FNCE90060 Chap.3 Investment Decision Rules
Investment Decision Rules
Week 3 asks how a firm turns discounted project cash flows into a decision. Net present value measures dollar value created at the project cost of capital. A stand-alone project is accepted when NPV is positive, while mutually exclusive alternatives are ranked by the highest positive NPV. Internal rate of return is the rate that makes NPV zero.
It often agrees with NPV for a conventional stand-alone project, but delayed investments, several cash-flow sign changes, different project scale and mutual exclusivity can create a nonexistent IRR, multiple IRRs or a misleading ranking. Payback measures how quickly an outlay is recovered but ignores later cash flows and, in its basic form, discounting.
The correct response is conditional: alternative rules can inform the analysis, while NPV controls when they conflict.
What this chapter covers
- 01
NPV for stand-alone projects
- 02
Ranking mutually exclusive projects
- 03
IRR definition and accept rule
- 04
Conventional cash-flow conditions
- 05
Multiple and nonexistent IRRs
- 06
Payback limitations and liquidity information
Worked example · free
Rank mutually exclusive projects
- 1The three-year annuity factor at 8% is approximately 2.5771.
- 1NPV A equals $38,000 times 2.5771 minus $90,000, or $7,930.
- 1NPV B equals $52,000 times 2.5771 minus $130,000, or $4,009 approximately.
- 2Only one project can be selected, so choose A because its positive NPV is larger.
Key terms
- Cost Of Capital
- The opportunity cost used to discount project cash flows of comparable risk.
- Internal Rate Of Return
- The discount rate that makes a project NPV equal zero.
- Payback Period
- The time required for cumulative inflows to recover the initial outlay.
- Mutually Exclusive Projects
- Alternatives that cannot both be undertaken, requiring a value ranking.
- Conventional Cash Flows
- A project pattern with initial negative cash flow followed by positive cash flows.
Investment Decision Rules FAQ
Why does NPV control when decision rules conflict?
NPV measures the dollar value created after discounting at the relevant opportunity cost. IRR is a percentage and payback is a timing screen, so either can ignore project scale, later cash flows or unusual sign patterns.
When is the IRR rule most reliable?
It is most reliable for a stand-alone conventional investment whose negative cash flows precede positive cash flows. Even then, the cost of capital and project relationship should be stated before the percentage is interpreted.
Why can a project have several IRRs?
Several cash-flow sign changes can make the NPV profile cross zero more than once. Each crossing is a mathematical root, so no single IRR necessarily provides an unambiguous economic decision.
What useful information can payback still provide?
Payback can describe how quickly invested funds return and therefore illuminate liquidity exposure. It should remain a secondary screen because it omits later value and may ignore the time value of money.
How does mutual exclusivity change the NPV rule?
Independent projects can each be accepted when their NPV is positive and resources permit. Mutually exclusive alternatives cannot all be chosen, so the task becomes ranking rather than applying separate zero thresholds. Compare them at appropriate risk-adjusted rates and select the feasible alternative with the highest positive NPV.
What does an NPV profile show that one IRR cannot?
The profile shows dollar value at every discount rate, the zero crossings that produce IRRs and any intersection where two projects change ranking. Mark the actual cost of capital on the horizontal axis. The preferred mutually exclusive project is the curve with greater positive height at that rate, not automatically the curve with the farther zero crossing.
Do two cash-flow sign changes guarantee two IRRs?
No. Several sign changes make multiple real roots possible, but they do not guarantee that each root exists or has a useful economic interpretation. The warning is enough to stop using a single IRR as the decision rule. Discount the complete cash-flow sequence at the opportunity cost and rely on NPV.
Why can project scale reverse an IRR ranking?
IRR measures a percentage return, while NPV measures dollars of value. A small project can earn a high percentage on little invested capital yet add fewer dollars than a larger alternative. When only one project can be chosen, the firm's value objective requires the higher positive NPV at the relevant cost of capital.
Exam move
For every project set, write stand-alone, independent or mutually exclusive before calculating. Sketch cash-flow signs and count changes before requesting IRR. Build small NPV profiles to see how the zero crossing differs from value at the actual cost of capital. When explaining a conflict, name the failure condition rather than calling IRR or payback generally wrong.
Close every answer with the controlling rule and the specific decision. Practise changing project scale, timing and sign pattern one at a time, then predict whether IRR and NPV can disagree. Keep a table that separates threshold decisions from rankings so the word mutually exclusive immediately changes the final comparison.
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