BFC2140 · Corporate Finance
Capital Budgeting I: Investment Decision Rules
Capital budgeting is how a firm decides which long-term projects to accept, and this chapter covers the four classic decision rules — net present value (NPV), internal rate of return (IRR), payback and the profitability index — plus the NPV profile. The key exam skill is knowing why NPV is the value-maximising rule and how IRR can mislead when projects are mutually exclusive or have non-conventional cash flows. It is examined as Section B numerical NPV/IRR/payback calculations and Section C reasoning about ranking conflicts, IRR pitfalls and unequal-life adjustments (EAA).
What this chapter covers
- 01Net present value (NPV): discount all cash flows at the required return, accept if NPV > 0
- 02Internal rate of return (IRR): the rate giving NPV = 0; accept if IRR > required return
- 03IRR pitfalls: lending vs borrowing, multiple/no IRRs with non-conventional cash flows, scale and timing conflicts
- 04Payback period and discounted payback — and why they ignore time value and later cash flows
- 05Profitability index PI = PV(inflows)/|initial outlay|, used under capital rationing
- 06The NPV profile (NPV vs discount rate) and the crossover rate where rankings flip
- 07Independent vs mutually exclusive projects; conventional vs non-conventional cash flows
- 08Unequal-life projects: the equivalent annual annuity (EAA) and replacement-chain methods
NPV vs IRR ranking conflict on mutually exclusive projects
- 2 marksValue Project S as a 4-year ordinary annuity less the outlay: NPV_S = 20,000 × [1 − 1.10^(−4)]/0.10 − 50,000 = 20,000 × 3.1699 − 50,000 = 63,397 − 50,000 = $13,397.18.
- 2 marksValue Project L as a single year-4 cash flow less the outlay: NPV_L = 95,000/1.10^4 − 50,000 = 64,886 − 50,000 = $14,886.30.
- 1 markDecide on NPV: NPV_L ($14,886.30) > NPV_S ($13,397.18), so accept Project L — it adds more value despite its later cash flows.
- 1 markExplain the IRR conflict: Project S's cash flows arrive earlier, giving it the higher IRR, so IRR would favour S while NPV favours L. With mutually exclusive projects that differ in cash-flow timing, the rules can disagree — trust NPV, which assumes reinvestment at the required return and measures dollar value added.
- 1 markCompute Project S's payback: it recovers $20,000 per year against a $50,000 outlay, so payback = 50,000/20,000 = 2.50 years.
Key terms
- Net present value (NPV)
- The sum of a project's cash flows each discounted at the required return, minus the initial outlay: NPV = Σ NCF_t/(1 + k)^t. Accept if NPV > 0. It directly measures the dollar value added to the firm and is the preferred rule whenever criteria conflict.
- Internal rate of return (IRR)
- The discount rate that makes a project's NPV equal to zero — its break-even return. Accept if IRR > the required return. IRR is intuitive but can mislead with non-conventional cash flows (multiple or no IRRs) or mutually exclusive projects of different scale or timing.
- Payback period
- The time to recover the initial outlay from a project's cash flows. Simple to compute but flawed: it ignores the time value of money (unless discounted) and all cash flows after the cut-off date, so it is at best a rough liquidity screen.
- Profitability index (PI)
- PI = PV(inflows)/|initial outlay|; accept if PI > 1. It expresses value created per dollar invested and is most useful for ranking projects under hard capital rationing, when the firm cannot fund every positive-NPV project.
- NPV profile
- A plot of a project's NPV against the discount rate; it slopes downward and crosses zero at the IRR. Two profiles can intersect at the crossover rate, which is where NPV-based rankings of mutually exclusive projects flip.
- Equivalent annual annuity (EAA)
- The level annual cash flow with the same NPV as a project, used to compare mutually exclusive projects of unequal lives on a like-for-like (per-year) basis. The replacement-chain method is the equivalent alternative.
Capital Budgeting I: Investment Decision Rules FAQ
Why is NPV preferred to IRR?
NPV measures the actual dollar value a project adds to the firm and assumes cash flows are reinvested at the required return — a realistic, value-maximising assumption. IRR is a percentage that assumes reinvestment at the IRR itself, which can be unrealistically high, and it can give multiple or no solutions with non-conventional cash flows and can rank mutually exclusive projects incorrectly when they differ in scale or timing. When the two rules conflict, always go with NPV.
What are the main IRR pitfalls?
Four to watch for: (1) the lending-vs-borrowing problem, where the accept rule reverses if the project is a financing rather than an investing pattern; (2) multiple IRRs when cash flows change sign more than once (non-conventional cash flows); (3) no real IRR at all for some cash-flow patterns; and (4) scale and timing conflicts on mutually exclusive projects, where a smaller or earlier project can have a higher IRR but a lower NPV. The NPV profile and the crossover rate are the tools that expose these conflicts.
When do I use the profitability index?
Use the PI to rank projects when the firm faces hard capital rationing — a fixed budget that cannot fund every positive-NPV project. Because PI measures value per dollar invested (PV of inflows over the outlay), it helps you select the combination of projects that maximises total NPV within the budget. With unlimited capital and independent projects, you simply accept every project with NPV > 0 and the PI ranking is unnecessary.
How do I compare projects with different lives?
Do not compare their raw NPVs directly — a longer project will tend to have a larger NPV simply because it runs longer. Convert each to an equivalent annual annuity (EAA): the level yearly cash flow with the same NPV as the project. The project with the higher EAA is preferred. The replacement-chain method (repeating each project to a common horizon) gives the same answer and is the alternative the unit also teaches.
How is Capital Budgeting I examined in BFC2140?
It is core to the Week 6 MST and recurs on the final. Expect Section B numerical questions computing NPV, IRR, payback or PI, and Section C questions that ask you to choose between mutually exclusive projects, explain an NPV/IRR conflict using the crossover rate, identify an IRR pitfall, or adjust for unequal lives with EAA. NPV/IRR ranking with conflicts is explicitly flagged as a high-yield recurring exam skill.
Exam move
Build the discipline of computing NPV first and treating every other rule as a supplement. Practise setting up the NPV of annuity-style and lump-sum projects quickly, and learn to read an NPV profile so you can explain crossover rates and IRR conflicts in words for Section C. Make the accept rules automatic (NPV > 0, IRR > required return, PI > 1) and memorise when each rule fails: payback ignores time value and later cash flows; IRR misleads with non-conventional cash flows and mutually exclusive timing/scale differences. For unequal lives, default to the EAA method and state why raw NPVs are not comparable. Above all, when any two rules disagree, follow NPV and be able to justify why — that judgement, not the arithmetic alone, is what the applied exam rewards.
