Problems 333
land, an earthen embankment can be constructed.
The height of tlIe embankment will be determined by
an economic analysis of the costs and benefits. The
following data have been gathered.
Embankment Height
Above Roadway (m)
2.0
2.5
3.0
3.5
4.0
Initial Cost
$100,000
165,000
300,000
400,000
550,000
Flood
Level Above
Roadway (m)
2.0
2.5
3.0
3.5
4.0
Average Frequency
That Flood Level
Will Exceed
Height in Col. 1
Once in 3 years
Once in 8 years
Once in 25 years
Once in 50 years
Once in 100 years
The embankment can be expected to last 50 years
and will require no maintenance. Whenever the flood
water flows over the embankment, $300,000 of dam-
age occurs. Should the embankment be built? ITso, to
which of the five heights above the roadway? A 12%
rate of return is required.
10-19 Should the following project be undertaken if its life
is 10 years and it has no salvage value? The firm
uses an interest rate of 12% to evaluate engineering
projects.
First Cost
$300,000
400,000
600,000
P
0.2
0.5
0.3
Net Revenue
$ 70,000
90,000
100,000
P
0.3
0.5
0.2
(Answer:$45,900, yes)
10-20 A robot has just been installed at a cost of $81,000.
It will have no salvage value at the end of its useful
life. Given the following estimates and probabilities
for the yearly savings and useful life, determine the
expected rate of return.
Savings
per year
$18,000
20,000
22,000
Useful
Life (years)
12
5
4
Probability
0.2
0.7
0.1
Probability
1/6
2/3
1/6
10-21 Five years ago a dam was constructed to impoun~
irrigation water and to provide flood protection for
the area below the dam. Last winter a 100-year flood
caused extensive damage both to the dam and to the
surrounding area. This was not surprising, since the
dam was designed for a 50-year flood.
The cost to repair the dam now will be $250,000.
Damage in the valley below amounts to $750,000. IT
the spillway is redesigned at a cost of $250,000 and
the dam is repaired for another $250,000, the dam
may be expected to withstand a 100-year flood with-
out sustaining damage. However, the storage capaCity
of the dam will not be increased and the probability
of damage to the surrounding area below the dam
will be unchanged. A second dam can be constructed
up the river from the existing dam for $1 million.
The capacity of the second dam would be more that
adequate to provide the desired flood protection. If
the second dam is built, redesign of the existing dam
spillway will not be necessary, but the $250,000 of
repairs must be done.
The development in the area below the dam is
expected to be complete in 10 years. A new 100-
year flood in the meantime will cause a $1 million
loss. After 10 years the loss would be $2 million. In
addition, there would be $250,000 of spillway dam-
age if the spillway is not redesigned. A 50-year
flood is also likely to cause about $200,000 of
damage, but the spillway would be adequate. Sim-
ilarly, a 25-year flood would cause about $50,000 of
damage.
There are three alternatives: (1) repair the exist-
ing dam for $250,000 but make no other alterations,
(2) repair the existing dam ($250,000) and redesign
the spillway to take a 100-year flood ($250,000), and
(3) repair the existing dam ($250,000) and build the
second dam ($1 million). Based on an expected an-
nual cash flow analysis, and a 7% interest rate, which
alternative should be selected? Draw a decision tree
to clearly describe the problem.
10-22 A new product's chief uncertainty is its annual net
JI... revenue. So far, $35,000 has been spent on devel-opment, but an additional $30,000 is required finish
development. The firm's interest rateis10%.
