Rate of Return and Incremental Analysis.ppt

1. RATE OF RETURN METHOD

3. INCREMENTAL ANALYSIS

4. Why Must Incremental Analysis be Used for
Competing Projects?
• Assume that an MARR of 16% per year is required, and $90000 is
available to invest:
• Project A requires $50000 upfront to obtain an IRR of 35% per year.
• Project B requires an $85000 first cost and returns an IRR of 29% per
year.
• What could we do with the un-invested money from Project A?
($40000)

5. Why Must Incremental Analysis be Used for
Competing Projects?
• It would be reasonable to invest the remaining $40000 at
the MARR:
• Overall IRRA = 50000(0.35) + 40000(0.16)
90000
= 26.6% per year
• Project B returns an IRR of 28.3% per year on ALL the
money available to invest.

6. Rs. 90000 MARR=16% p.a
• If we take a big picture of the scenario, Alternative
B would be better as the overall RoR on Rs.90000
available is more.
Particulars Project A Project B
Initial Investment -50000 -85000
Rate of Return 35% 29%
Overall RoR 26.6% 28.3%

7. • To overcome this drawback, compute incremental analysis of RoR

8. Incremental Analysis (Procedure)
Step 1: Compute the cash flow for the difference between the
projects (A,B) by subtracting the cash flow of the lower
investment cost project (A) from that of the higher
investment cost project (B).
Step 2: Compute the IRR on this incremental investment (IRR)
Step 3: Accept the investment B if and only if
IRR B-A > MARR
NOTE: Make sure that both IRRA and IRRB are greater than MARR

9. Incremental Analysis
MARR= 10%
Incremental IRR (B-A)= -4000 + 5000 (P/F, I, 1) =0
Adopt the trial and error approach and get the value of interest rate which turns the above
equation to zero.
Incremental IRR (B-A)= 25%
Since incremental IRR > MARR; Select B
Particular A B B-A
Initial Investment -1000 -5000 -4000
Revenue in year 1 2000 7000 5000
RoR 200% 40% 25%

10. General Decision Rule:
• If Incremental IRR >MARR, Go for B (Project with higher initial Investment)
• If incremental IRR=MARR, Either A or B
• If Incremental IRR<MARR, Go for A (Project with lesser Initial Investment)

11. Solved Problems
1. John Covington, a college student, wants to start a small-scale painting
business during his off-school hours. To economize the start-up business, he
decides to purchase some used painting equipment. He has two mutually
exclusive options: Do most of the painting by himself by limiting his
business to only residential painting jobs (B1) or purchase more painting
equipment and hire some helpers to do both residential and commercial
painting jobs that he expects will have a higher equipment cost, but provide
higher revenues as well (B2). In either case, John expects to fold up the
business in three years, when he graduates from college. The cash flows for
the two mutually exclusive alternatives are as follows. Assume a MARR of
10% : n B1 B2
0 -$ 3,000 -$ 12,000
1 1,350 4,200
2 1,800 6,225
3 1,500 6,330
IRR 25% 17.43%

12. Solved Problems
• As both the projects are attractive at a MARR of 10%, select the best
alternative by performing incremental analysis.
NPV=0
-9000+2850(P/F,i,1) + 4425 (P/F, i, 2)+ 4830 (P/F, i, 3) = 0
Incremental IRR (B2-B1)= 15%
As Incremental IRR (B2-B1)> MARR, Select B2
n B1 B2 B2-B1
0 -$ 3,000 -$ 12,000 -9000
1 1,350 4,200 2850
2 1,800 6,225 4425
3 1,500 6,330 4830
IRR 25% 17.43%

13. Solved Problems
2. Consider the following three sets of mutually exclusive alternatives:
Which project would you select on the basis of the rate of return on
incremental investment, assuming that MARR=15%?
Solution:
Since Project IRR of all the three alternatives are greater than MARR, all
the three projects qualify for an incremental analysis.
n D1 D2 D3
0 -$ 2,000 -$ 1,000 -$ 3,000
1 1,500 800 1,500
2 1,000 500 2,000
3 800 500 1,000
IRR 34.37% 40.76% 24.81%

14. n D1 D2 D1-D2
0 -$ 2,000 -$ 1,000 -1000
1 1,500 800 700
2 1,000 500 500
3 800 500 300
IRR 34.37% 40.76%
• First compare D1 and D2 as the first additional investment of Rs.
1000 is going into D1.
NPV=0
-1000+ 700(P/F, I, 1)+ 500 (P/F, I, 2) + 300 (P/F, I, 3)=0
Incremental IRR (D1-D2)= 27.61%
As incremental IRR (D1-D2)> MARR, Select D1
Now compare D1 with D3 and select the best alternative.

15. n D1 D3 D3-D1
0 -$ 2,000 -$ 3,000 -1000
1 1,500 1,500 0
2 1,000 2,000 1000
3 800 1,000 200
IRR 34.37% 24.81%
NPV=0
-1000+1000(P/F, I, 2) + 200 (P/F, I, 3) =0
Incremental IRR (D3-D1)= 8.8%
Since Incremental IRR (D3-D1)= 8.8%< MARR, Select D1 (Lower
Investment Alternative)
Thus out of the $3000 available, invest $2000 on D1, retain the
remaining $1000 at MARR=15%.

16. Solved Problems
3. Incremental IRR – Unequal life. MARR = 10%
NPV=0
-1000+3000(P/F, I, 3)= 0 Incremental IRR (E2-E1)=?
n E1 E2
0 -$ 2,000 -$ 3,000
1 1,000 4,000
2 1,000
3 1,000
n E1 E2 E2 E2-E1
0 -$ 2,000 -$ 3,000 -3000 - $ 1000
1 1,000 4,000 - 3000 1000 0
2 1,000 4,000 – 3000 1000 0
3 1,000 4000 4000 3000

17. 4. Compute Incremental IRR and select the best alternative. Assume
MARR 10%
n Alt 1 Alt 2
0 -15000 -21000
1-25 -8200 -7000
25 +750 +1050
n Alt 1 Alt 2 Alt2-Alt1
0 -15000 -21000 -6000
1-25 -8200 -7000 +1200
25 +750 +1050 +300
NPV=0
-6000+1200 (P/A, I, 25)+ 300 (P/F, I, 25)=0
Incremental IRR=?