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 $8.25. Each stone can be removed at a cost of $2.50. The interest rate is 2 %.

Required:
a. Compute the benefit/cost ratio for the individual if he alone removed the 100 stones.
b. Compute the benefit/cost 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 organizes the group effort if the minimum acceptable benefit/cost ratio is 2?

Answer 1

a. B/C Ratio = 0.296

b. B/C Ratio = 2.964

c. Y = 12.05 USD will be the maximum amount charged by the manager.

Y = 12.05 x 10 = 120.54 USD for the whole group of 10

Step-by-step explanation:

Solution:

Data Given:

Number of Individuals = 10

Number of Stones = 100

Life Expectancy = 10 Years

Annual benefit = 8.25 USD

Stone Removal Cost = 2.50 USD

Interest Rate = 2%

a. If all the stones are removed by one individual:

Cost = 100 stones x Stone Removal Cost

Cost = 100 x 2.50 = 250 USD

Now, we have to calculate the Benefit/Cost Ratio for this individual by using the following formula:

B/C Ratio =
`(AB (P/A, 2, 10))/(Cost)`

Where,

AB = Annual Benefit = 8.25 USD

(P/A, 2%, 10) = 8.983 (From the compound interest table)

Cost = 250 USD

B/C Ratio =
`(8.25 * 8.983)/(250)`

B/C Ratio = 0.296

b. Each individual removing 10 stones.

Number of individuals = 10

So, the cost of removing the stones will be:

Cost = 10 x 2.50 = 25 USD

So,

B/C Ratio =
`(AB (P/A, 2, 10))/(Cost)`

B/C Ratio =
`(8.25 * 8.983)/(25)`

B/C Ratio = 2.964

c.

In this part, we are already given the B/C ratio, now we need to calculate the maximum amount charged by the manager for the help.

B/C ratio = 2

Let, Y be the amount of the manager. So,

B/C Ratio =
`(AB (P/A, 2, 10))/(Cost + Y)`

Plugging in the values and solving for Y:

2 =
`(8.25 * 8.983)/(25 + Y)`

50 + 2Y = 8.25 x 8.983

2Y = 74.109 - 50

2Y = 24.109

Y = 24.109/2

Y = 12.05 USD will be the maximum amount charged by the manager.

Y = 12.05 x 10 = 120.54 USD for the whole group of 10