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What Exam 3 covers

Exam 3 is about one question every business faces: is this investment worth more than it costs? Answering it takes four skills, and this unit builds all four:

1. What money costs the firm. The return investors demand on debt, preferred stock and equity, blended into the WACC.
2. How to judge a project. Payback, NPV, IRR and MIRR, and what to do when they disagree.
3. Which cash flows count. Taxes, depreciation, working capital, and the sale of old equipment.
4. How to handle risk and choices. Uncertain forecasts, projects of different lengths, the option to wait, and a budget that runs out.

This material is calculator-heavy. Most problems take several steps, and one early slip (a wrong sign, the wrong year, a missing tax effect) leads straight to a wrong answer. That's why the practice problems here build their wrong choices from those exact slips, and tell you which one you made.

The 12 topics

1. Component Costs of Capital: what debt, preferred and common equity each cost the firm, after taxes and flotation.
2. WACC, the Break Point & the MCC: blending the costs, and the point where cheap retained earnings run out.
3. The Optimal Capital Budget: lining up projects against the rising cost of money to decide how much to invest.
4. Payback & Discounted Payback: how fast the money comes back, with and without discounting.
5. NPV & IRR: the two workhorse decision rules, including quarterly cash flows.
6. Modified IRR: a fix for IRR's reinvestment problem, even with negative cash flows mid-project.
7. NPV Profiles, Crossover & Multiple IRRs: reading the graph, and projects with more than one IRR.
8. Relevant Cash Flows, MACRS & Expansion Projects: which cash flows count and how depreciation cuts taxes.
9. Replacement Projects: swapping an old machine for a new one using only the differences.
10. Unequal Lives & Optimal Economic Life: comparing projects of different lengths, and when to sell an asset.
11. Stand-Alone Risk: sensitivity analysis, scenarios (expected NPV, σ, CV) and Monte Carlo simulation.
12. Investment Timing Options & Capital Rationing: valuing the choice to wait, and picking projects on a fixed budget.

Where students usually get tripped up

These are the spots that tend to cause trouble in corporate finance courses generally, and the reasons are predictable:

• Replacement projects (topic 9). Expansion projects are taught first, and replacement adds a second machine running in reverse: you lose the old machine's depreciation, its sale has its own tax effect, and at the end you give up the sale you would have made. Getting every sign right in one long timeline is the hard part.
• The break point and the optimal capital budget (topics 2–3). Students mix up net income with retained earnings, or forget that a project can straddle the break point and pay a blended cost.
• NPV profiles and "most FALSE" statement questions (topic 7). These test whether you understand the shapes, not just the arithmetic. One misread statement costs the whole question.
• MIRR with negative cash flows in the middle (topic 6). The calculator steps are unfamiliar, and a misplaced zero changes the answer.
• Unequal lives and economic life (topic 10). The instinct is to pick the bigger NPV. With different lives, that instinct is wrong.
• Decision trees for the option to wait (topic 12). Seven-plus steps, and the two classic slips are forgetting to discount back and counting the bad branch as a loss.

Each of these has its own lesson section, worked example and set of practice problems with feedback on the exact mistake you made.

A taste: the bigger NPV loses

A coffee roaster needs one bean grinder. Grinder A's cash flows are (5,400), 3,300, 3,300 over 2 years. Grinder B's are (9,800), 3,200, 3,200, 3,200, 3,200 over 4 years. Either can be replaced with the same model when it wears out, and the cost of capital is 9%.

Step 1: NPVs. NPV of A = $405.07. NPV of B = $567.10. Grinder B looks better.

Step 2: put them on equal footing. B's NPV covers 4 years; A's covers 2, and A could be bought again in Year 2 and earn a second round. To compare fairly, convert each NPV into an equal amount per year over its own life, the equivalent annual annuity (EAA). On a TI-84: TVM Solver with N = life, I% = 9, PV = −NPV, FV = 0, solve PMT.

Step 3: compare per year. EAA of A = $230.27. EAA of B = $175.05. Grinder A wins by $55.22 a year.

The project with the bigger NPV is the wrong choice. In a multiple-choice question, "Grinder B" is sitting right there as an answer, waiting for anyone who stopped at Step 1. The full lesson shows why this works, how it connects to deciding when to sell an aging machine, and the four other ways students go wrong on it.

Your study plan

The best plans space practice out and bring back what you missed. Keep a miss list: every question you get wrong goes on it, and you retry it a day or two later without looking at the solution first.

7 days out

• Day 1: Topics 1–3 (cost of capital). Lesson, video, quick check for each. Add misses to your list.
• Day 2: Retry yesterday's misses first. Then topics 4–6.
• Day 3: Retry misses. Topics 7–8.
• Day 4: Retry misses. Topics 9–10. Replacement projects take the longest; give them a full sitting.
• Day 5: Retry misses. Topics 11–12, then a game to mix everything up.
• Day 6: Take a practice exam in one timed sitting (75 minutes). Read the walkthrough for every miss, then reread the lesson sections it links to.
• Day 7 (day before): Redo every question on your miss list and take a second practice exam. Stop early and sleep.

3 days out

• Day 1: Take a practice exam cold to find your weak spots. Study the lessons for your three weakest topics and do their quick checks.
• Day 2: Retry yesterday's misses first. Study the next weakest topics, then take a second practice exam.
• Day 3 (day before): Redo everything on your miss list, then one more pass at the longest problem types: replacement, the decision tree, and economic life. Stop early.

Short on time? Practice exams first. They show exactly which topics need work and link each missed question to the lesson section and video chapter that fix it.

What's in the full course

Lessons. Twelve 10–15 minute lessons, one per topic. Each opens with why it matters, builds the idea in plain language, works a simple example and then an exam-style one step by step, hands you a similar problem to try, shows the TI-84 keystrokes, and lists the common mistakes and how to catch them. Behind them sits a problem bank of about 15 practice problems per topic, from warm-ups to challenge problems. Every wrong answer tells you which mistake produces it and links to the section that fixes it.

Videos. A 3–8 minute explainer for every topic, with captions and the same visual style throughout, so timelines and formulas look the same in every video. Good for the topics that click better when you see the cash flows move.

Games. Fast practice that doesn't feel like homework: a speed round of quick calculations where every wrong choice names the mistake behind it, and a timeline builder where you place each piece of an expansion or replacement project in the right year with the right sign. Your results show which topics to go back to.

Practice exams. Five 25-question practice exams, timed (75 minutes) or untimed, mixing topics from across the unit so you practice choosing the method, not just carrying it out, including multi-question data sets. Every question has a full walkthrough: what it's really asking, how to spot the method, the setup, the solution, a quick sanity check, and the trap to avoid. Each exam also has its own explainer video with a chapter for every question, and your score breaks down by topic so you know exactly where to spend your remaining time.

Start here: watch the free 5-minute exam overview video, then try the free game.