New on FinoLib · Volume II: Capital Markets
My latest article is now live on FinoLib, the free finance library I write: Capital Budgeting: NPV, IRR and Payback Explained, from Volume II: Capital Markets. Read the summary below for the substance of the topic, then continue to FinoLib for the complete treatment.
1.10 Triangulating Valuation — Putting It All Together
The idea in plain words
No single valuation method is trusted on its own. Professionals line up each method’s range as bars on one chart, called a football field. It shows the trading range, the buyout analysis, the DCF, comparable companies and precedent deals. Where the standalone methods overlap is the most defensible value. Precedent deals show what a sale might fetch, and the buyout analysis gives a floor.
Key points
■A football field compares methods; a sensitivity table is a grid within one method that sets the DCF bar’s ends.
■Ridgeline’s standalone bars overlap at $18.98 to $21.00; precedents sit at $24.30 to $28.20.
■Delaware courts give heavy weight to deal prices from robust sale processes (DFC, Dell, Aruba).
A closer look
No professional valuation rests on a single method. The standard practice is to build a DCF, a comps analysis, and — where relevant — a precedent transactions analysis and an SOTP, then plot all of them on a single chart of valuation ranges, commonly called a football field. Where the ranges overlap is treated as the most defensible zone of value; where they diverge sharply, that divergence itself becomes the analytical story — is the market undervaluing intrinsic cash generation, or is the DCF’s growth assumption too aggressive?
Decision rule
Match the bars to the question: standalone value from the DCF, comps and trading range; a sale price from precedents and synergy capacity; a floor from the LBO. If at least three standalone bars overlap, present the overlap as the central range. If the DCF midpoint sits more than about 15% outside the comps range, reconcile the two (growth, margins, WACC) before presenting either. Never average the bars into one number. When a competitive sale process has produced a price, treat it as the strongest single piece of evidence.
The costliest mistake
Trusting one bar over the market evidence. In the Aruba appraisal, the dissenting shareholders turned down HP’s $24.67 a share and claimed a fair value of $32.57, a figure built on discounted cash flows. The Delaware Supreme Court awarded $19.10: deal price less synergies. Measured against the deal they refused, they gave up $5.57 a share, 22.6%, before statutory interest; against their own claim, the award was 41.4% lower. A DCF that sits far above every market-based bar is a hypothesis to test, not a value to bet on.
1.11 Capital Budgeting: NPV, IRR, Payback and the Profitability Index
The idea in plain words
Companies decide which long projects to fund by comparing the cash a project will bring in with the cash it costs, with future cash discounted at a rate that matches the project’s risk. Net present value, or NPV, is the deciding measure: it tells you how much value the project adds in today’s money. IRR, payback and the profitability index are helpful aids, but they can mislead, so they should not overrule NPV.
Key points
■A $10m production line has NPV $2.552m, IRR 17.0%, payback 3.45 years, discounted payback 4.21 years and PI 1.23 at 9%.
■100% bonus depreciation for property acquired after January 19, 2025, adds $0.293m of NPV in the example.
■Cash flows that change sign twice can have two IRRs (10% and 20%); MIRR or NPV resolves them.
A closer look
Capital budgeting is how a company decides which long-term projects to fund. It discounts (1.2) a project’s incremental cash flows, the cash that changes only because the project happens, at a rate matched to the project’s risk; the company’s WACC (1.4) fits only projects like its existing business. Four measures dominate:
Of 392 CFOs surveyed by Graham and Harvey (2001), 75.7% always or almost always used IRR, 74.9% NPV, 56.7% payback and 29.5% discounted payback.
Decision rule
Accept independent projects with positive NPV at a risk-matched rate. Between mutually exclusive projects, take the higher NPV whatever the IRRs say. Quote IRR only when cash flows change sign once; otherwise use MIRR or NPV. Payback is a liquidity screen, not a measure of value. Under a hard budget, pick the affordable combination with the highest total NPV.
The costliest mistake
Ranking mutually exclusive projects by IRR. Choosing Project B (IRR 21.9%) over the production line (17.0%) adds $1.184 million of value instead of $2.552 million, forgoing $1.368 million, 53.6% of what was available, at any cost of capital below the 15.0% crossover. Rank exclusive choices by NPV.
What the full article covers
In the full article I take you through these sections:
■1.10 Triangulating Valuation — Putting It All Together
■1.11 Capital Budgeting: NPV, IRR, Payback and the Profitability Index
It includes worked examples, a look under the hood at the mechanics, a clear decision rule, the one mistake that costs people the most, a recap, a reveal-on-click quiz and the official sources behind every figure.
Volume II: Capital Markets
Read the full article on FinoLib
The complete article, Capital Budgeting: NPV, IRR and Payback Explained, with every worked example, diagram, quiz and source, is free to read in Volume II, Capital Markets on finolib.com.
Explore the Finance Education Series: Vol. II — Capital Markets · Vol. I — Global Economy · Vol. III — Finance Encyclopedia · Vol. IV — Finance Careers · Vol. V — Personal Finance