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 $325,000 per year in years 1 through 5. At the end of that time, a mild recession slowed the development, so the parties signed another contract for $155,000 per year for 4 more years. Determine the present worth of the two contracts at an interest rate of 9% per year.

Answer 1

Total Present Value = $2,890,983.32

Step-by-step explanation:

The present value of the two contracts would be done as follows using the present value of an annuity formula:

The present value of an annuity is given as follows:

PV = A× (1- (1+r)^(-n))/r

Where

AV = Present value

A- annual income

n- numbers of years

r- annual interest rate

The first contract

DATA-

A- 325,000, n- 5, r- 0.09

PV = 325,000× ((1.09^(-5) -1)/0.09 = 1,264,136.66

Contract 2

The present value would be done in two (2) steps:

Step 1:

Present value in year 5 terms:

Data- A- 155,000, r- 0.09, n- 4

PV = 155,000 × 1-1,09^(-4)/0.09 = 502,156.58

Step 2:

PV in year 0 term:

=PV in year 4 × 1-1.09^(-5)

= PV = 502,156.58 × = 1,626,846.66

Total present value = 1,264,136.66 + 1,626,846.66 = 2,890,983.32

Total Present Value = $2,890,983.32