A Practitioner’s Guide to Three Values for One Company, and the Arithmetic of the Gap
Julian R. Sterling
These are the four Excel workbooks that go with the book. Every figure the book prints is
reproduced in them by a live formula rather than a typed constant — change the growth, the
margin, the cost of capital or the peer set and every dependent number moves. Each one ends with
a Checks sheet setting the printed figure beside the computed one:
58 controls in all, every one green. If a control ever reads FAIL, the workbook
is wrong, not the book.
Free to download. No sign-up, no email address, nothing to fill in.
Everything described below is inside it, with the read-me.
The four workbooks
Chapters 1, 7, 9, 11 and 13
Cawdrey — the three values
All three methods on one set of facts, so the spread between them is a computed quantity
rather than a picture. The discounted cash flow at 73,060,585, the comparable
set at 8.20x giving 68,880,000, the transaction set at 10.40x giving
87,360,000, and a gap of 18,480,000, or 26.8 per cent of the
lowest. The bridge to equity value is run for each, so the three appear in the currency the
seller actually cares about as well as in enterprise value.
Then the line the book is built on. Each of the three values is put back into the same model
at the same cost of capital, and the perpetual growth rate that would produce it is solved for:
1.44, 2.00 and 3.41 per cent. The entire
26.8 per cent spread is 1.96 points of growth — and once it is stated
that way it becomes a disagreement about the world rather than about method.
The_Three_Values.xlsx · XLSX · 13 KB
Chapters 4 to 8
The discounted cash flow
The five-year build line by line, with year one taken apart from revenue through EBITDA, tax,
depreciation, capital expenditure and working capital to a free cash flow of 4,664,000, and
every ratio held as an input rather than typed into a formula. Change the margin and the whole
forecast moves; change the capital intensity and it moves differently.
The terminal value has its own block, and its share of the answer —
72.78 per cent — is on the page rather than buried, because that is the
number a reviewer should see first. The sensitivity grid runs the cost of capital from 8.0 to
10.0 per cent against growth, and reports the finding of Chapter 8: two hundred basis
points move the value 21,578,578, which is 1.17 times the
entire spread between the three methods. The argument everyone has in the room is smaller than
the one nobody has.
The_Discounted_Cash_Flow.xlsx · XLSX · 12 KB
Chapters 9, 11 and 12
Multiples, and the premium decomposed
The peer set and the transaction set with their medians, their quartiles and the effect of
dropping any one name, so the fragility of a five-company median is visible rather than
asserted. Type a sixth peer in and watch the enterprise value move.
The second half is the test of Chapter 12, and it is the sheet most worth running on your
own numbers. The 26.8 per cent control premium is converted into the perpetual after-tax cash
flow it requires — 1,293,600 a year — and then into the pre-tax figure a management
team would actually have to deliver: 1,724,800 every year, for ever, which is
20.53 per cent of the target’s entire EBITDA and 3.59 per cent of its
revenue. A percentage is a feeling. That is a test somebody either passes or fails.
Multiples_and_the_Premium.xlsx · XLSX · 11 KB
Chapters 13, 15 and 16
Backing out the assumption
The reverse solve, in closed form rather than by goal seek, so it recomputes the moment you
type. Enter any enterprise value and read the perpetual growth rate that would produce it,
holding the forecast and the cost of capital fixed; or hold growth and read the cost of capital
instead. The identity is on the sheet:
g = (K × WACC − FCF5) / (FCF5 + K), where K is the terminal value the
target price implies, rolled forward.
The last sheet follows the money to the seller. A headline equity value of 76,160,000, disposal
costs, a tax base and a capital gains rate produce 64,109,440 —
15.8 per cent below the headline, and equivalent, put back through the bridge,
to 8.97x. Which is almost exactly the discounted cash flow value the seller
was offered before the negotiation began. The tax assumptions are inputs and are the
case’s own; replace them with your jurisdiction’s and the conclusion is still there.
Backing_Out_the_Assumption.xlsx · XLSX · 13 KB
Conventions used throughout
Blue text
a hardcoded input — you may edit these
Yellow fill
an input cell; everything else on the sheet is a formula
Black text
a formula — do not overtype these
Checks sheet
the printed figure beside the computed one, with a PASS or a FAIL
Why the checks matter more than the models
A workbook that agrees with a book proves nothing on its own — the author wrote both. What
the Checks sheets do is different: they force the model to reproduce a number that was printed
before the model existed, from a formula rather than from the number itself.
On this book the discipline mattered most in workbook 4. The reverse solve is the argument of the
whole text, and it is the one place where an iterative answer would have been easy and unfalsifiable.
Writing it in closed form meant the three implied growth rates had to fall out of an identity
rather than out of a search — and the identity had to reproduce 2.00 per cent exactly when
fed the model’s own enterprise value, which is the only check that could have caught an
error in it.
Where the book uses an assumption rather than a fact — the 2 per cent disposal cost, the 20
per cent gains rate, the 22,000,000 tax base — the workbook carries it as an input on the
Inputs sheet and says so. None of them is a statement about any jurisdiction.
Opening the files
The workbooks open in Microsoft Excel, LibreOffice Calc, Google Sheets and Numbers. They use
no macros and no add-ins, so nothing needs to be enabled or trusted. If your spreadsheet asks
to update links on opening, decline — there are none.
Closing the DealTwo defensible bridges 20.70 million apart, a peg worth 7.00 million, and the six choices that remove 6.60 of a 12.00 earn-out.
CMBS and CRE CLOsWhere the loss actually lands, from appraisal reduction to realised severity, and what the B-piece is really being paid for.
How to Read a Commercial LeaseThe three refinements chapter 19 names and never performs, and the renewal rate below which the mark-to-market is worth nothing.
How to Read a Credit AgreementWhere the default actually comes from, the cure that costs 5.5 times the other, and the capacity nobody adds up.
How to Read a Real Estate Loan AgreementThe cure ratio in closed form, the four-point window in which the cheap cure works, and the cure sized to the wrong threshold.
Office Real EstateA six per cent yield that returns 3.2 per cent once the re-letting cycle is paid for, and the headline-to-net-effective rent arithmetic.
Private Equity Real EstateBoth worked waterfalls to the dollar, the two capital stacks, and the arithmetic of the promote made changeable.
Private Markets PerformanceThirty-one of the thirty-three figures chapter 19 publishes reproduce exactly — and the two that do not are named rather than quietly adopted.
Raising a Real Estate FundThe chapter 17 funnel run on a calendar — when the first close actually lands, and why more travel does not help.
Real Estate FinanceFour people look at one building and reach four numbers; the lender is whole only above 105,109,489, twelve per cent below today’s value rather than forty.
Real Estate Financial ModelingProperty, development and fund models built line by line, and the modelling test worked end to end.
Real Estate Fund ManagementThe waterfall of 6.11, the build-to-core of 8.7 and the proceeds gap, reproduced as live formulas rather than asserted.
REIT Analysis and ValuationFFO of 532.0, AFFO of 381.0, net asset value and dividend safety — every figure a formula you can change.
Retail Real EstateThe occupancy cost of every unit in a centre, the sixteen per cent of the rent roll no tenant can sustain, and the right-size-convert-or-hold decision priced.
Sale and LeasebackA €179.5 million transaction end to end, with rent cover measured on the entity that actually signs the lease.
Self-Storage Real EstateThe cohort engine behind a 590-unit store, and the rate increase on existing customers priced against the move-outs it causes.
The Fund Finance ProfessionalChapter 8 builds the reported-to-eligible NAV bridge; chapter 9 computes every ratio without it. Two points at every state — and what a subscription line does to the IRR.
The Growth Equity InvestorWhat a pro rata cheque really costs, and the band where defending your ownership loses money.
The Private Credit InvestorThe two coverage ratios are not measured on the same thing: the erosion is 47.7 per cent, not the 28.7 the headline implies.
The Private Equity Fund Controller PlaybookThe book defines IRR, DPI, RVPI and TVPI, tells you to update them at the exit, and prints not one value. Computed: a 1.833× deal inside a fund at 0.892 TVPI.
The Venture Capital AssociateWhat defending a position costs, and how many companies a reserve pool actually defends.
Financial Risk ManagementA fund inside every limit that cannot meet a redemption — and the number that decides it is the one with no currency attached.
Quantitative FinanceThree models agree to a quarter of one per cent about a number that one unobservable input moves a hundred and three times as much.
Asset ManagementFour people quote four returns for one mandate, all correct and 2.7017 points apart — forty-eight times the manager’s net skill.
Alternative InvestmentsA manager reports 13.29 per cent and the endowment earns 6.26 — both correct, and only a third of the advertised advantage arrives.
Credit AnalysisFour defensible EBITDAs on one borrower give leverage from 3.19x to 6.47x — and the add-back argument is fifty times the covenant headroom.
Venture CapitalOne company out of twenty-eight returns 56.7 per cent of the fund, and half the capital goes in after the decision — at half the return.
Machine Learning for FinanceFive people quote the accuracy of one credit model, all five are right, and the number that decides how much money it makes is none of them.
Commercial Real Estate InvestingThe equity earned 8.6647 per cent and the investor received exactly 8.0000 — the preferred return, and nothing above it.
Mergers and AcquisitionsThe board paper says the deal creates 13,436,667 of value. The arithmetic says it destroys 17,530,855. Nobody is lying.
DerivativesThe treasury report says the hedge cost 1,233,698. That is the interest differential, not a cost.
Treasury ManagementFive cash balances for one company, all correct and 145,600,000 apart — and the revolver that is two-thirds of the liquidity leaves at a revenue fall of 8.4127 per cent.
Financial Planning and AnalysisRevenue 3.0190 per cent above budget and operating profit 16.3209 per cent below it, in the same quarter, with every figure correctly stated.
Energy TradingA position report that is 91.7031 per cent hedged and correctly computed, on a book that is short 2,542,000 MWh — and a margin call of 198,400,000 the next morning.
Construction Cost ControlA contract sum of 26,301,102 became a final account of 29,153,363 on the building that was drawn — and 85.8 per cent of what was lost was knowable on the day it was signed.