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Rate-of-Return Analysis
Rate of Return (RoR)
Rate of return analysis is preferred by many engineers and financial managers that prefer analyzing investments in terms of percentage rates instead of dollars of present worth.
3 Definitions of rate of return:
Rate of Return Definitions
Definition 1: Rate of return is the interest earned on the unpaid balance of an amortized loan.
Definition 2: Rate of return is the break-even interest rate i* at which the present worth of a project is zero or PW(i) = PW cash inflows – PW cash outflows = 0.
Definition 3: The internal rate of return is the interest rate charged on the unrecovered project balance of the investment such that, the project terminates, and the unrecovered project balance is zero.
3
Methods for Finding Rate of Return
Classifying investments:
Classification is done by counting the number of sign changes in its net cash flow sequence.
A change from either “-” to “+” or “+” to “-” counts as one sign change (zero cash flow is ignored).
A simple investment is only one sign change in the net cash flow series.
Simple-investment cash flow if initial cash flows are negative.
Simple-borrowing cash flow is initial cash flows are positive
A nonsimple investment is an investment in which more than one sign change occurs in a cash flow series.
Computational Methods
There are several ways to determine rate of return:
Direct-solution method
Solve for i.
Trial-and-error method
Estimated guess for i:
If PW(i) < 0, lower the interest rate to raise PW to 0.
If PW(i) > 0, raise interest rate to lower PW to 0.
Excel method
=IRR( range, guess)
Evaluating Single Projects
For simple investments,
If IRR > MARR, accept the project.
If IRR = MARR, remain indifferent.
If IRR < MARR, reject the project.
For non-simple investments,
Find true i* (multiple i*)
Abandon IRR approach, use NPW criterion
Flaws in Project Ranking with IRR
Under PW and AE analysis, the mutually exclusive project with the highest worth figure was preferred.
The project with the highest IRR may not be the preferred alternative, IRR measure ignores the scale of the investment.
Incremental Analysis
For two mutually exclusive projects, we can use rate-of-return analysis by computing the internal rate of return on incremental investment (IRR B-A) between the projects.
Cash flow is computed for the difference between the projects by subtracting the cash flow for the lower investment-cost project (A) from the higher investment-cost project (B).
Incremental Analysis
The decision rule, where B-A is an investment increment (the sign of the first cash flow should be always negative):
If IRR B-A > MARR, select B.
If IRR B-A = MARR, select either one.
If IRR B-A < MARR, select A.
