Question

Final Finishing is considering three mutually exclusive alternatives for a new polisher. Each alternative has an expected life of 10 years and no salvage value. Polisher 1 requires an initial investment of $20,000 and provides annual benefits of $4,465. Polisher 2 requires an initial investment of $10,000 and provides annual benefits of $1,770. Polisher 3 requires an initial investment of $15,000 and provides annual benefits of $3,580. MARR is 15%/year.
Show the comparisons and internal rates of return used to make your decision:

Based on an internal rate of return analysis, which polisher should be recommended?

Answer 1

Answer:

1. 18.09%

2. 12%

3. 20.02%  

Explanation:

As the MARR is 15%, we will accept projects which have IRR more than 15%. As the projects are mutually exclusive, we will choose only one project.

An IRR (Internal Rate of Return) is the rate which makes the NPV (Net Present Value) = ZERO.

The formula to calculate IRR is: 0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n where P0 = Initial cash outflow

And P1, . . . Pn equals the cash inflows in periods 1, 2, . . . n, respectively.      

1) IRR of project 1:

0 = -$20,000 + $4,465/(1+IRR)1 + $4,465/(1+IRR)2 + $4,465/(1+IRR)3 + . . . + $4,465/(1+IRR)10

Solving for IRR we have = 18.09%

2) IRR of project 2:

0 = -$10,000 + $1,770/(1+IRR)1 + $1,770/(1+IRR)2 + $1,770/(1+IRR)3 + . . . + $1,770/(1+IRR)10

Solving for IRR we have = 12%

3) IRR of project 3:

0 = -$15,000 + $3,580/(1+IRR)1 + $3,580/(1+IRR)2 + $3,580/(1+IRR)3 + . . . + $3,580/(1+IRR)10

Solving for IRR we have = 20.02%

We will choose project 3 as it has the highest IRR.