PART 3: CAPITAL BUDGETING
The general rule of thumb is that the maximum number of IRRs that a project can have equals the
number of sign changes in the cash flow stream. Therefore, in the typical project with one negative cash
flow up front and only positive cash flows later on, there is just one sign change, and there will be at most
one IRR. In the previous example, there are four sign changes in the cash flow stream and four different
IRRs. In the event that you have to evaluate a project with more than one sign change in the cash flows,
beware of the multiple IRR problem. In this situation, the NPV profile must be analysed because use of
the IRR typically does not result in the correct decision.No Real Solution
After entering the cash flows from a particular investment into a calculator or a spreadsheet, you may
receive an error message indicating that there is no solution to the problem. For some cash flow patterns,
it is possible that there is no real discount rate that equates the project’s NPV to zero. In these cases, the
only solution to the IRR equation involves imaginary numbers, hardly something that we can compare
with a company’s hurdle rate.FIGURE 9.7 NPV PROFILE FOR A PROJECT WITH MULTIPLE IRRs
This project with alternating cash inflows and outflows has an NPV profile that reflects multiple IRRs. At each discount rate
for which the NPV = $0, there is an IRR. In this case, IRRs occur at 0%, 10%, 20% and 30%.Discount rate (%)NPV ($ in millions)