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 $9.00. Each stone can be removed at a cost of $2.25. The interest rate is 2 %

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

Answer 1

Each stone can be removed at a cost of $2.25. If the stone is removed by one indivitual, the total cost of removing 100 stones = $2.25 * 100 = $225

Thus, the present worth of the costs = $225.

The annual benefit to each individual if the stones were removed is $9.00.

The Present Worth of the benefits = A(P/A, i, n)

                                                       = 9.00(P/A, 2%, 10)

                                                       = 9.00(8.983)

                                                        = $80.847

The benefit/cost ratio = Present Worth of the benefits / Present Worth of the costs

                                   = $80.847 / $225

                                   = 0.36

Therefore, the benefit/cost ratio for the individual is 0.36.