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 I requires an initial investment of $20,000 and provides annual benefi ts of $4,465. Polisher II requires an initial investment of $10,000 and provides annual benefi ts of $1,770. Polisher III requires an initial investment of $15,000 and provides annual benefi ts of $3,580. MARR is 15%/yr. Based on an internal rate of return analysis, which polisher should be recommended?

Answer 1

Answer:

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.

I hope my solution solves your query.

Answer 2

Answer:

Polisher 3

Explanation:

The internal rate of return is the discount rate that equates the after tax cash flows from an investment to the amount invested.

The internal rate of return can be calculated using a financial calculator.

For polisher 1 :

Cash flow in year 0 = $-20,000 

Cash flow each year from year 1 to 10 = $4,465

IRR = 18.09%

For polisher 2 :

Cash flow in year 0 = $-10,000

Cash flow each year from year one to ten = $1,770

IRR = 12.00

For polisher 3 :

Cash flow in year 0 = $-15,000

Cash flow each year from year one to ten = $3,580

IRR = 20.02%

Polisher 3 has the highest IRR and should be chosen based on this criteria.

To find the IRR using a financial calacutor:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. After inputting all the cash flows, press the IRR button and then press the compute button.

I hope my answer helps you