Suppose that the government wants to keep the sidewalks clean by installing 100

Question

Suppose that the government wants to keep the sidewalks clean by installing 100 new garbage cans. The garbage cans are purchased this year at a cost of $200 per can.

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3. Suppose that the government wants to keep the sidewalks clean by installing 100 new garbage cans. The garbage cans are purchased this year at a cost of $200 per can. They will rust and need to be removed in four years at a cost of $500 per can. The value of the clean sidewalks to all people in town totals S15,000 per year, and people receive this benefit for five years, starting this year. Below shows the total costs of the cans starting this year (t -0) through the year the cans are removed (t-4) and the total benefit in each year. The discount rate is 3 percent 1-2 Costs Benefits t-0 20,000 15,000 t-4 50,000 15,000 15,000 15,000 ?15,000 a. What is the present discounted cost of the 100 garbage cans over their lifetime? b. Should the government buy the garbage cans?

Explanation / Answer

(a)

Present discounted cost ($) = 15,000 x P/A(3%, 4) - 20,000 - 50,000 x P/F(3%, 4)

= 15,000 x 3.7171** - 20,000 - 50,000 x 0.8885**

= 55,756.50 - 20,000 - 44,425

= - 8,668.50

(b)

Since present discounted cost is negative, government should not buy the cans.

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