For the next four questions, refer to the following prompt. Now that the economi
ID: 1126255 • Letter: F
Question
For the next four questions, refer to the following prompt. Now that the economists have derived a demand curve for the San Fransokyo bay oil clean-up, they have determined that the benefits, accruing after restoration is complete, are equal to $15 million/year Costs associated with cleanup are quite costly in year 0 ($50 million) but after the restoration effort, costs are reduced drastically (only $2 million per year Benefits (millions 0 15 15 15 Costs (millions 50 2 2 Year 2 3+ Assuming an interest rate of 4%, how long would it take the restoration project to become a socially optimal project? A. Never B. 3 years C. 4 years D. 5 years (8) What do the economists working for the government of San Fransokyo determine the net benefits the first 5 years to be assuming an interest rate of 4%? A.-$10.4 million -$0.3 million C.$7.9 million $8.6 millionExplanation / Answer
ANSWER:
7) IN ORDER TO FIND WHEN THE PROJECT WILL BECOME SOCIALLY OPTIMAL , WE NEED TO FIND THE NO OF YEARS AT WHICH THE PW OF THE PROJECT WILL BE ZERO.
FIRST OF ALL WE NEED TO FIND THE NET CASH FLOWS WHICH WILL BE AS FOLLOWS:
FOR YEAR 0 = $0 MILLION - $50 MILLION = -$50 MILLION
FOR YEAR 1 MILLION - $2 MILLION = $13 MILLION
PW OF PROJECT = -50 + 13(P/A,I,N)
WHERE PW WILL BE EQUATED TO ZERO AND I WILL BE 4% AS GIVEN IN THE QUESTION.
0 = -50 + 13(P/A,4%,N)
50 = 13(P/A,4%,N)
SOLVING FOR N EQUAL TO 3 , 4 AND 5 WE GET
50 = 13 * 2.775 = 36.075 ( P/A VALUE AT N = 3 YEARS)
50 = 13 * 3.63 = 47.19 ( P/A VALUE AT N = 4 YEARS)
50 = 13 * 4.452 = 57.876 ( P/A VALUE AT N = 5 YEARS)
FROM THIS WE CAN SAY THAT THE INVESTMENT WILL BE BETWEEN 4 AND 5 YEARS BECAUSE AS AT 4 YEARS THE VALUE IS $47.19 MILLION WHILE AT 5 YEARS IT IS $57.876 MILLION AND THEREFORE ACCOEDING TO THE OPTIONS IT WILL BE AT THE END OF 5 YEARS THAT IS OPTION D.
8) IN ORDER TO FIND THE NET BENEFITS AT 4% INTEREST RATE AFTER 5 YEARS , WE NEED TO THE PW OF THE PROJECT WITH INITIAL INVESTMENT AT $50 MILLION AND NET BENEFIT AT $13 MILLION AT 4% WITH A TIME PERIOD OF 5 YEARS.
PW = -50 + 13(P/A,I,N)
PW = -50 + 13 * 4.452
PW = -50 + 57.876
PW = 7.876 OR $7.9 MILLION APPROX.
HENCE THE CORRECT OPTION IS C.