Question

Three options are under review for controlling neighborhood flooding during heavy rainstorms. All options are expected to be in place for 50 years. The options differ both in cost and damage averted when a heavy rain event occurs. A promise has been made to build one option so ‘doing nothing’ is not a political acceptable alternative. When considering weather driven damage the usual method is to list the level of damage in currency terms and to state the likelihood that the damage will occur in terms of frequency that the weather event will occur. For example, a damage estimate of 500,000 for a twenty year event is interpreted that the event will occur on average once every 20 years or has a probability of 0.05 occurring this year so the expected damage this year is 0.05 times 500,000 which equals 25,000. If an intervention prevented all damage from such an event the benefit would be shown as 25,000 every year. Apply incremental benefit cost analysis to this situation using an interest rate of 7.0% and answer the questions that follow.

Option	A	B	C
Investment	2.4 Million	1.6 Million	4.1 Million
Annual Operating Cost	85,000	92,000	35,000
Annual Benefit	160,000	140,000	290,000
Annual Disbenefit	12,000	1,000	21,000

a. What is the B/C for option A?

b. What is the B/C for option B?

c. What is the B/C for the difference between option B and A?

d. Complete the analysis for all options and based on the analysis, which option is the best public investment?

Answer 1

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. Y The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $.

Option	Linkage	A	B	C	B - A
Investment	A	2,400,000	1,600,000	4,100,000	(800,000)
Annual Operating Cost	B	85,000	92,000	35,000	7,000
Annual Benefit	C	160,000	140,000	290,000	(20,000)
Annual Disbenefit	D	12,000	1,000	21,000	(11,000)
Net Benefit	E = C - D	148,000	139,000	269,000	(9,000)
Period	F	50	50	50	50
Interest rate	G	7%	7%	7%	7%
PV of net benefits	H = E/G x (1 - (1 + G)^(-F))	2,042,510	1,918,304	3,712,401	(124,207)
PV of costs	I = B/G x (1 - (1 + G)^(-F))+ A	3,573,063	2,869,669	4,583,026	(703,395)
B/C	J = H / I	0.571641	0.668476	0.810033	0.176582

You can see the answer of Part (a), (b ) & (c) in the yellow colored row above.

Part (d) Analysis for all the options are shown above. Based on B/C ratio, Option C has the highest B/C ratio, even though it's not > 1. Hence, among all the options  available, Option C is the best one.