Question

When conducting a ROR analysis, why can you not compare two projects simply based on ROR?

Answer 1

When conducting a ROR analysis, you can not compare two projects simply based on ROR because of the following reasons-

When ROR analysis is applied for mutually exclusive projects; two steps need to be considered:

1) the rate of return on total individual project investment must be greater than or equal to the minimum rate of return,

2) the ROR on incremental investment compared to the last satisfactory level of investment must be greater than or equal to the minimum ROR,

The largest level of investment that satisfies both criteria is the economic choice.\

Therefore, in mutually exclusive projects, a smaller ROR on a bigger investment often is economically better than a big ROR on a smaller investment. Therefore, it is often preferable to invest a large amount of money at a moderate rate of return rather than a small amount at a large return with the remainder having to be invested elsewhere at a specified minimum rate of return.

For example-

Assume an investor has two alternatives, project A and project B and other opportunities exist to invest at 15% ROR. The total money that investor has is 400,000 dollars.

Project A: Includes investment of 40,000 dollars at present time which yields the income of 40,000 dollars for 5 years and the salvage value in the end of the fifth year is 40,000 dollars.

	C=$40,000	I=$40,000	I=$40,000	I=$40,000	I=$40,000	I=$40,000	L=$40,000
A)
	0	1	2	3	4	5

Project B: Includes investment of 400,000 dollars at present time which yields the income of 200,000 dollars for 5 years and the salvage value in the end of fifth year is 400,000 dollars.

	C=$400,000	I=$200,000	I=$200,000	I=$200,000	I=$200,000	I=$200,000	L=$400,000
B)
	0	1	2	3	4	5

C: Cost, I:Income, L:Salvage

ROR analysis for project A:
0 =−40,000+40,000(P/Ai,5)+40,000( P/Fi,5)0 =−40,000+40,000(P/Ai,5)+40,000( P/Fi,5)
With trial and error or using the IRR function in Excel, we can calculate i = RORA = 100% > 15%i = RORA = 100% > 15%. So project A is satisfactory.

ROR analysis for project B:
0 =−400,000+200,000(P/Ai,5)+400,000(P/Fi,5)0 =−400,000+200,000(P/Ai,5)+400,000(P/Fi,5)
With trial and error or using the IRR function in Excel, we can calculate i = RORB = 50% > 15%i = RORB = 50% > 15% . So project B is also satisfactory.

Many people think because project A has a higher ROR, project A has to be selected over project B. But remember, we assumed 400,000 dollars is available for the investment, and the investor can only choose one of the projects. Project A takes just 10 percent of the money and gives 100% ROR, while project B takes the entire 400,000 dollars and gives 50% ROR. If the investor chooses project A and spends 40,000 dollars on this project, the rest of the money (400,000−40,000=360,000 dollars) (400,000−40,000=360,000 dollars)  can only be invested with a 15% ROR. So, we need one more step that is called incremental analysis to be able to compare two projects and determine which project is better. Incremental analysis helps up to find a common base to compare two projects. To do so, incremental analysis breaks project B into two projects: one is similar to project A and the other is an incremental project.

Project B is equivalent to Project A + Project(B−A)Project A + Project(B−A)

Please note that investing on Project B (requires $400,000) is equivalent to investing $40,000(Project A)+$360,000(Project B−A)$40,000(Project A)+$360,000(Project B−A)

Consequently, the investor faces the following alternatives:

Choosing project A with 100% ROR + investing the rest of money with 15%

Or

Choosing project B, which is equivalent to an investment in project A with 100% ROR+ investment in the incremental project (B-A)

The incremental analysis has to be done for the bigger project minus the smaller one as:

		C=$360,000	I=$160,000	I=$160,000	I=$160,000	I=$160,000	I=$160,000	L=$360,000
B-A
		0	1	2	3	4	5

0 =−360,000+160,000(P/Ai,5)+ 360,000(P/Fi,5)0 =−360,000+160,000(P/Ai,5)+ 360,000(P/Fi,5)
This investment gives 44.4 % return.

So, incremental analysis shows that investment in project B is equivalent to investing in A (which gives 100% ROR) plus investing in project B-A (which gives 44%).

Thus, the second alternative, project B, is more desirable.