rate of return analysis: multiple alternatives consider the following: you have $20,000 to invest in...

Rate of Return Analysis:Multiple Alternatives

Consider the following:

You have $20,000 to invest in either alternative A or alternative B. Your MARR is 8%.

Alternative A: Has an initial investment of $10,000 and an ROR of 20%.

Alternative B: Has an initial investment of $18,000 and an ROR of 18%.

Which alternative should you choose?

Rate of Return Analysis:Multiple Alternatives

Since you originally had $20,000, what happens to the amount left over after your investment?

Assumption: you can only invest the left over at your MARR.

Therefore your realized ROR is a weighted average of the investment and the remainder at MARR.

ROR for Alternative A:

ROR for Alternative B:

%14000,20$

)000,10($*%8)000,10($*%20

%17000,20$

)000,2($*%8)000,18($*%18

Incremental Cash Flowsfor ROR Analysis

An approach to comparing multiple projects is to conduct an incremental cash flow ROR.

The incremental cash flow between a project A and B is:

Incremental cash flow = cash flowB - cash flowA

Where project B is the one with the larger initial investment.


The incremental cash flow is calculated for each end of period as follows:

For projects with different lives, the cash flows must continue through the LCM.

Incremental Cash Flow

Year Alternative A Alternative B B-A012:

Cash Flow


Example: The first alternative has an initial cost of $20,000 and subsequent annual costs of $2000 for 3 years. A second alternative has an initial cost of $15,000 and subsequent annual costs of $2500 for 2 years.


Year Alternative A Alternative B B-A0 ($15,000) ($20,000) ($5,000)1 ($2,500) ($2,000) $5002 ($17,500) ($2,000) $15,5003 ($2,500) ($22,000) ($19,500)4 ($17,500) ($2,000) $15,5005 ($2,500) ($2,000) $5006 ($2,500) ($2,000) $500

Cash Flow


Interpretation of incremental cash flow:

The incremental cash flow represents the extra investment required if the alternative with the larger initial cost is selected.

If the ROR available through the incremental cash flow equals or exceeds the MARR, the alternative associated with the extra investment (Alternative B) should be selected.


For multiple revenue alternatives, calculate the internal rate of return i* for each alternative, and eliminate all alternative that have an i* < MARR. Compare the remaining alternatives incrementally.

For independent projects, there is no comparison on the extra investment. The ROR value is used to accept all projects where i* > MARR, assuming an unlimited budget.

ROR Analysis

For mutually exclusive alternatives, the procedure for an incremental ROR analysis is:

1) Develop the incremental cash flow diagram using the LCM of years. The alternative with the greatest initial investment should be identified as alternative B.

2) Draw the incremental cash flow diagram.3) Calculate the ROR of the incremental cash flow

column using the trial and error method, or using the spreadsheet IRR function .

4) If the ROR < MARR, select alternative A.If the ROR > MARR, the extra investment is justified; select alternative B.

ROR Analysis

From the previous example, the IRR function returned an ROR of 44%.

Therefore, alternative B is preferable to alternative A.


Year Alternative A Alternative B B-A IRR0 ($15,000) ($20,000) ($5,000) 44%1 ($2,500) ($2,000) $5002 ($17,500) ($2,000) $15,5003 ($2,500) ($22,000) ($19,500)4 ($17,500) ($2,000) $15,5005 ($2,500) ($2,000) $5006 ($2,500) ($2,000) $500

Cash Flow

ROR Analysis

In this example, the incremental cash flow changes signs 4 times, indicating multiple ROR values. The correct method of finding the ROR of this cash flow would have been using the composite ROR as described in Chapter 7.

ROR AnalysisMultiple Mutually Exclusive Alternatives

If there are multiple mutually exclusive investment alternatives, the following procedure ensures the correct project is chosen.

1) If the investment is a revenue investment, you must include the do nothing (DN) alternative.

2) List all projects in order of least to greatest initial investment (note the DN alternative would be listed first for revenue projects).

3) Find the first project whose ROR (i*) is > MARR, discarding alternatives whose i* is < MARR. Call this first project the defender. For the revenue projects, the DN alternative assumes the role as the initial defender.

4) Continue searching to find the next alternative with i* > MARR, and call this the challenger.


5) Determine the incremental cash flow:

incremental cash flow = challenger cash flow – defender cash flow

Obtain the ROR for this incremental cash flow.

6) If the ROR > MARR, then the challenger becomes the defender and the defender is eliminated. If ROR < MARR, then the challenger is eliminated and the defender remains against the next challenger.

7) Repeat steps 3-5 until only one alternative remains.


A B C DInitial cost, $ -200,000 -275,000 -190,000 -350,000Annual cash flow, $ 22,000 35,000 19,500 42,000Life years 30 30 30 30

MARR = 10% C A B D(1) (2) (3) (4)

Initial cost, $ -190,000 -200,000 -275,000 -350,000Cash flow, $ 19,500 22,000 35,000 42,000Alternatives Compared C to DN A to DN B to A D to BIncremental Cost, $ -190,000 -200,000 -75,000 -75,000Incremental Cash flow, $ 19,500 22,000 13,000 7,000ROR % (Incremental Cash flow) 9.63 10.49 17.28 8.55Increment justified? No Yes Yes NoAlternative Selected DN A B B

rate of return analysis: multiple alternatives consider the following: you have $20,000 to invest in...

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