Civil engineering consulting firms that provide services to outlying communities

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 $395,000 per year in years 1 through 7. At the end of that time, a mild recession slowed the development, so the parties signed another contract for $165,000 per year for 6 more years. Determine the present worth of the two contracts at an interest rate of 8% per year. The present worth of the two contracts is determined to be $

Explanation / Answer

According to the first contract, an income of $395,000 per year would be received from Year 1 to Year 7.

Calculate the present worth of Ist contract -

PW = $395,000(P/A, 8%, 7)

PW = $395,000 * 5.2064 = $2,056,528

The present worth of Ist contract is $2,056,528

Second contract starts at the end of Year 7 and creates income of $165,000 per year for 6 more years.

So, present worth of second contract will be calculated in two steps.

STEP 1 - Calculate the present worth of annual income at Year 7

PW at Year 7 = $165,000(P/A, 8%, 6)

PW at Year 7 = $165,000 * 4.6229 = $762,778.5

STEP 2 - Calculate PW at Year 0 using PW at Year 7 -

PW at Year 0 = $762,778.5(P/F, 8%, 7)

PW at Year 0 = $762,778.5 * 0.5835 = $445,081.25

The present worth of the IInd contract is $445,081.25

Present worth of two contracts = PW of Ist contract + PW of IInd contract

Present worth of two contracts = $2,056,528 + $445,081.25 = $2,501,609.25

Thus,

The present worth of the two contracts is determined to be $2,501,609.25

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