Barron Chemical uses a thermoplastic polymer to enhance the appearance of certain RV panels. The initial cost of one process was $130,000 with annual costs of $49,000 and revenues of $78,000 in year 1, increasing by $1000 per year. A salvage value of $23,000 was realized when the process was discontinued after 8 years. What rate of return did the company make on the process? Solve by trial and error and verify i * by spreadsheet.

19.17%

Explanation:

initial cost = - $130,000

cash flow year 1 = $78,000 - $49,000 = $29,000

cash flow year 2 = $29,000 + $1,000 = $30,000

cash flow year 3 = $30,000 + $1,000 = $31,000

cash flow year 4 = $31,000 + $1,000 = $32,000

cash flow year 5 = $32,000 + $1,000 = $33,000

cash flow year 6 = $33,000 + $1,000 = $34,000

cash flow year 7 = $34,000 + $1,000 = $35,000

cash flow year 8 = $35,000 + $1,000 + $23,000 = $59,000

using an excel spreadsheet and the IRR function, we can determine the project's IRR = 19.17%

The IRR is the discount rate at which the NPV of the project would equal 0. If you are going to try to solve it by trial and error you can prepare an equation and then try to solve it by approximation:

$130,000 = $29,000 / (1+r) + $30,000 / (1+r) ² + $31,000 / (1+r) ³ + $32,000 / (1+r) ⁴ + $33,000 / (1+r) ⁵ + $34,000 / (1+r) ⁶ + $35,000 / (1+r) ⁷ + $59,000 / (1+r) ⁸

Just replace r and start increasing or decreasing as the value approaches to $130,000