Question

Civil Engineering consulting firms that provide services to outlying communities are vulnerable to a number of factors that affect the financial condi- tion 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 $320,000 per year in years 1 through 4. At the end of that time, a mild recession slowed the develop- ment, so the parties signed another contract for $150,000 per year for two more years. Determine the present worth of the two contracts at an interest rate of 10% per year. in steps please don't copy from other answers

Answer 1

An interest rate of 10% per year is $1,274,689.97.

Step-by-step explanation:

To determine the present worth of the two contracts, we need to calculate the present value of each cash flow and then sum them up. First, let's calculate the present value of the stable income of $320,000 per year for years 1 through 4. The formula to calculate the present value is: PV = CF / (1 + r)^n Where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of years. For each year from 1 to 4, we calculate the present value using the formula: PV = $320,000 / (1 + 0.10)^n Plugging in the values, we get: Year 1: PV = $320,000 / (1 + 0.10)^1 = $290,909.09 Year 2: PV = $320,000 / (1 + 0.10)^2 = $264,463.07 Year 3: PV = $320,000 / (1 + 0.10)^3 = $240,421.88 Year 4: PV = $320,000 / (1 + 0.10)^4 = $218,565.35 Next, let's calculate the present value of the contract for $150,000 per year for two more years. Using the same formula, we have: Year 5: PV = $150,000 / (1 + 0.10)^1 = $136,363.64 Year 6: PV = $150,000 / (1 + 0.10)^2 = $123,966.94 Now, we add up the present values of the two contracts: Present worth = $290,909.09 + $264,463.07 + $240,421.88 + $218,565.35 + $136,363.64 + $123,966.94 Calculating the sum, we get: Present worth = $1,274,689.97 Therefore, the present worth of the two contracts at an interest rate of 10% per year is $1,274,689.97. If this helps let me know.