• Objective: Learnhow to choose the best
investment from multiple options using the
Rate of Return (ROR) method.
• - Compare mutually exclusive alternatives
• - Use Incremental ROR (Δi*) to guide decisions
• - Understand when to accept or reject options
Introduction
3.
• Rate ofReturn (ROR or i*): Percentage profit
from an investment
• Minimum Attractive Rate of Return (MARR):
The lowest return you’re willing to accept
• Internal Rate of Return (i*): The interest rate
that makes Net Present Worth = 0
• Incremental Rate of Return (Δi*): Extra return
between two options
• Cash Flow: Money going in (revenue) or out
(cost) each year
Key Terms (Simple Definitions)
4.
• Problem: Comparingoptions of different costs
• Solution: Calculate Δi* (the return on the extra
cost)
• Example:
• - Alt A: $50,000, i* = 35%
• - Alt B: $85,000, i* = 29%
• - MARR = 16%
Why Incremental Analysis?
5.
• 1. Rankby initial cost (low to high)
• 2. Subtract cash flows (B − A = ΔCF)
• 3. Calculate Δi* using PW = 0 or AW = 0
• 4. If Δi* ≥ MARR, pick the higher cost option
• 5. Repeat if more than 2 alternatives
Steps for Incremental ROR
6.
• Alt A:
•- Initial Cost: $15,000
• - O&M: $8,200/year
• - Salvage: $750
• - Life: 10 years
• Alt B:
• - Initial Cost: $21,000
• - O&M: $7,000/year
Example Problem (2 Alternatives)
7.
• Incremental CashFlows (B - A):
• - Δ Initial Cost: $6,000
• - Δ Annual O&M: $1,200 savings
• - Δ Salvage: $300 gain
• Solve:
• 0 = -6,000 + 1,200(P/A, i, 10) + 300(P/F, i, 10)
• Use Excel or trial-and-error to find Δi* ≈
Example Solution
8.
• Steps:
• 1.Eliminate all with i* < MARR
• 2. Start from cheapest option
• 3. Compare 2 at a time using Δi*
• 4. If Δi* < MARR, eliminate the more
expensive one
Comparing More Than 2 Options
9.
• Four dealeroptions (costs and benefits vary):
• - Compare 1 vs 2 → Δi* = 14.57% → Keep 2
• - 2 vs 3 → Δi* = -18.77% → Eliminate 3
• - 2 vs 4 → Δi* = 13.60% → Choose 4
• Final Choice: Dealer 4 if MARR = 13%
Larger Example
10.
• - UseΔi* to compare between alternatives
• - If Δi* ≥ MARR → accept costlier alternative
• - Use cash flow tables or Excel (IRR, NPV
functions)
• - Incremental analysis is fair and simple!
Summary
11.
• - Alwayscompare using equal service lives
• - Be careful with multiple IRRs
• - Combine with PW or AW for double-checking
Bonus Tips
