How can one project have IRRs of 4%, 7% and 10% at once, and how do incremental cash flows repair an IRR ranking?
Loading…
Multiple IRRs from sign changes
Sketch NPV against the rate for Projects 1 and 2, mark each axis crossing as an IRR, and record Project 1's single IRR near 7% versus Project 2's three IRRs of 4%, 7% and 10%.
Scale, and the incremental-cash-flow repair
Work the pair −10,000/20,000 and −20,000/36,000 at 10%: record each IRR and NPV, the opposite rankings, then the IRR and NPV of the increment −10,000/16,000 and the resulting decision.
Timing: front-loaded versus long-lived cash flows
Compare −90 followed by 60, 50, 40 with −90 followed by 18 forever at 10%, recording each IRR and NPV and that IRR and NPV rank the two oppositely.
Where IRR fits: bonds and private equity
State yield to maturity as a bond's IRR, record IRR's use in private equity computed tranche by tranche, and note that beyond the quadratic case IRR needs a numerical solution.