EFN507 Chap.3 IRR, Payback and Rival Investment Rules
IRR, Payback and Rival Investment Rules
Judging the alternatives
The lecture tests every rival to NPV against two questions: does it respect the time value of money, and does it use cash flows?
Payback ignores both timing within the window and everything after it; discounted payback fixes the timing but still stops at the cutoff; the average book rate of return uses accounting income and no opportunity cost.
The trouble with IRR
IRR is the discount rate that sets NPV to zero and agrees with NPV for a conventional project, but it assumes interim cash flows are reinvested at the IRR, which the modified IRR replaces with a stated reinvestment rate.
Treating NPV as a polynomial in one plus the rate shows why a project whose cash flows change sign more than once can have several IRRs, bounded by Descartes' rule of signs. Whether you want a high or a low IRR depends on whether the project is like lending or like borrowing, and mutually exclusive projects of different scale are ranked correctly only by the IRR of the incremental cash flows.
What this chapter covers
- 01
Payback and why it cannot rank projects
- 02
Discounted payback as a half-built NPV
- 03
The average book rate of return and its flaws
- 04
IRR, the reinvestment assumption and modified IRR
- 05
Multiple IRRs and Descartes' rule of signs
- 06
Lending versus borrowing projects and the incremental IRR
Worked example · free
A project with two internal rates of return
- +1Signs run −, +, −: two changes, so Descartes' rule allows two positive roots or none.
- +2With x = 1 + r: −100x2 + 230x − 132 = 0 ($000), so x = (230 ± 10)/200.
- +1The roots are x = 1.1 and x = 1.2, giving IRRs of 10% and 20%.
- +1The leading coefficient is negative, so NPV is positive only between 10% and 20%; at 15% it is about +$189.
Key terms
- Payback period
- The number of periods before a project's undiscounted cash inflows repay its initial outlay.
- Internal rate of return
- The discount rate at which a project's net present value equals zero.
- Descartes' rule of signs
- A rule that bounds the number of positive roots of a polynomial by the number of sign changes in its coefficients.
- Incremental cash flows
- The difference between two projects' cash flows, analysed as a project in its own right to rank them.
- Average book rate of return
- Average profit after tax divided by average book value of the investment.
IRR, Payback and Rival Investment Rules FAQ
Why is payback a poor way to rank projects?
It ignores the time value of money within the payback window and ignores every cash flow after it. A project with a huge inflow just after the cutoff can be rejected in favour of one that barely recovers its cost, so payback can choose the project that destroys value.
Does switching to discounted payback fix the problem?
Not with the same cutoff. Discounting shrinks the early inflows, so fewer long-lived projects pass a five-year test, making matters worse. Once you have summed the present values to the cutoff, adding the rest simply gives NPV.
What is wrong with the average book rate of return?
It uses accounting profit rather than cash, ignores the time value of money, depends on how revenue and expenses are capitalised, and is not compared with an opportunity cost that reflects the project's risk. Its percentage is not a return in the usual sense.
When should I want a low IRR rather than a high one?
When the project is like borrowing: cash comes in first and goes out later. Then the IRR is the rate you are effectively paying, so it should be below the cost of capital. For a lending pattern, outflow first, you want the IRR above the cost of capital.
How do I rank mutually exclusive projects with IRR?
Check the smaller project first. Then compute the IRR of the incremental cash flows, larger minus smaller, checking the sign of its first flow. If the increment is acceptable, take the larger project; if not, take the smaller. This matches the NPV ranking.
Why use modified IRR?
Ordinary IRR implicitly reinvests interim cash at the IRR itself, which may be unrealistic for a high-return project. MIRR compounds inflows at a stated reinvestment rate and discounts outflows, giving a single, more defensible rate and avoiding multiple roots.
Exam move
Take one non-standard cash flow stream, count its sign changes, solve the quadratic in x = 1 + r, and plot the NPV profile. Then rank two mutually exclusive projects with the incremental IRR and confirm with NPV.
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