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Engineering Economics and Finance Dr. Omar El-Anwar Dr. Dina Saad Lecture #5b: Rate of Return Analysis: MulGple Projects
Agenda Ø Why Incremental Analysis Ø CalculaGng Incremental ROR Ø More Than Two Projects
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Why Incremental Analysis • If RORA > RORB, is project A beSer economically? • E.g. MARR = 16%, there is 90,000 to invest – RORA = 35%, PA = 50,000 – RORB = 29%, PB = 85,000 – What remains is invested at MARR Overall RORA= [50,000x0.35 + 40,000x0.16]/90,000 = 26.6% Overall RORB= [85,000x0.29 + 5,000x0.16]/90,000 = 28.3% Project B is beSer! ROR should not be used to rank projects 3
CalculaGng Incremental ROR • AssumpGon: equal service – Must use LCM for each pair-wise comparison
• Procedure for each pair of projects: – Project with higher P is project B – For LCM: Incremental cash flow = CFB – CFA , might need a diagram – Find Δi*B-A (for incremental CF) – If Δi*B-A ≥ MARR, select Project B 4
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CalculaGng Incremental ROR • E.g. using incremental ROR, which project to select? MARR = 12% A
B
IniGal Cost, P ($)
8000
13000
Annual Cost, A ($/yr)
3500
1600
Salvage Value, S ($)
0
2000
Life (years)
10
5
5
Project A 1 0
2
3
4
5
6
8000
13000
9
10
3
4
1600
1
2
2000
2000 5
3
6
7
8
9
10
13000
Project B – A (Incremental CF)
5000
8
3500
Project B with LCM 1 0 2
0
7
2000
1900 4
5
6
7
8
9
10
11000
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Project B – A (Incremental CF) 1
0
2
5000
3
2000
1900 4
5
6
7
8
9
10
11000
• Find Δi*B-A • There are three sign changes in NCF, and three sign changes in CCF • Then, there are mulGple RORs • PW = 0 -5000+1900(P/A, Δi*,10)-11000(P/F, Δi*,5)+2000(P/F, Δi*,10) = 0 • Using some analysis, there will be only one realisGc ROR = 12.65% • Therefore, 12.65% is used • Δi*B-A = 12.65% > MARR • Select Project B
More Than Two Projects • Procedure: 1. Order projects from smallest to largest iniGal cost 2. For revenue generaGng projects only: Compute i* for 1st project • •
3. 4. 5. 6.
If i* < MARR: eliminate project and go the next project If i* ≥ MARR: go to step 3
Develop incremental CF with next project Compute Δi* and compare to MARR Decide which project to eliminate Pick a new project to compare with and go to step 3
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Note • For independent projects: – No comparison between projects – No need for incremental ROR analysis – Accept project if ROR ≥ MARR
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Midterm exam • Rules: – No phones – No borrowing – No talking – Bring your staGonary, calculator, and watch
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QuesGons?
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