Investment Decisions
Capital budgeting from start to finish: estimating relevant after-tax cash flows, evaluating them with NPV, IRR, payback and the profitability index, and testing how the answer changes under risk. This section is 10% of Part 2 and almost entirely computational.
About 10 of the 100 multiple-choice questions, often with a written-response case. Estimated study time: 18 hours.
Your learning path
Three topics. Get the cash flows right first: most wrong answers come from the cash flows, not the discounting.
Capital budgeting process
The stages of a capital budgeting decision and how to build the three blocks of relevant after-tax cash flow.
The process and relevant cash flowsWhat to include and what to leave out
- Identify opportunities linked to strategy; evaluate cash flows and risk; select projects (within any capital limit); implement and monitor; post-audit actual against forecast results.
| Include | Exclude |
|---|---|
| Incremental after-tax revenues and cash costs | Sunk costs (feasibility studies already paid) |
| Opportunity costs (a building that could be rented out) | Allocated overhead that does not change |
| Changes in net working capital | Financing costs (interest, dividends): the discount rate already reflects them |
| Cannibalization of existing products' cash flows | Depreciation itself (only its tax shield is a cash flow) |
| Tax effects, including the depreciation tax shield | Accounting profit figures without cash adjustment |
Initial investmentCost, installation, working capital, sale of the old asset
A sale below book value produces a tax saving, so after-tax proceeds exceed the sale price.
Replacing a packaging line
A new line costs $500,000 plus $20,000 to install, and needs $30,000 of extra working capital. The old line, with a book value of $40,000, can be sold for $60,000. The tax rate is 25%.
Operating and terminal cash flowsThe depreciation tax shield and the end of the project
D × t is the depreciation tax shield. Equivalent: net income + depreciation (with no financing).
Cash flows for the packaging line
Same line (basis $520,000, five-year straight-line life, no salvage for tax). It raises revenue by $300,000 and cash costs by $120,000 a year. At the end of year 5 it can be sold for $50,000, and the $30,000 of working capital is recovered.
Finished Capital budgeting process?
Mark it complete when you can build a full after-tax cash-flow timeline.
Capital budgeting methods
The five decision rules, how to compute each with tables or formulas, and what to do when NPV and IRR disagree.
NPV, IRR and the profitability indexDiscounted cash-flow methods
Accept if NPV ≥ 0. With even flows: NPV = CF × PVA(k, n) − CF0.
Accept if IRR ≥ the hurdle rate. Even flows: the PVA factor at the IRR = CF0 ÷ CF.
Accept if PI ≥ 1. Under capital rationing, rank independent projects by PI.
Evaluating the packaging line at 10%
Timeline from topic 1: −$495,000; $161,000 in years 1–5, plus a $67,500 terminal flow in year 5. The required return is 10%.
Payback and discounted paybackHow fast the investment comes back
Uneven flows: accumulate until the investment is recovered, then add the fraction of the next year. Discounted payback uses discounted flows.
How long to recover $495,000?
Same timeline, 10% required return.
NPV vs IRR ranking conflictsTiming, scale and the crossover rate
- For mutually exclusive projects, NPV and IRR can rank differently when cash-flow timing or project scale differ.
- NPV assumes reinvestment at the cost of capital; IRR assumes reinvestment at the IRR, which is usually unrealistic. Use NPV.
- The crossover rate is the discount rate at which the two NPV profiles intersect (the IRR of the difference in cash flows).
- Non-conventional flows (sign changes more than once) can produce multiple IRRs; modified IRR (MIRR) avoids this.
Two ways to spend $100,000
Project A: −$100,000 now, $145,000 in year 3. Project B: −$100,000 now, $70,000 in year 1 and $50,000 in year 2. They are mutually exclusive; the cost of capital is 10%.
Finished Capital budgeting methods?
Mark it complete when you can compute all five measures and resolve an NPV–IRR conflict.
Risk analysis
Testing how the NPV changes when the forecast is wrong, and valuing the flexibility to change course later.
Sensitivity, scenario and simulationThree ways to model uncertainty
- Sensitivity analysis changes one input at a time (volume, price, cost, life, discount rate) and shows which matters most; a break-even value is the input level that makes NPV zero.
- Scenario analysis changes several inputs together (best, base, worst) and weights the NPVs by probability.
- Monte Carlo simulation draws all uncertain inputs from distributions thousands of times, giving a distribution of NPV and the probability that it is negative.
- Risk-adjusted discount rate: discount riskier projects at a higher rate than WACC.
How far can cash flow fall?
A $400,000 project has a six-year life and a 12% required return; forecast annual cash flow is $115,000. Scenario NPVs: best $250,000 (25%), base $80,000 (50%), worst −$120,000 (25%).
Real optionsThe value of flexibility
- Option to expand (follow-on investments if the product succeeds), abandon (sell assets if it fails), delay (wait for information), and flexibility (switch inputs or outputs).
- Options have value because they let management act on new information; static NPV ignores that, so it can undervalue strategic projects.
- Option value rises with uncertainty and with the time available to exercise.
The option to abandon
A new product has a 60% chance of success (NPV $300,000) and a 40% chance of failure (NPV −$150,000). If the company can abandon after one year and sell the equipment, the failure NPV improves to −$40,000.
Finished Risk analysis?
Mark it complete when you can compute a break-even cash flow, an expected NPV and the value of a real option.
Interactive tools
Each tool is pre-filled with an example from the lessons. Change any input; the results show the method, your numbers and what they mean.
NPV, IRR and payback calculator
Builds the full after-tax cash-flow timeline (initial outlay, operating cash flows with the depreciation tax shield, terminal salvage and working-capital recovery), then evaluates it with every method and draws the NPV profile.
Formula sheet
Every formula in Investment Decisions, followed by present- and future-value interest tables. Print it from here: the sidebar is hidden and the sheet prints black on white.
Flashcards
Recall first, then flip. Your grade schedules the next review (SM-2-lite).
Practice MCQs
Practice mode gives instant feedback; timed mode allows 1.8 minutes per question, like the exam. Filter by topic, difficulty, or questions you missed.
Written-response practice
Write your answer first (aim for about 30 minutes per case), then compare it with the model answer and score yourself against the rubric. Show your calculations: the exam awards marks for method.
Glossary
Search the section's vocabulary. Underlined terms in the lessons show these definitions on hover or keyboard focus.