Question

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, real estate developments, etc. A small consulting firm entered into a fixed-price contract with a spec home builder, resulting in a stable income of $330,000 per year in years 1 through 4. At the end of that time, a mild recession slowed the development, so the parties signed another contract for $195,000 per year for 5 more years. Determine the present worth of the two contracts at an interest rate of 12% per year. The present worth of the two contracts is determined to be $ 446725.58%

Answer 1

Given,

Rate of interest = r = 0.12

(1 + r) = 1 + 0.12 = 1.12

Present worth (PW) of annuity would be calculated as below.

PW = {330,000/ 1.12^1} + {330,000/ 1.12^2} + {330,000/ 1.12^3} + {330,000/ 1.12^4} + {195,000/ 1.12^5} + {195,000/ 1.12^6} + {195,000/ 1.12^7} + {195,000/ 1.12^8} + {195,000/ 1.12^9}

         = (330,000/1.12) + (330,000/1.2544) + (330,000/1.40492) + (330,000/1.57351) + (195,000/1.76234) + (195,000/1.97382) + (195,000/2.21068) + (195,000/2.47596) + (195,000/2.77308)

         = 294,642.85 + 263,073.98 + 234,887.81 + 209,722.21 + 110,648.34 + 98,793.20 + 88,208.15 + 78,757.33 + 70,317.00

         = 1,449,050.87

Answer: $ 1,449,050.87