The plan for one of the Princes\' Islands in Istanbul is to ban vehicular traffi

Question

The plan for one of the Princes' Islands in Istanbul is to ban vehicular traffic on the main street and turning this street into a pedestrian mall with tree plantings and other beautification features.This plan will involve actual costs of 6.7 M and,according to its proponents, the plan will produce benefits and disbenefits to the town as follows:

Compute the conventional B-C ratio of this plan based on a MARR of %10 per year and a 15-year project life.Use AW as the equivalent worth method.

Conventional B-C ratio

BENEFITS Increased sales tax revenue per year 570000 Increased real estate property taxes per year 305000 Benefits due to decreased air pollution per year 90000 Quality of life improvements to users per year 80000

Explanation / Answer

Consider the given problem here “Total Benefit = 570,000 + 305,000 + 90,000 + 80,000 = 1,045,000.

So, the PW of “benefit” is “1,045,000* [(1.1^15 – 1)/0.1*(1.1^15) ]”

=> PW(B) = 1,045,000* [(1.1^15 – 1)/0.1*(1.1^15)] = 1,045,000* (3.1772 / 0.4177) = 1,045,000*7.6064.

=> PW(B) = 7,948,688

Now, the PW of the “dis benefits” is given below.

=> PW(DB) = 190,000* [(1.1^15 – 1)/0.1*(1.1^15)] = 190,000*7.6064 = 1,445,216.

=> AW(B) = PW(B)*[i*(1+i)^15 / (1+i)^n – 1] = PW(B)*[0.1*(1.1)^15 / (1.1)^15 – 1].

=> AW(B) = PW(B)*[0.1*(1.1)^15 / (1.1)^15 – 1] = PW(B)*[1/7.6064] = 1,045,000.

Now, the AW(DB) is given below.

AW(DB) = PW(DB)* [i*(1+i)^15 / (1+i)^n – 1] = PW(DB)* [1/7.6064] = 190,000.

Similarly the AW(C) = 6,700,000*(1/7.6064) = 880,837.1899

So, the “B-C” ratio is given below.

=> AW(B) / [AW(C) + AW(DB)] = 1,045,000 / (190,000 + 880,837.1899) = 1,045,000 / 1,070,837.1899.

=> B-C ratio = 1,045,000 / 1,070,837.1899 = 0.97 < 1.

So, as we can see that the “B-C ratio” is less than 1, => the given project is not profitable.

Now, consider the following cases, => if “benefit” will reduced by the amount of “dis benefit”, => the amount of benefit will reduced by “190,000” per year, => AW(B) will further reduced by the amount of the “dis benefits”. So, “B-C ratio” will be reduced” further => the project is still rejected.

Now, consider another possibility the “Cost” will increased by the amount “190,000”, => the AW(C) will increase by “190,000*(1/7.6064)”. So, “B-C ratio” will be reduced” further => the project will be rejected.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.