Check my work Civil engineering consulting firms that provide services to ou tly

Question

Check my work Civil engineering consulting firms that provide services to ou tlying 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 f entered into a fixed-price contract with a spec home builder, resulting in a stable income of through 5. At the end of that time, 185,000 per year for 4 more years. Determine the present worth of th rm a mild recession slowed the development, so the parties signed another contract for e tw°contracts at an interest rate of 7% per year. The present worth of the two contracts is determined to be

Explanation / Answer

Here we have to find the present value of the future annuity payment.

Payment from Y1 to Y5= $305,000

Payment from Y6 to Y9= $185,000

interest rate r= 7%

The formula for present value of annuity

PV = PMT*((1-(1/1+r)^n))/r)

Here PMT for the first contract = 305,000

r =7%

n= 5 years

Hence PV= 305000*((1-(1/1.07))^5/0.07

PV= $1,250,560.22

NOw for the second contract

PMT= $185,000

r= 7%

n=4 years

here since for intital 5 years there is no paymet for contract 2, hence to calculate the PV for the last 4 years, we will calculate the PV of annuity for 9 years and subtract it by PV of annuity for 5 years:

PV= 185000*(1-1/1.07)^9/0.07 - 185000*(1-1/1.07)^5/0.07

PV= $446,781.44

Hence the present value of two contract will be = 1,250,560.22+446,781.44= $1,697,341.66

Thanks

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