1. Civil engineering consulting firms that provide services to outlying communities are vulnerable to a number of factors that affect the financial condition of the communities, such as bond issues and real estate developments. A small consulting firm entered into a fixed-price contract with a large developer, resulting in a stable income of $260,000 per year in years 1 through 3. At the end of that time, a mild recession slowed the development, so the parties signed another contract for $190,000 per year for 2 more years. Determine the present worth of the two contracts at an interest rate of 10% per year.
2. Revenue from the sale of ergonomic hand tools was $300,000 in years 1 through 4 and $465,000 in years 5 through 9. Determine the equivalent annual revenue in years 1 through 9 at an interest rate of 10% per year.
3. Costs associated with the manufacture of miniature high-sensitivity piezoresistive pressure transducers are $73,000 per year. A clever industrial engineer found that by spending $16,000 now to reconfigure the production line and reprogram two of the robotic arms, the cost will go down to $58,000 next year and $52,000 in years 2 through 5. Using an interest rate of 10% per year, determine (a) the equivalent annual cost of the manufacturing operations and (b) the equivalent annual savings in years 1 through 5.
4. Austin Utilities is planning to install solar panels to provide some of the electricity for its groundwater desalting plant. The project would be done in two phases. The first phase will cost $4 million in year 1 and $5 million in year 2. This investment will result in energy savings (phase 2) of $540,000 in year 3, $546,000 in year 4, and amounts increasing by $6000 each year through year 10. Let i = 10% per year.
(a) What is the future worth of the savings?
(b) Is the cost of the solar project justified by the savings? (Hint: Calculate the difference between savings and cost).
5. Use the cash flow diagram to determine the single amount of money Q4 in year 4 that is equivalent to all of the cash flows shown. Use i = 10% per year.
6. A low-cost noncontact temperature measuring tool may be able to identify railroad car wheels that are in need of repair long before a costly structural failure occurs. If BNF Railroad saves $100,000 in years 1 through 5, $110,000 in year 6, and constant amounts increasing by $10,000 each year through year 20, what is the equivalent annual worth over the 20 years of the savings? The interest rate is 10% per year.