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Five years ago a dam was constructed to impoundirrigation
Chapter , Problem 10-44(choose chapter or problem)
Five years ago a dam was constructed to impoundirrigation water and to provide flood protection forthe area below the dam. Last winter a 100-year floodcaused extensive damage both to the dam and to thesurrounding area. This was not surprising, since thedam 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.If the spillway is redesigned at a cost of$250,000and the dam is repaired for another $250,000, thedam may be expected to withstand a 100-year floodwithout sustaining damage. However, the storagecapacity of the dam will not be increased andthe probability of damage to the surrounding areabelow the dam will be unchanged. A second damcan be constructed up the river from the exist-ing dam for $1 million. The capacity of the sec-ond dam would be more than adequate to providethe desired flood protection. If the second dam isbuilt, redesign of the existing dam spillway will notbe necessary, but the $250,000 of repairs must bedone.The development in the area below the dam isexpected to be complete in 10 years. A new 100-year flood in the meantime would cause a $1 millionloss. After 10 years the loss would be $2 million. Inaddition, there would be $250,000 of spillway dam-age if the spillway is not redesigned. A 50-year floodis also likely to cause about $200,000 of damage,but the spillway would be adequate. Similarly, a25-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 redesignthe spillway to take a100-year flood ($250,000),and (3) repair the existing dam ($250,000) andbuild the second dam ($1 million). Based on anexpected annual cash flow analysis, and a 7% inter-est rate, which alternative should be selected? Drawa decision tree to clearly describe the problem
Questions & Answers
QUESTION:
Five years ago a dam was constructed to impoundirrigation water and to provide flood protection forthe area below the dam. Last winter a 100-year floodcaused extensive damage both to the dam and to thesurrounding area. This was not surprising, since thedam 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.If the spillway is redesigned at a cost of$250,000and the dam is repaired for another $250,000, thedam may be expected to withstand a 100-year floodwithout sustaining damage. However, the storagecapacity of the dam will not be increased andthe probability of damage to the surrounding areabelow the dam will be unchanged. A second damcan be constructed up the river from the exist-ing dam for $1 million. The capacity of the sec-ond dam would be more than adequate to providethe desired flood protection. If the second dam isbuilt, redesign of the existing dam spillway will notbe necessary, but the $250,000 of repairs must bedone.The development in the area below the dam isexpected to be complete in 10 years. A new 100-year flood in the meantime would cause a $1 millionloss. After 10 years the loss would be $2 million. Inaddition, there would be $250,000 of spillway dam-age if the spillway is not redesigned. A 50-year floodis also likely to cause about $200,000 of damage,but the spillway would be adequate. Similarly, a25-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 redesignthe spillway to take a100-year flood ($250,000),and (3) repair the existing dam ($250,000) andbuild the second dam ($1 million). Based on anexpected annual cash flow analysis, and a 7% inter-est rate, which alternative should be selected? Drawa decision tree to clearly describe the problem
ANSWER:Problem 10-44
Five years ago, a dam was constructed to impound 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. If the spillway is redesigned at a cost of$250,000and the dam is repaired for another $250,000. The dam may be expected to withstand a 100-year flood without 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 than 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 would 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. Similarly, a25-year flood would cause about $50,000 of damage. There are three alternatives: (1) repair the existing dam for $250,000 but make no other alterations, (2) repair the existing dam ($250,000) and redesign the spillway to take a100-year flood ($250,000), and (3) repair the existing dam ($250,000) and build the second dam ($1 million). Based on an expected annual cash flow analysis, and a 7% interest rate, which alternative should be selected? Draw a decision tree to clearly describe the problem
Step by Step Solution
Step 1 of 6
Expected cost can be defined as that cost which is expected to be incurred for the purpose of a project or an investment. This cost serves as the basis of the decision making for the firm. When this cost is less than the expected revenue then the alternative is a good alternative.