Question

Ten cavemen with a remaining average life expectancy of 10 years use a path from their cave to a spring some distance away. The path is not easily traveled due to 100 large stones that could be removed. The annual benefit to each individual if the stones were removed is $9.50. Each stone can be removed at a cost of $1.50. The interest rate is 2 %.

a.Compute the benefit/cost ratio for the individual if he alone removed the 100 stones.

enter the benefit to cost ratio rounded to 2 decimal places?

B.compute the benefit ratio for the individual if the task was undertaken collectively, with each individual removing 10 stones

c.What maximum amount may be charged by a manager who organize the group effort if the minimum acceptable benefit/cost ratio is 2?

Answer 1

Given, cost of removing each stone = $1.5

Life expectancy = 10 years

No of cavemen = 10

Interst Rate = 2%

Annual benefit to each individual if stones were removed = $9.5

a.

If only one individual removes, cost of removing = $1.5 x 100 = $150

Benefit-Cost Ratio = Annual Benefit x (P/A, 2%, 10) / Cost of removing

*From discrete compounding table. P/A for 2% at 10 years = 8.983

Benefit-Cost Ratio = 9.5 x 8.983 / 150 = 0.5689

= 0.57

b.

If undertaken collectively, and assuming each one does the same amount of work. Cost of removing the stones will be $100/10 x 1.5 = $15

Benefit-Cost Ratio = Annual Benefit x (P/A, 2%, 10) / Cost of removing

*From discrete compounding table. P/A for 2% at 10 years = 8.983

Benefit-Cost Ratio = 9.5 x 8.983 / 15 = 5.689

= 5.69

c.

Let X denotes the amount charged by manager from each individual for organising the group effort.

So, Cost of removing = 15 + X

Benefit-Cost Ratio = Annual Benefit x (P/A, 2%, 10) / Cost of removing

*From discrete compounding table. P/A for 2% at 10 years = 8.983

Benefit-Cost Ratio = 9.5 x 8.983 / (15 + X)

Since the minimum accepted Benefit- Cost Ratio =2

2 = 9.5 x 8.983 / (15 + X)

85.3385 = 30 + 2X

X = 27.66925

So manager gets 27.67$ from each cavemen or a total of 276.69$

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