Question 1 Answer
Correct Answer: C
The probability of selling between 201 and 400 units is 45%, and the
probability of selling between 401 and 600 units is 25%. Hence, the
probability of selling between 201 and 600 units is the sum of these
probabilities, or 70%.
Incorrect Answers:
A: There is a 70% probability of selling between 201 and 600 units.
B: There is a 70% probability of selling between 201 and 600 units.
D: This percentage is the probability of selling between 401 and 600 units.
SU 8.4 - Question 2
The expected value of perfect information is the
A. Same as the expected profit under certainty.
B. Sum of the conditional profit (loss) for the best event of each act
times the probability of each event occurring.
C. Difference between the expected profit under certainty and the
expected opportunity loss.
Correct D. Difference between the expected profit under certainty
and the expected monetary value of the best act under uncertainty.
SU 8.4 - Question 2 Answer
A.
The expected value of perfect information is the difference between the
expected profit under certainty and the profit from the best decision
under uncertainty.
B. The expected value of perfect information is the excess of the total
conditional profits under certainty over the profit from the best decision
under uncertainty.
C. There is no expected opportunity loss under conditions of certainty.
D. *Correct Answer* Perfect information permits certainty that a future state
of nature will occur. The expected value of perfect information determines
the maximum amount a decision maker is willing to pay for information. It is
the difference between the expected value without perfect information, that
is, the expected value of the best action under uncertainty and the expected
value under certainty. Under certainty, a decision maker knows in each case
which state of nature will occur and can act accordingly
SU 8.4 - Question 3
In decision making under conditions of uncertainty, expected
value refers to the
A. Likely outcome of a proposed action.
B. Present value of alternative actions.
C. Probability of a given outcome from a proposed action.
D. Weighted average of probable outcomes of an action.
SU 8.4 - Question 3 Answer
A. The expected value is a long-range average; it is likely
that the expected value will never be exactly achieved for
a particular event.
B. Expected value does not consider present values.
C. Probability is only one component of expected value.
D. *Correct Answer* The expected value of an action is
found by multiplying the probability of each possible
outcome by its payoff and summing the products. It
represents the long-term average payoff for repeated
trials. In other words, expected value is the weighted
average of probable outcomes.
SU 8.5 – Sensitivity Analysis
• How sensitive expected value calculations are
to the accuracy of the initial estimate
• Example: How much are my sales affected by
a change in price?
• See example B on page 257
SU 8.5 - Question 1
A quantitative technique useful in projecting a firm’s sales and
profits is
A.
B.
C.
D.
Probability distribution theory.
Gantt charting.
Learning curves.
Queuing theory.
SU 8.5 - Question 1 Answer
A. *Correct Answer* Probability distribution theory can be used to
project sales. It is a mathematical method for making decisions about
the likelihood of future events (such as sales) in the face of
uncertainty. Various estimates of sales (generated from the sales force)
can be weighted with different probabilities.
B. A Gantt chart is a bar chart used to measure progress toward a goal.
C. A learning curve measures the benefit of experience in the early
stages of a new task.
D. Queuing (waiting-line) theory is used to determine the optimum
balance between the cost of providing service to reduce waiting lines
and the cost of allowing waiting lines to exist when items in the queue
arrive at random.
SU 8.5 - Question 2
A widely used approach that managers use to recognize
uncertainty about individual items and to obtain an immediate
financial estimate of the consequences of possible prediction
errors is
A.
B.
C.
D.
Expected value analysis.
Learning curve analysis.
Sensitivity analysis.
Regression analysis.
SU 8.5 - Question 2 Answer
A. Expected value is the probabilistically weighted average of the outcomes of
an action.
B. Learning curve analysis quantifies how labor costs decline as employees
learn their jobs through repetition.
C. *Correct Answer* Sensitivity analysis determines how a result varies with
changes in a given variable or parameter in a mathematical decision model.
For example, in a present value analysis, a manager might first calculate the
net present value or internal rate of return assuming that a new asset has a
10-year life. The NPV or IRR can then be recalculated using a 5-year life to
determine how sensitive the result is to the change in the assumption.
D. Regression, or least squares, analysis determines the average change in the
dependent variable given a unit change in one or more independent
variables.