An area on the Colorado River is subject to periodic flood damage that occurs, on the average, every two years (i.e., probability of flooding in any year is 0.5) and results in a $2,200,000 loss. It has been proposed that the river channel be improved by straightening and deepening it at a cost of$2,400,000, to reduce the annual probability of flooding to 0.364 during a period of 18 years before it would have to be deepened again. This procedure would also involve annual expenditures of $90,000 for minimal maintenance.
One legislator in the area has proposed that a better solution would be to construct a flood-control dam at a cost of $8,000,000, which would last indefinitely, with annual maintenance costs of not over $50,000.
She estimates that this project would reduce the annual probability of flooding to 0.205. In addition, this solution would provide a substantial amount of irrigation water that would produce annual revenue of $150,000
and recreational facilities, which she estimates would be worth at least $45,000 per year to the adjacent populace.
If the state's capital is worth 11%, perform B-C analysis and recommend the proposal to be adopted. Note that one of the two proposals must be adopted, as the do-nothing alternative will not be accepted by the legislature, no matter what the analysis shows. This means that only the incremental analysis between the two proposals need be done.
The B-C ratio for the "Improve channel" proposal is ______ (Round to 2 decimal places)
The B-C ratio for the "Construct dam" proposal is ________ (Round to 2 decimal places)
The incremental B-C ratio of "Construct dam" vs. "Improve channel" is _____ (Round to 2 decimal places)
Therefore, the recommended proposal is to
A.Improve the channel
B.Construct Dam
General Definition of BCR
A benefit-cost ratio (BCR) is an indicator showing the relationship between the relative costs and benefits of a proposed project, expressed in monetary or qualitative terms. If a project has a BCR greater than 1.0, the project is expected to deliver a positive net present value to a firm and its investors.
Calculation of Benefit - Cost Ratio or B-C Analysis
= Present Value of Projects Benefits/ Present Value of Project Cost
Discount rate = 11%
Yearly Loss on account of periodic Floods = 2,200,000*0.5 = $ 1,100,000
Option A - Improve the channel
Life of Channel = 18 Years
Annual Loss Reduction if channel is improved (Cash Inflow) = (0.5 - 0.364) * $1,100,000 = $149,600
Present Value of Annual Loss Reduction at 11% discount rate for 18 years
= 149,600 * Present Value Annuity Factor (11%, 18 Years) = 149,600 * 7.7016 = $1,152,162
Annual Maintenance Cost (Cash Outflow) = $90,000
Present Value of Annual Maintenance at 11% discount rate for 18 years
= 90,000 * Present Value Annuity Factor (11%, 18 Years) = 90,000 * 7.7016 = $693,144
Cost of Project (Cash Outflow) = $2,400,000
B-C Ratio = Benefits from Project/Cost of Project
= 1,152,162 / (693,144 + 2,400,000)
= 1,152,162 / 3,093,144 = 0.37
Option B - Construct Dam
Life of Dam = Indefinite (Perpetual)
Annual Loss Reduction if dam is constructed (Cash Inflow) = (0.5 - 0.205) * $1,100,000 = $324,500
Present Value of Annual Loss Reduction at 11% discount rate for perpetual period
= 324,500 / Discount Rate = 324,500 / 0.11 = $2,950,000
Annual Maintenance Cost (Cash Outflow) = $50,000
Present Value of Annual Maintenance at 11% discount rate for perpetual period
= 50,000 / Discount Rate = 50,000 / 0.11 = $454,545
Annual Revenue from water for Irrigation and Recreational Facilities (Cash Inflow) = (150,000 + 45,000) = $195,000
Present Value of Annual Additional Revenue at 11% discount rate for perpetual period
= 195,000 / Discount Rate = 195,000 / 0.11 = $1,772,727
Cost of Project (Cash Outflow) = $8,000,000
B-C Ratio = Benefits from Project/Cost of Project
= (2,950,000 + 1,772,727) / (8,000,000 + 454,545)
= 4,722,727 / 8,454,545 = 0.56
Decision = Under both the options, BCR is coming out to be less than one which implies that neither of the projects will deliver a positive Net Present Value to legislature.
However, since one of the options has to be adopted, Option B of Constructing the Dam is better compared to improving the channel since the BCR of option B is 0.56 which is greater than 0.37 of Option A of improving the channel.
Incremental BCR of the two projects
Increasing Order
Option B = Benefit = 4,722,727
Cost = 8,454,545
Option A = Benefit = 1,152,162
Cost = 3,093,144
Incremental BCR = Incremental Benefits / Incremental Costs
= (4,722,727 - 1,152,162) / (8,454,545 - 3,093,144)
= 3,570,565 / 5,361,401 = 0.67
For any clarification, please leave a comment.
An area on the Colorado River is subject to periodic flood damage that occurs, on the average, every two years (i.e., probability of flooding in any year is 0.5) and results in a $2,200,000 loss....