## sexta-feira, setembro 08, 2006

### PMP Question - IRR ( TIR in portuguese ) in Project Analysis

Question :

"The Internal Rate of Return formula as a method of project analysis:

a. uses the opportunity cost of funds as the discount rate in its formula.

b. solves for the interest rate that makes the net present value of benefits and costs from a project equal to zero.

c. results in ambiguity in some cases since there will generally be more than one internal rate of return solving its formula.

d. is preferred to net present value for business projects but not for environmental projects.

e. both b. and c. are true."

To analyse this question we must first address the question on how to calculate the IRR.

If the internal rate of return is less than the cost of borrowing used to fund your project, the project will clearly be a money-loser. However, usually a business owner will insist that in order to be acceptable, a project must be expected to earn an IRR that is at least several percentage points higher than the cost of borrowing, to compensate the company for its risk, time, and trouble associated with the project.
IRR analysis is generally used to evaluate the project's cash flows ( CF ). That means we need to use the NPV formula in order to get the IRR :

If we make NPV=0, given the CFs, we have a polynomial with n-root. As lots of you will remember, it's impossible to solve this equation analitically. That means we must use an iterative method in order to find the root ( r = IRR ) of the polynomial.
By making NPV=0, we are in fact saying that IRR is the highest rate by which someone might borrow money for an investment without loosing money !

By looking at the options it's easy to see that "b" must be true. Due to the fact that we are trying to solve a polynomial, it means that we might get more than one solution to the equation ! That means that "c" must also be true.

All in all the correct answer is "e" !

#### 2 comentários:

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