Final answer:
The fair offer for acquiring a right-of-way with yearly lease payments and a given interest rate is calculated by finding the present value of an ordinary perpetuity using the annual payment and the effective annual interest rate, derived from the quarterly compounded rate.
Step-by-step explanation:
The question is asking to determine a fair offer for acquiring a right-of-way based on a perpetual lease payment, given a certain interest rate that's compounded quarterly. The correct financial tool for this scenario is a present value calculation of a perpetuity. Since the payments are made at the end of each year, it is considered an ordinary perpetuity. To find the present value of an ordinary perpetuity, the formula is:
PV = PMT / i
where PV is the present value, PMT is the annual payment, and i is the interest rate per period. In this case, since the interest is compounded quarterly at 6.5%, the interest rate per period is (6.5% / 4) or 1.625% per quarter. To convert this quarterly rate to an effective annual rate, we use the formula:
(1 + r)^n - 1
where r is the quarterly rate, and n is the number of periods (quarters in a year, which is 4). This gives us the effective annual rate, and we can use this to find the present value of the perpetuity as follows:
PV = 3000 / (1 + 0.01625)^4 - 1
This will give us the present value, which is the fair offer for the right-of-way.