The one operation
A pound today is not the same as a pound next year, so before you can compare, add or judge cash flows, you have to move them all to the same point in time. That is discounting, and it's the whole subject's spine.
| It looks like | It's actually |
|---|---|
| NPV | Discount every cash flow to today; sum; compare to the cost |
| Bond price | Discount the coupons and the face value to today |
| Perpetuity formula | The same sum, when payments never stop, collapsed algebraically |
| Annuity formula | The same sum, when payments stop at year n |
| Dividend discount model | A growing perpetuity, with dividends as the payment |
| IRR | The discount rate that makes the sum come out to zero |
Derive the perpetuity and annuity formulas from the summation once, by hand. It takes fifteen minutes and it converts six memorised expressions into one you understand — the same trade covered in how to memorise formulas.
The discount rate is where the real difficulty is
The mechanics of discounting are arithmetic. What's genuinely hard, and what distinguishes strong exam answers, is justifying which rate to use — because the rate encodes risk, and getting it wrong invalidates a technically perfect calculation.
- Whose cash flows are these? Flows to equity are discounted at the cost of equity; flows to the whole firm at WACC. Mixing these is the most common serious error in the subject.
- Nominal or real? Nominal cash flows need a nominal rate, real need real. Mismatching them silently produces an answer that's out by inflation.
- Does the risk match? A project riskier than the firm's average needs its own rate, not the company WACC — a favourite exam discussion point.
- After tax? The tax shield on debt is why WACC uses the after-tax cost of debt, and forgetting it is a standard trap.
Learn the statements as a system, not three documents
If your course includes financial statements, the highest-yield thing you can learn is how the three link: net income flows from the income statement into retained earnings on the balance sheet and into the top of the cash flow statement, and cash from the cash flow statement lands back on the balance sheet.
Test it the way interviews do — "depreciation rises by 10, walk me through all three statements" — because tracing one change through the loop proves you understand the system rather than the definitions. See how to study accounting for the bookkeeping side of the same material.
Build the mechanics in a spreadsheet, not on paper
- 1
Build a DCF from a blank sheet, twice
Not from a template. Forecast, discount, terminal value, sum. The second build is when you find out which parts you were copying rather than following.
- 2
Break your own assumptions on purpose
Change the growth rate by half a percent and watch the valuation move. Sensitivity intuition is what exam discussion questions are testing, and you can't get it from prose.
- 3
Rebuild the annuity and bond formulas as columns
Seeing each period's discount factor as a row makes the collapsed formula obvious in a way an algebraic derivation doesn't.
- 4
Then do it by hand under time pressure
The exam is handwritten and calculator-based. Spreadsheet fluency doesn't transfer automatically to a four-cash-flow NPV in ninety seconds.
- 5
Check every answer for plausibility
Is the bond above par when the coupon exceeds the yield? Does the NPV move the right way when the rate rises? These checks take seconds and catch sign and setup errors that cost whole questions.
The theory questions carry more marks than students expect
Finance papers are rarely pure calculation. Modigliani–Miller, market efficiency, agency costs, capital structure, dividend policy — these carry substantial marks and are usually the difference between a good mark and a top one, because most candidates prepare only the numerical side.
For each theory, be able to state the assumptions, what follows from them, and what changes when each assumption is relaxed. That third part is where the marks concentrate: MM with no taxes says capital structure is irrelevant, and the entire subject after that point is what happens when you add taxes, bankruptcy costs and asymmetric information back in.
Practise identification, not just execution
The hard part of an exam question is deciding which model applies. A textbook chapter tells you; an exam gives you a scenario and expects you to see that it's a growing perpetuity with a two-stage structure.
- Drill classification alone. Take twenty past questions and write only which model, which rate and which time horizon. No solving. Fifteen seconds each.
- Interleave across chapters — see interleaving — because grouped practice hides exactly the skill being tested.
- Collect the phrasing cues. "In perpetuity", "expected to grow at a constant rate", "the firm is all-equity financed" each specify a model and a rate.
- Keep an error log with the misreading that caused each mistake, not just the correct answer — learning from mistakes is unusually valuable in a subject where one wrong rate ruins a whole question.
If you're heading for interviews as well as exams
Technical interviews test the same material with different emphasis: fast mental arithmetic, the three-statement walkthrough, valuation methods compared, and clear verbal explanation under mild pressure. The overlap with exam preparation is large, but the delivery skill is separate and only trains by speaking.
Practise explaining WACC or the difference between enterprise and equity value out loud, in ninety seconds, without notes. It's the Feynman technique with a job attached, and it exposes the gaps that reading a summary sheet conceals.