Question

A state department of health is considering a public awareness campaign to encourage vaccination. It determines that the cost of this campaign would be $700,000 per year for the next 6 years. It estimates that the campaign would reduce rates of illness and communicable disease. At the end of the first year of the campaign, the resulting savings would be $1,300,000; the savings would decrease by $80,000 each of the following 5 years. Assuming a discounting factor of 4%, compute the benefit cost ratio.

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B/C = ?

Carry all interim calculations to 5 decimal places and then round your final answer to two decimal places. The tolerance is ±0.01.

Would you recommend the department of health launch the public awareness campaign?

Answer 1

Cost of campaign = 700,000 per year

Life = 6 years

Savings in the first year = 1,300,000

The savings decreases by 80,000 each year

Discounting factor = 4%

Calculate benefit cost ratio.

Calculate B/C Ratio (using PW Method)

Step 1 Calculate PW of annual costs

PW = 700,000 (P/A, 4%, 6)

PW = 700,000 (5.242136) = 3,669,495.2

Step 2 Calculate PW of annual savings

PW = 1,300,000 (P/A, 4%, 6) - 80,000 (P/G, 4%, 6)

PW = 1,300,000 (5.242136) - 80,000 (12.506242) = 5,814,277.44

Step 3 Calculate B/C Ratio

B/C Ratio = PW of Benefits/PW of Costs

B/C Ratio = 5,814,277.44 / 3,669,495.2

B/C Ratio = 1.58448 or 1.58

The benefit cost ratio is greater than 1, the program is accepted.