Rate of Return Evaluation for Multiple Alternatives

1. Rate of Return Evaluation for Multiple Alternatives • Consider the following situation: A friend of yours who has recently graduated tells you he has heard of some investment opportunities being offered at the Student Center. He offers to underwrite any one investment you choose, with the following conditions: • The investment must meet or exceed an MARR of 20%. • Only one “share” of the investment can be purchased. • Once you have rejected an investment, you are no longer allowed to consider it.

2. Option A: Outside the Student Center A. You go to the student center and see a table set up outside where Acme National Bank is offering to give $1.50 next year to everyone who invests $1 now. What is the rate of return on this investment?

3. Option A: Outside the Student Center Assuming there are no other investment opportunities in sight, would you ask your friend to invest $1 for you? Just as you are about to announce your decision to your friend, someone comes out of the student center to tell you that there is an investment opportunity inside that promised a 40% rate of return. Knowing that you can only invest in one, would you pass up the opportunity to invest with Acme National Bank and go inside to invest?

4. Option B: Inside the Student Center B. You are in the lobby of the student center and see a table set up where Mercer Bank and Trust is offering to give $140 next year to everyone who invests $100 now. What is the rate of return on this investment?

5. Option B: Inside the Student Center Assuming there are no other investment opportunities in sight, would you ask your friend to invest $100 for you? Just as you are about to announce your decision to your friend, someone comes in to tell you that there is an investment opportunity outside that promises a 50% rate of return. Knowing that you can only invest in one of them, would you pass up an investment in Mercer Bank and Trust and go outside to invest?

6. Incremental Rate of Return Is the rate of return on the increased cost relative to the increased revenue sufficient to justify making a higher cost investment? In our example, Year A B B – A 0 $1 $100 $99 1 1.50 140 138.50 ROR =

7. $3,000 A =$4,000 $18,000 $2,700 A =$3,600 $35,000 A =$400 $15,000 $15,000 $300 $17,000 Incremental Rate of Return Analysis Example: 2 alternatives, MARR = 20% Alt. P Alt. Q Q – P

8. Incremental Rate of Return Analysis Solution: Use PW 17000 = 400 (P/A, i%, 9) + 15000 [(P/F, i%, 3) + (P/F, i%, 6)] - 300 (P/F, i%, 9) Trial and Error,

9. In Excel

10. Incremental Rate of Return Analysis Solution Steps: • (For revenue projects) Evaluate each alternative separately to ensure MARR is met. • Find net cash flow = higher cost – lower cost for the LCM of lives of the alternatives. • Find ROR of net cash flow • If ROR > MARR, select higher cost alternative ROR < MARR, select lower cost alternative

11. Incremental Rate of Return Analysis for Multiple Alternatives Solution Steps: • (For revenue projects) Evaluate each alternative separately to ensure MARR is met. Eliminate any alternative that does not meet the MARR. • Order the alternatives from smallest initial cost to largest initial cost. • Compare smallest initial cost (defender) to next smallest initial cost (challenger) over LCM of lives. • If ROR > MARR, select challenger (challenger is now the defender) ROR < MARR, select defender • Compare current defender to next lowest cost alternative over LCM of lives. Losing alternative is eliminated (no longer considered.) • Continue until all alternatives have been investigated.

12. Incremental Rate of Return Analysis Example: 4 alternatives, MARR = 12% A B C D 0 -15000 -18000 -25000 -35000 1 4000 5000 6000 8000 2 4000 5000 6000 8000 3 4000 5000 6000 8000 4 4000 5000 6000 8000 5 4000 5000 6000 8000 6 4000 5000 6000 8000 7 4000 5000 6000 8000 8 4000 5000 6000 8000 9 4000 5000 6000 8000 10 5000 6000 5500 7300 • ROR

13. Incremental Rate of Return Analysis b) Incremental analysis