A city of about 30,000 people is trying to attract a manufacturing business. It

Question

A city of about 30,000 people is trying to attract a manufacturing business. It has offered to install and operate a water pumping plant to provide service to the proposed factory site. This would cost the city $160,000 now, plus $19,000 per year in annual operating costs for the next 5 years, all in Year-0 dollars. To reimburse the city, the new business must pay a fixed uniform annual fee, A, at the end of each year for 5 years. At the end of the 5 years, the business will buy the plant from the city for $160,000. All the payments by the business to the city will be in actual dollars. It has been agreed that the city should get realrate-of-return of 6% on this investment. If inflation is expected to average 3.77% per year over the five years, determine the amount of the uniform fee, A, that the business should pay the city.

The PW of the investment from the point of the city is $           . (Round to the nearest dollar.)

Note: Include the initial cost, annual operating costs and the salvage value (exclude the annual payments, A). Use negative sign for costs.

The annual fee, A, to be paid by the business to the city is $ (Round to the nearest dollar.)

Explanation / Answer

Step 1 : Firstly we have to calculate the actual rate of return from the given real rate of return and inflation rate

real rate(r) = 6%

Inflation rate(i) = 3.77%

Actual rate of Return = R

(1+R) = (1+r)(1+i) = (1+0.06)(1+0.0377)

R = (1.06*1.0377)-1 = 0.0999 (i.e. 9.99%) or 10%

Step 2 : Now, we should calculate Present Value of investment from the point of the city

Step 3 : After calculating PV of Investment, the annual payments(A) is calculated as follows:-

Total PV of Annual Payment over the 5 years should be equal to PV of Investment from the point of city as the new business must pay a fixed uniform annual fee to reimburse the city.

Annual Payments(A) = PV of Investment/PVAF(10%,5yrs) = $132,650/3.791 = $34,991

Year Particulars Amount in $ PVF@10% PV of cash flows 0 Initial Investment -160,000 1 -160,000 1 Annual Operating Cost -19,000 0.909 -17,271 2 Annual Operating Cost -19,000 0.826 -15,694 3 Annual Operating Cost -19,000 0.751 -14,269 4 Annual Operating Cost -19,000 0.683 -12,977 5 Annual Operating Cost -19,000 0.621 -11,799 5 Salvage Value 160,000 0.621 99,360 Total PV of Investment -132,650

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