Question

2. In a proposed flood control project, there are two possible sites, A and B, for a dam and storage reservoir. One or the other of these sites may be used but not both. Certain channel improvement is also considered; this will increase the capacity of the stream to carry flood discharge. Estimated first costs, lives, and annual operation and maintenance costs are as follows:

	Site A	Site B	Channel Improvement
First cost	$6,000,000	$8,000,000	$1,000,000
Life	75 years	75 years	25 years
Annual O & M	$100,000	$140,000	$230,000

Annual capital recovery costs are to be computed using an interest rate of 5.5%. Assume zero salvage values at the end of the estimated lives.

The average annual amount of damages due to floods is estimated under various possible plans of development, as follows:

No flood control works at all	$1,200,000
Development at site A only	380,000
Development at site B only	260,000
Channel improvement only	520,000
Site A plus channel improvement	200,000
Site B plus channel improvement	120,000

Compute the benefit to cost ratio for each of the five plans of development as compared to the alternative having no flood control (i.e. what is the derived benefit between an alternative and having no flood control). Assume that the annual costs of a dam and reservoir plus channel improvement alone. Compute any incremental benefit to incremental cost ratios for the combined projects as needed. Which plan of development, if any, would you recommend? Justify your answer using the engineering economics calculations you have performed.

3. A number of years have gone by with no flood control structures put in place for the flood control projects noted in problem 2. The estimated first costs, lives, and annual operation and maintenance costs are the same as stated in problem 2. The average annual damages without flood control are now double that shown in problem 2 and the interest rate for the projects is now 8%. Using these changes in data, calculate the benefit to cost ratios and incremental benefit to incremental cost ratios necessary to choose an alternative. Which plan to your recommend? Justify your answer using the engineering economics calculations you have performed.

Answer 1

Benefit to cost ratio=Present value of benefit/Present value of cost

	Site A	Site B
First cost	$6,000,000	$8,000,000
Total Initial Cost	$6,000,000	$8,000,000
Annual O & M	$100,000	$140,000
Present Value Of Annual O & M((Annual O& M*((1.055)^75-1)/(1.055^75*.055))	$1,785,395	$2,499,553
Total Present Value	$7,785,395	$10,499,553
Benefit at Site A(No flood control works at all-Development at site A only $1,200,000-380,000)	$820,000
Present Value of Benefit at Site A	$14,640,237
Benefit to Cost ratio	1.88
Benefit at Site B(No flood control works at all-Development at site B only $1,200,000-260,000)	$940,000
Present Value of Benefit at Site B	$16,782,710
Benefit to Cost ratio	1.60

Channel Improvement	$1,000,000
Annual O & M	$230,000
Present Value Of Annual O & M	$3,085,205
Total Present Value of cost	$4,085,205

Benefit of Channel Improvement Only(No flood control works at all-Channel Improvement Only $1,200,000- 520,000)	$680,000
Present Value of Benefit of Channel Improvement Only	$9,121,474
Benefit to Cost ratio	2.23

Total Present Value of cost At Site A+channel Improvement	$11,870,599
Total Present Value of cost At Site B+channel Improvement	$13,584,757

Benefit of Site A plus channel improvement(No flood control works at all-Site A plus channel improvement $1,200,000- 200,000)	$1,000,000
Present Value of Benefit of Site A plus channel improvement	$17,853,947
Benefit to Cost ratio	1.50
Benefit of Site B plus channel improvement(No flood control works at all-Site B plus channel improvement $1,200,000- 120,000)	$1,080,000
Present Value of Benefit of Site B plus channel improvement	$19,282,263
Benefit to Cost ratio	1.42

Development at site A plus channel management must be pursued since Benefit to cost ratio is both above 1 and evenly balanced.

	Site A	Site B
First cost	$6,000,000	$8,000,000
Total Initial Cost	$6,000,000	$8,000,000
Annual O & M	$100,000	$140,000
Present Value Of Annual O & M((Annual O& M*((1.08)^75-1)/(1.08^75*.055))	$1,246,108	$1,744,552
Total Present Value	$7,246,108	$9,744,552
Benefit at Site A(No flood control works at all-Development at site A only $1,200,000-380,000)	$820,000
Present Value of Benefit at Site A	$10,218,089
Benefit to Cost ratio	1.41
Benefit at Site B(No flood control works at all-Development at site B only $1,200,000-260,000)	$940,000
Present Value of Benefit at Site B	$11,713,419
Benefit to Cost ratio	1.20
Channel Improvement	$1,000,000
Annual O & M	$230,000
Present Value Of Annual O & M	$2,455,199
Total Present Value of cost	$3,455,199
Total Present Value of cost At Site A+channel Improvement	$10,701,307
Total Present Value of cost At Site B+channel Improvement	$12,199,750
Benefit of Channel Improvement Only(No flood control works at all-Development at site B only $1,200,000- 520,000)	$680,000
Present Value of Benefit of Channel Improvement Only	$7,258,848
Benefit to Cost ratio	2.10
Benefit of Site A plus channel improvement(No flood control works at all-Site A plus channel improvement $1,200,000- 200,000)	$1,000,000
Present Value of Benefit of Site A plus channel improvement	$12,461,084
Benefit to Cost ratio	1.16
Benefit of Site B plus channel improvement(No flood control works at all-Site B plus channel improvement $1,200,000- 120,000)	$1,080,000
Present Value of Benefit of Site B plus channel improvement	$13,457,971
Benefit to Cost ratio	1.10

Development at Site A only should be pursued since BCR is 1.41.

*Please not that First cost are initial costs which are paid upfront and hence cannot be discounted.