Upon completion of this chapter you should understand: Approach to solving time value of money applications; uncertainty, risk and decision trees; determining operating costs; calculating annual costs. Inviting you refer.
Trang 1Chapter 6 – Unit 1
Time Value of Money Application
IET 350 Engineering Economics
Learning Objectives – Chapter 6
Upon completion of this chapter you should understand:
Approach to solving time value of money applications
Uncertainty, risk and decision trees
Determining operating costs
Calculating annual costs
2
Learning Objectives – Unit 1
Upon completion of this unit you should understand:
Approach to solving time value of money applications
Uncertainty, risk and decision trees
Determining operating costs
Calculating annual costs
3
Trang 2Annual cost calculation is a frequent application for time
value of money techniques
Annual cost determination includes:
Product unit costs
Product unit costs
Purchase versus lease comparison
Equipment economic justification
Loan calculations
Additionally, annual cost calculations are used for a wide
variety of investment decision analysis
4
Solving TVM Relationships
Steps for solving time value of money applications:
1 Describe situation using cash flow diagram
2 Summarize known and unknown factors using the diagram
3 Determine the unknown factors using equivalence and time g q
value of money calculations
4 Consider the affect of uncertainty and risk using decision trees,
what‐if analysis and sensitivity analysis
5 Review how the problem will impact other projects and sources
of funds
6 Consider noneconomic effects on the solution
7 Combine economic and noneconomic factors to make a
Solving TVM Relationships
Problem solving forms part of thinking. Considered the most
complex of all intellectual functions, problem solving has been
defined as higher‐order cognitive process that requires the
modulation and control of more routine or fundamental skills
(Goldstein & Levin 1987) It occurs if an organism or an artificial
The first step to solving a problem is defining it.
6
(Goldstein & Levin, 1987). It occurs if an organism or an artificial
intelligence system does not know how to proceed from a given state
to a desired goal state. It is part of the larger problem process that
includes problem finding and problem shaping.
http://en.wikipedia.org/wiki/Problem_solving
Trang 3Determination of the ROI value (interest rate) to be used in
time value of money calculations is critical since it directly
affects the analysis
ROI determination uses one of the following methods:
7
g
Management sets a target or minimum ROI
ROI is set equal to alternative investments such as
Treasury bills, mutual funds or other investments
ROI is set equal to the interest rate for corporate loans
Minimum or target ROI set based on recent projects ROI
Combination of above methods
Selecting ROI Value
Minimum or target ROI values change over time due to
factors such as:
Economic environment factors such as the inflation rate
Investment opportunities in financial instruments at high
8
Investment opportunities in financial instruments at high
ROI rates
Federal discount loan rate – prime interest rate
Organization’s cash flow situation – high cash flow may
result in lower ROI projects being funded.
End Unit 1 Material
Additional Reading Ö How to Think About Time Value
of Money Problems:
http://www.tvmcalcs.com/tvm/how_to_think_about_time_value_problems
Go to Unit 2 Uncertainty and Risk
9
Trang 4Chapter 6 – Unit 2
Uncertainty and Risk
IET 350 Engineering Economics
Learning Objectives – Unit 2
Upon completion of this unit you should understand:
Approach to solving time value of money applications
Uncertainty, risk and decision trees
Determining operating costs
Calculating annual costs
11
Definitions
Uncertainty is the state of having limited knowledge.
Uncertainty makes it impossible to exactly describe
existing state or future outcome
Uncertainty means there may be more than one possible
12
outcome
Risk is the degree or state of uncertainty where some
possible outcomes have an undesired effect.
Probability is the likelihood or chance that some state or
result will happen
Probability of a future event occurring can be estimated
Trang 5We have assumed certainty to this point regarding costs,
returns, life, salvage value, ROI, etc
Reality is that all factors associated with financial and
economic analysis are variable and can only be estimated.
13
This is especially true of future values and analysis over
extended periods of time
Since economic analysis and decision making necessitates
determining future states, we need to consider the effects of
uncertainty
Tools for Uncertainty
Tools that can assist in estimating future values:
Historical, theoretical and subjective probabilities
Estimating expected values and variation
14
Best case/worst case (scenario) estimating
What‐if analysis
Sensitivity analysis
Decision trees
Probability
Probability can be estimated using:
Historical data – reviewing the actual (historical) results for
similar factors such as machine life, ROI and annual costs
Mathematical functions – certain types of events have
15
Mathematical functions certain types of events have
known probability distributions. Annual costs are often
distributed normally. Lives of buildings and equipment
tend to follow exponential and Poisson distributions
Subjectivity – estimated based on knowledge, experience
and all other factors
Combination of the above
Trang 6Expected value is determined by the average of previous
events. Examples for time value analysis:
Expected life based on the average time to failure of
several computer monitors
16
Expected life based on the average miles of delivery
trucks based on replacement
Variation is typically determined by either the range or
standard deviation of the historical data used to determine
the expected value
Little or no variation permits analysis without considering
uncertainty
Optimistic/Pessimistic Estimates
Simplified approach to uncertainty is to estimate the most
likely occurrence and the extremes – best and worst case
Worst case – assume everything that can go wrong, will
Best case – assume everything meets ideal conditions
17
y g
The three scenarios are used to estimate the future results by
providing three outcomes for what if analysis
Also, a weighted average using probabilities can be found.
Example, if the most likely is judged to have a 60% chance of
occurring and the other two cases have a 20% change each:
Optimistic Likely
Most c
Pessimisti
expected 0.2T 0.6T 0.2T
What‐If Calculations
What‐if analysis allows a complete economic analysis
incorporating uncertainty
Future results are determined by analyzing all possible
outcomes of the factors in the decision process
18
p
What‐if can incorporate optimistic/most likely/pessimistic
estimates for each factor or other estimates and project a
future result for all combinations
Typically what‐if calculations are done using a spreadsheet to
allow quick changes of each factor.
Trang 7What‐if analysis considers how the result (output) changes
with changes in the factors or variables (inputs)
The degree of change is referred to as sensitivity:
If the result changes slightly with changes to a variable
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If the result changes slightly with changes to a variable,
the result has low sensitivity to that variable.
If the result changes significantly with changes to a
variable, the result has high sensitivity to that variable.
Sensitivity can be measured by varying each variable a fixed
amount (example 10%) and determining the percentage
change in the result
Decision Trees
Decision trees are an organized method of displaying and
analyzing projects with complex uncertainties
Decision trees can be combined with what‐if, sensitivity and
optimistic/pessimistic analysis to clearly display the possible
20
scenarios
Decision trees incorporate:
Branches for each possible state or outcome
Probability of that state or outcome occurring
Cost or benefit associated with each possible state or
outcome
Decision Trees
Variables with outcomes and probabilities (text pages 203‐204):
Life:
8 yrs – 50%
10 yrs – 50%
21
y
Salvage:
$5,000 – 50%
$10,000 – 50%
Annual Costs:
$10,00/yr – 25%
$15,00/yr – 50%
$20,00/yr – 25%
Trang 822
Example Problem 6.1 Solution
End Unit 2 Material
Additional Reading Ö Risk Analysis & Risk Management:
http://www.mindtools.com/pages/article/newTMC_07.htm
Go to Unit 3 Operating Costs
23
Chapter 6 – Unit 3
Operating Costs
IET 350 Engineering Economics
Trang 9Learning Objectives – Unit 3
Upon completion of this unit you should understand:
Approach to solving time value of money applications
Uncertainty, risk and decision trees
Determining operating costs
Calculating annual costs
25
Operating Costs
Operating costs are the annual costs related to the project or
equipment. Notation → Aoperatingor AO
Operating costs are stated on an annual basis and do not
have time value of money associated with them
26
y
Operating costs include:
o Materials
o Labor
o Insurance
o Heat
o Utilities
o Salaries
o Maintenance
o Repairs
o Property taxes
o Advertising
o Marketing expenses
o Any other cost associated with the investment
Salvage Value
Salvage value is the revenue realized when a piece of
equipment is sold at the end of its useful life
Salvage value is adjusted by the cost of removing the
equipment at the end of its life:
27
q p
If equipment has zero value and requires removal costs,
the net salvage value may be negative
Salvage value is included in the operating costs for a project
or equipment purchase decisions
Trang 10Salvage value and removal costs are estimated values since
they occur in the future and are uncertain.
Estimated salvage value and removal costs may be based on:
Similar equipment previously salvaged
28
Similar equipment previously salvaged
Used equipment values on the open market
Scrap value of the metal and component content
Percentage of the first cost of the equipment
Percentage derived from previous equipment sales
Combination of above methods
Salvage Value
Salvage value is annualized using the A/F time value of
money factor
Typically salvage value is included in the annual operating
cost of the project or equipment:
29
Positive salvage value is treated as a revenue
Negative salvage value is treated as a cost
However, if the annualized salvage value is small compared to
other operating costs, it may be neglected without major
impact on the decision‐making process
First Cost
First cost is the negative cash flow associated with purchasing
equipment or other types of assets and the associated
installation costs
First costs are included in the operating costs for a project or
30
equipment purchase decisions. First cost and installation cost
are annualized using the A/P time value of money factor
Typically, first costs can be included in operating cost with
certainty since the purchase price of the asset will be known.
Some uncertainty may occur regarding the installation costs
Depreciation costs are not included in operating costs since
they are essentially the same cost as the annualized first cost
Trang 11Go to Unit 4 Annual Costs
31
Chapter 6 – Unit 4
Annual Costs
IET 350 Engineering Economics
Learning Objectives – Unit 4
Upon completion of this unit you should understand:
Approach to solving time value of money applications
Uncertainty, risk and decision trees
Determining operating costs
Calculating annual costs
33
Trang 12Total annual costs (Atotal) for a project or equipment include
three components:
First cost → P which is annualized and becomes → AP
Operating costs → AO
34
Salvage cost → S which is annualized and becomes → AS
Annualizing first cost and salvage cost results in the equation:
i) n, S(A/F, A i)
n,
P(A/P,
A
A A A
A
O total
S O P
total
− +
=
− +
=
Note: A S is a negative value since we are determining total cost and salvage is usually a revenue.
Example Problem 6.2
35
Example Problem 6.2 Solution
Calculating Annual Costs
Operating costs (AO) are not always constant over the life of
equipment. Typically costs such as maintenance and repair
increase yearly and can be estimated as gradient costs
Adding a gradient maintenance cost (AM) to the annual cost
36
calculation results in the equation:
[A G(A/G, n, i)] S(A/F, n, i) A
i)
n,
A/P,
(
P
A
A A A A A
O total
S M O P total
− +
′ + +
=
− + +
=
Reminder: A′= Initial annual cost ($)
G = gradient amount ($)
Trang 1337
Example Problem 6.3 Solution
Equipment Justification
Equipment is not only an asset to an organization, equipment
is also an investment.
Like any investment, equipment must produce a return to the
organization.
38
g
Therefore, time value of money is the appropriate method to
calculate the annual cost or return related to equipment
including:
Comparisons between alternate equipment
Make versus buy decisions (product)
Lease versus purchase decisions (equipment)
Equipment Justification
Equipment can be justified by determining:
Whether the annual revenue generated by the
equipment is positive – requires both operating cost and
revenue estimates
39
Comparing equipment ROI to the firm’s target ROI
Total annual cost is less than existing equipment
performing the same task
Combination of above approaches
Non‐economic factors are also considered such as the impact
of training, required space, process changes and quality
Trang 14Second component to equipment justification is determining
the source of funds necessary to acquire the equipment.
Sources include:
Purchase equipment with internal funds
40
Lease equipment – lease cost and purchase cost must be
compared at the same point in time
Purchase using borrowed funds (loan) – cost of borrowing
the funds would be included in the total annual cost
Selling debt securities (bonds) to finance the purchase.
Combination of above approaches
Equipment Justification
Borrowed funds (loan) can be used when the firm does not
have sufficient retained earnings to reinvest in equipment or
when the firm wishes to retain is liquid assets (cash) for other
purposes
41
Various loan approaches are available:
Traditional loan with repayment of interest and principle
Interest‐only loans which requires payment of interest
only with principle repaid within a specified time
Product Unit Cost
Determination of unit product costs may include equipment
costs along with the product costs of direct materials, direct
labor and overhead
Equipment and product costs are annualized then divide by
42
annual volume to determine unit product cost
year units
A Cost Product
i) n, A/F, ( S A i) n, A/P, ( P A
A
A A A A A
total Unit
O O
L
M
total
S O P O L M total
=
− + +
=
− + +
=
+
+
Trang 1543
Example Problem 6.4 Solution
End Chapter 6 Material
Student Study Guide Ö Chapter 6
Homework Assignment Ö Problem Set 6
44