Transcript Net Present Worth Examples

Reviewing…
Net Present Worth:
• Used to select among alternative
projects.
• Used to compare mutually exclusive
alternatives.
• If all expenses and revenues are
included, select the largest NPW that is
greater than zero.
• If some or none of the revenues are
included, select the largest NPW.
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Reviewing…
Salvage Value –
What value does it have when you are
done with it?
MARR –
Minimum Attractive Rate of Return
The MARR quantifies the risk of the project
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Example Problem
A company is considering the purchase of a new piece of
testing equipment that is expected to produce $8,000
additional income during the first year of operation. This
amount will decrease by $500 per year for each
subsequent year of ownership.
The equipment costs $20,000 and will have an estimated
salvage value of $3,000 after 8 years of use.
For a MARR of 15% compounded annually, determine the
net present worth of this investment.
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Problem 2
Project #1 costs $10,000 and has annual, end of
the year revenues of $10,000 over its 5 year
life. There is no salvage value.
Project #2 costs $20,000 and has annual end of
year revenues of $10,000 over its 10 year life.
There is no salvage value.
Conduct an economic analysis to select the
preferred project using a MARR of 15% per
year, compounded annually.
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Calculating NPWs…
NPW1 = $23,522
NPW2 = $30,188
Why is it wrong to select Project 2 based
on this analysis?
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(Net) Present Worth Analysis
When comparing projects, it is
necessary to compare
alternatives with the same
project life (i.e., over the same
period of time).
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(Net) Present Worth Analysis
Two possible approaches when project
lives are different:
Common Multiple Period: Projects are
assumed to be repeated until a
common multiple point in time is
established.
Study Period: Select a study period for
both projects and estimate cash
flows to conform to the study period.
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Problem 3
A firm is considering the purchase of one of two
new machines. The data on each are as below:
Machine
A
B
Service Life
3 years
6 years
Initial Cost
$3,400
$6,500
Annual Net
Operating Expense:
$2,000
$1,800
Salvage Value
$100
$500
Use a MARR of 12% compounded annually and
the lowest common multiple assumption to
determine the alternative to be selected.
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Problem 4 (Bonus)
Two alternatives are being considered regarding construction of
a new high-voltage transmission line. Alternative I would build
the transmission towers and the line at a capacity of 230 kVA,
which is expected to be adequate for 15 years. After 15 years the
230 kVA lines would be removed and 560 kVA lines placed on the
existing towers. Alternative II would build the transmission
towers and the 560 kVA lines immediately. Given below are the
pertinent data on the costs of these facilities.
Expected
Expected
Item
Present Cost
Service Life
Salvage Value
Trans. Towers $15,000,000
55 years
0 after 30 yrs
230 kVA lines
$8,000,000
15 years
10% of 1st cost
560 kVA lines
$12,000,000
35 years
10% of 1st cost
Salvage values for both transmission lines are 10% of first cost
regardless of age at retirement.
The cost of 560 kVA lines will inflate at the rate of 10% per year.
The MARR is 15%. Use Present Worth analysis to determine
which alternative is least expensive for a 35 year study period.
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