QUESTION 3 The City of Ft Myers is considering three mutually exclusive designs

Question

QUESTION 3 The City of Ft Myers is considering three mutually exclusive designs for enhancing the capacity of a canal to reduce flooding. The interest rate is 6% and the project is designed to last for 25 years. Ans.xxx What Using incremental benefit-cost analysis what is the incremental B/C ratio for the first pair when ordering the alternatives in order of increasing investment? is the BIC ratio for th second pair? Ans xxx Based on the analysis which alternative would you select? Ans. X Investment. SS Benefits, S Siyear O&M;'S/year $ SV, $ CR Syear S (120,000) S 140,000) (150,000) 96,000 (52,300) 31,500 11.160 87,000 S (46,000) S 23,000 S 8,968 S 91,000 S (49,500) S 29,000 S 10,423 S

Explanation / Answer

PVAF (6%,25 years)= 12.78 or P/A= 1/12.78=0.0782

PVF (6%,25 years)= 0.2329 P/F=0.2329

Present Value of Costs

Present value of costs -Plan A= 120000 +46000(P/A, 6%,25 years)= 120000 +46000*0.0782 = 123597.2

Present value of costs -Plan B= 140000+ 49500(P/A, 6%,25 years)=140000+ 49500*0.0782= 143870.9

Present value of costs -Plan C= 150000 +52300(P/A, 6%,25 years)= 150000+ 52300*0.0782= 154090

hence the order of alternatives from lowest to highest cost is plan A, Plan B and then Plan C

Present Value of Benefits

Present Value of Benefits of Plan A=23000*(P/F, 6%,25 years)+(8968+87000)(P/A, 6%,25 years)

                          =5356.7+7504.69 =12861.39

Present Value of Benefits of Plan B=29000*(P/F, 6%,25 years)+(10423+91000)(P/A, 6%,25 years)

                       =6754.1+ 7931.27=14685.37

Present Value of Benefits of Plan C=31500*(P/F, 6%,25 years)+(11160+96000)(P/A, 6%,25 years)

                        =7336.35+8380= 15715.91

Benefit-cost ratio= Present Value of Benefits/ Present Value of Costs

Benefit-cost ratio of Plan A=12861.39/123597.2=0.104

Benefit-cost ratio of Plan B= 14685.37/143870.9=0.1020

Benefit-cost ratio of Plan C=15715.91/154090/=0.1019

After looking upon all the Plans, we can see not any of the plan has B/C ratio more than 1, hence not recommended to invest in any of the Plan among all.

Alternatively, using challenger (c)-defender (f)approach:

First Pair= bf-bd/cf-cd = 14685.37-12861.39/143870.9-123597.2 =1523.98/20273.7=0.075 (less than 1) Not acceptable

Second pair=15715.91-14685.37/154090-143870.9=1030.54/10220=0.10

Hence in any of the pair ratio is not greater than 1, hence defender reains defender, otherwise defender becomes challenger. No option is preferable in this case.

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