Question

A public project with social discount rate of 6% has determined that its initial costs will be spread out over the first 2 years of construction. They will be $10,000,000 in year 0, $15,000,000 in year 1, and $5,000,000 in year 2. Beginning in year 3 and continuing until year 22, the project will have an annual operating expense of $1,000,000. In addition, the city government sponsoring the project will receive $100,000 per year in revenue because of the project. The private businesses in the area expect to gain $4,000,000 per year in new business because of the project in years 3 - 22. However, the construction will disrupt several local business during year 1 and 2 resulting in a loss of $750,000 per year during those two years for those businesses. What is the present worth of the net benefits/disbenefits in this project (Enter in the box to the nearest dollar with no dollar sign)?

Answer 1

PW ($) = PW of First cost + PW of government revenue + PW of (private business gain - annual costs) + PW of loss to business

= - 10,000,000 - 15,000,000 x PVIF(6%, 1) - 5,000,000 x PVIF(6%, 2) + 100,000 x PVIFA(6%, 22) + (4,000,000 - 1,000,000) x PVIFA(6%, 20) x PVIF(6%, 2) - 750,000 x PVIFA(6%, 2)

= - 10,000,000 - 15,000,000 x 0.9434** - 5,000,000 x 0.8900** + 100,000 x 12.0416** + 3,000,000 x 11.4699** x 0.8900** - 750,000 x 1.8334**

= - 10,000,000 - 14,151,000 - 4,450,000 + 1,204,160 + 30,624,633 - 1,375,050

= 1,852,743

**Using PVIFA and PVIF Factor tables