Question

In a paper mill, a new conveyor system is being considered to move the freshly chipped wood to the next stage in the production line. The cost of the new conveyor is $55,250. Yearly operating and maintenance costs for the conveyor are estimated to be $13,260. The conveyor is expected to last for 20 years with no salvage value. Because of the new conveyor’s design, more paper product can eventually be produced by the mill. This new production level results in an increase in annual income of $28,500. Determine the rate of return on the investment in the new conveyor.

please use unique solution

Answer 1

initial cost = 55250

Annual revenue = 28500

Annuall cost = 13260

Life = 20 years

Net profit per year = 28500 - 13260 = 15240

Let i be the rate of return, then PW at i should be equal to zero, so

-55250 + 15240*(P/A, i%,20) = 0

(P/A, i%,20) = 55250/15240 = 3.625328

Using trail and error method

At i = 20%, (P/A, i%,20) = 4.869579

At i = 25%, (P/A, i%,20) = 3.95388

At i = 28%, (P/A, i%,20) = 3.545804

At i = 27%, (P/A, i%,20) = 3.672617

using interpolation

i = 0.27 + [(3.672617-3.625328)/(3.672617-3.545804)] * (0.28-0.27)

i = 0.27 + 0.003729

i = 0.273729 = 27.37% (Approx)