Two mutually exclusive projects both have positive NPV at a 10% discount rate. Project A has NPV = $50,000 and IRR = 15%. Project B has NPV = $80,000 and IRR = 12%. Which should the firm choose?
AProject A — a higher IRR always indicates a more profitable investment
BProject B — NPV directly measures value created and consistently ranks mutually exclusive projects correctly
CProject A — the higher percentage return dominates in absolute value terms
DIt cannot be determined without knowing each project's payback period
NPV is the correct decision rule for mutually exclusive projects. Project B creates $80,000 of value above the opportunity cost of capital; Project A creates only $50,000. The IRR rankings conflict with NPV because IRR is a percentage return that ignores project scale — a smaller project with a higher percentage return can create less total value than a larger project with a lower percentage return. NPV correctly measures the dollar amount of value created, which is what maximizes wealth. IRR is useful for evaluating a single project but unreliable for ranking competing ones.
Question 2 Multiple Choice
A project has NPV = 0 at the firm's discount rate. This means:
AThe project should be rejected — it generates no surplus and therefore wastes capital
BThe project exactly earns the opportunity cost of capital and is borderline acceptable — it neither creates nor destroys value above the benchmark
CThe project's total cash inflows are exactly equal to its initial cost in nominal terms
DThe discount rate used was 0%, so cash flows were not adjusted for time value
NPV = 0 means the project exactly matches the benchmark return (the discount rate). Investors get exactly what they could earn on equally risky alternatives — no more, no less. This is not a failure — it means the project is fairly priced relative to its risk. It would be acceptable (returns the opportunity cost of capital) but does not add value beyond what the market demands. The common misconception is confusing NPV = 0 with 'no cash flows' or 'no profit' — it means zero excess return, not zero return.
Question 3 True / False
Net present value and accounting profit measure the same underlying concept — how much an investment earns — but use different scales.
TTrue
FFalse
Answer: False
NPV and accounting profit are fundamentally different concepts, not the same thing at different scales. Accounting profit applies matching principles and ignores the time value of money — $1,000 received in year 1 and $1,000 received in year 10 contribute equally to accounting profit. NPV discounts all cash flows to present value, so $1,000 in year 10 is worth far less than $1,000 in year 1. Accounting profit also includes non-cash items (depreciation) and excludes capital outlays in ways that can make a value-destroying investment look profitable.
Question 4 True / False
A project can have a positive NPV at a low discount rate and a negative NPV at a high discount rate — the accept/reject decision can flip entirely based on the chosen discount rate.
TTrue
FFalse
Answer: True
This is illustrated directly by the machine example in the explainer: at r = 9% the project has positive NPV; at r = 10% it turns negative. Higher discount rates reduce the present value of future cash flows more aggressively, eventually making even profitable-seeming projects fail the benchmark. This sensitivity to r is why valuation disagreements in practice almost always trace back to discount rate disagreements, not cash flow forecast disagreements — and why choosing the right r for the project's actual risk is the most important judgment in NPV analysis.
Question 5 Short Answer
Why is the discount rate in an NPV calculation not just a technical parameter but a judgment about risk, and what are the consequences of choosing the wrong rate?
Think about your answer, then reveal below.
Model answer: The discount rate r encodes the opportunity cost of capital for investments of comparable risk — it represents what investors could earn on equally risky alternatives. More volatile, uncertain cash flows warrant a higher r because investors require a higher return to bear that risk. Using the wrong r means mispricing risk: too low a rate accepts bad projects that don't compensate for their risk; too high a rate rejects good projects that actually do. The right rate for a specific project depends on that project's risk, not just the firm's average cost of capital.
This is why NPV is often called 'the right answer to the right question' but is also the hardest to implement correctly. Computing the arithmetic of NPV is mechanical once you have r. Determining the right r is a judgment that requires understanding the risk of the specific cash flows, the relevant benchmark investments, and the difference between project risk and firm-wide average risk. Two analysts with identical cash flow forecasts can reach opposite investment conclusions simply by disagreeing on r.