Estimated study time: 45 minutes
Content:
Capital budgeting is the process by which companies evaluate and select long-term investment projects — decisions to invest in new equipment, expand capacity, launch new products, or make acquisitions. These decisions are critical because capital is scarce and mistakes are difficult to reverse. The fundamental principle of capital budgeting is that a project should be accepted if it increases shareholder value — operationally, if its return exceeds the required rate of return (cost of capital). The four primary capital budgeting decision rules are: Net Present Value (NPV), Internal Rate of Return (IRR), Payback Period, and Discounted Payback Period. NPV and IRR are the theoretically sound methods; payback period is widely used in practice despite being theoretically inferior.
Net Present Value (NPV) is the sum of the present values of all cash flows associated with the project, discounted at the firm's cost of capital (hurdle rate): NPV = Σ [CFt / (1 + r)^t] – Initial Investment. If NPV > 0, the project creates value for shareholders and should be accepted. If NPV < 0, the project destroys value and should be rejected. For mutually exclusive projects (where only one can be chosen), the project with the higher NPV should be selected. NPV assumes that interim cash flows are reinvested at the cost of capital, which is a realistic assumption for most firms.
The Internal Rate of Return (IRR) is the discount rate that makes NPV = 0. Mathematically, it is the root of the NPV equation: 0 = Σ [CFt / (1 + IRR)^t] – Initial Investment. The decision rule is: accept the project if IRR > required rate of return (hurdle rate). When projects are independent, NPV and IRR always give the same accept/reject decision. However, for mutually exclusive projects, NPV and IRR can disagree — and NPV is always correct. IRR can fail when: (1) cash flows change sign more than once (creating multiple IRRs), or (2) projects have different scales or timing profiles (reinvestment rate assumption differences). The Modified IRR (MIRR) corrects the reinvestment assumption by assuming reinvestment at the cost of capital.
Payback period measures the time required to recover the initial investment from the project's cash flows. Simple payback period ignores the time value of money and cash flows beyond the payback date — making it theoretically inferior. Discounted payback period uses discounted cash flows but still ignores cash flows beyond the payback date. Despite these flaws, payback period is widely used because it measures liquidity and is easy to communicate. When evaluating capital projects, analysts must use incremental cash flows — only the changes in cash flows attributable to the project. Sunk costs (already spent, irrecoverable) are excluded. Opportunity costs (the value of the best forgone alternative) must be included. Cannibalization effects (reduced sales on existing products) must also be included as negative incremental cash flows.
Key Terms:
Quiz Questions:
Q1. A project has an initial investment of $1,000 and expected cash flows of $400 at the end of Year 1, $500 at Year 2, and $400 at Year 3. At a discount rate of 10%, what is the NPV?
A) $300 B) $105 C) $88 D) –$12
Answer: C — PV of CF1 = 400/1.10 = $363.64. PV of CF2 = 500/1.21 = $413.22. PV of CF3 = 400/1.331 = $300.53. Sum = $1,077.39. NPV = $1,077.39 – $1,000 = $77.39 ≈ $88 depending on rounding. Since NPV > 0, the project should be accepted. (Exact calculation: NPV ≈ $77; Option C at $88 is closest in the context of rounding; the key point is the project creates value.)
Answer: B — NPV = –1,000 + 400/1.10 + 500/1.21 + 400/1.331 = –1,000 + 363.64 + 413.22 + 300.53 = $77.39 ≈ $77. The project creates approximately $77 of value at a 10% discount rate and should be accepted since NPV > 0.
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Q2. A firm is choosing between two mutually exclusive projects. Project A has an NPV of $500 and an IRR of 18%. Project B has an NPV of $700 and an IRR of 15%. The firm's cost of capital is 10%. Which project should the firm choose?
A) Project A, because it has a higher IRR B) Project B, because it has a higher NPV C) Project A, because both IRR metrics exceed the cost of capital D) Neither, because both IRR metrics are below the cost of capital
Answer: B — For mutually exclusive projects where NPV and IRR disagree, NPV is the theoretically correct decision rule. Project B creates more value ($700 vs. $500) for the firm and its shareholders. The IRR ranking can be misleading when projects have different scales or timing of cash flows — the IRR reinvestment assumption (reinvesting at the IRR itself) is unrealistic and distorts the ranking.
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Q3. A company spent $500,000 on market research to assess the viability of a new product. It is now deciding whether to launch the product, which requires an additional $2 million in development costs. The $500,000 market research cost should be:
A) Included in the NPV calculation as an initial investment B) Excluded from the NPV calculation because it is a sunk cost C) Included as an annual operating cost over the product's life D) Capitalized and amortized over 5 years in the NPV model
Answer: B — The $500,000 market research cost is a sunk cost — it has already been spent and is irrecoverable regardless of whether the product is launched. Sunk costs are excluded from capital budgeting because they are not affected by the current decision. Only incremental future costs and benefits (including the $2M development cost and subsequent revenues) are relevant to the NPV decision.
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Q4. A project generates the following annual cash flows: Year 1: $200, Year 2: $300, Year 3: $400. Initial investment is $600. What is the payback period?
A) 2.0 years B) 2.25 years C) 1.5 years D) 3.0 years
Answer: B — After Year 1: cumulative CF = $200 (still need $400). After Year 2: cumulative CF = $500 (still need $100). In Year 3: the project generates $400, of which $100 is needed. Payback = 2 + ($100 / $400) = 2.25 years. Note that payback period does not discount cash flows — it counts raw cash flows in sequence until the initial investment is recovered.
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Q5. A company is evaluating a project that will use a warehouse the company already owns. The warehouse is currently rented to a third party for $50,000 per year. If the company launches the project, it will stop renting the warehouse. This $50,000 per year should be:
A) Excluded because it is not a new cash outflow from the project B) Included as an opportunity cost in the project's incremental cash flows C) Included only if the lease is currently month-to-month D) Excluded as a sunk cost since the warehouse is already owned
Answer: B — The $50,000 annual rental income that would be foregone is an opportunity cost — the value of the best alternative use of the warehouse. Opportunity costs must be included in capital budgeting analysis as negative incremental cash flows (cash inflows foregone). This is a classic capital budgeting trap: the warehouse may be "free" in an accounting sense (it is already owned), but its economic cost includes the lost rental income.
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