A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $100,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $75,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 33% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes their cost?

Question

Business

Gianni

8 February, 18:18

A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $100,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $75,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 33% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes their cost?

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Answers (1)

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Clay Massey · Answer 1

vinyl liner

Explanation:

expected costs:

concrete shell pool = $100,000 (100% guaranteed to last 10 years) vinyl liner = ($75,000 x 67% chance of lasting 10 years) + ($115,000 x 33% chance of needing repairs) = $50,250 + $37,950 = $88,200

The expected costs of the vinyl liner option are lower than the costs of paying for a concrete shell. There is a 67% chance that the vinyl liner will cost less money and only 33% chance that it will cost more money.