Question

The Western Railway Company (WRC) has been offered a 100-year contract to haul a fixed amount of coal each year from Wyoming to Illinois. Under the terms of the agreement, WRC will receive $4,200,000 now in exchange for its hauling services valued at $360,000 per year through end-of-year 50. If WRC’s cost of capital is 12% per year, is this a profitable agreement for WRC? What is the minimum equivalent uniform amount for this agreement?

Answer 1

Annual revenue = $360000

R = 12%

Time = 50 years

Present value of the annual revenue = 360000*(1- 1/1.12^50)/.12

Present value of the annual revenue = $2989619.46

Since the lump-sum payment of $4200000 is more than the $2989619.46, then it is a profitable agreement. WRC should receive $4200000.

Let, minimum equivalent amount = P

Then,4200000 = P*(1- 1/1.12^50)/.12

4200000 = P*8.3045

P = 4200000/8.3045

P = $505750 approx.

So, annual value for 50 years should be $505750 approx.