Interviewers want the assumptions narrated, not the answer, so the arithmetic is
deliberately simple and every line is contestable.
Question: how big is invoice scanning for our accounting SaaS?
BASE
paying accounts today 12,000 known
small-business tier, who key invoices by hand 55% billing data
addressable accounts 6,600
WHO HAS THE PAIN
in 9 interviews in that tier, 6 named manual
entry as a top-three monthly annoyance
taking that as roughly 60% - a weak number
from a tiny sample, flagged as such x 60%
accounts with the pain 3,960
ATTACH
comparable paid add-ons attached 10-20% of the
accounts with the pain in year one. Take the
middle, 15% x 15%
paying accounts, year one 594
REVENUE
594 x GBP 15/month x 12 GBP 106,920
round to GBP 107k ARR
COST TO SERVE
OCR vendor GBP 0.02/page, est. 200 pages per
account per month = GBP 4/account/month
594 x 4 x 12 GBP 28,512
gross contribution GBP 78k
COST TO BUILD
2 engineers + 0.5 design, 4 months, loaded
~GBP 11k/person-month GBP 110k
READ payback in year two, on a 15% attach rate that is itself the
softest number in the model. Halve the attach rate to 8% and it
still pays back, just later: 3,960 x 8% = 317 accounts, at
GBP 11 net per account per month that is GBP 41.8k a year, so
the GBP 110k build is recovered during year three.
SENSITIVITY move each input by 1% and see what happens to the
GBP 78k gross contribution:
price +1.36% 594 x GBP 0.15 x 12 = GBP 1,069
attach rate +1.00% contribution is linear in attach
OCR cost -0.36% 594 x GBP 0.04 x 12 = GBP 285
Price is the most leveraged input, because the net margin per
account is GBP 11 on a GBP 15 price, so a price move lands
almost entirely on the bottom line.
WHAT I WOULD DO spend the next money on attach rate anyway. It is
not the most leveraged input, it is the least evidenced one -
six of nine interviews and a borrowed 10-20% range - whereas
price is a number we set and can revisit at any time. A
fake-door test measuring intent to attach costs a fortnight and
moves the widest error bar in the model.
The purpose of the exercise is not the £107k. It is the identification, in the
final lines, of which input to go and reduce the uncertainty on — and an
interviewer is listening for whether you find it, because that is what tells you
what to do next.
Notice that the answer is not simply "the input with the biggest coefficient".
Price has the larger sensitivity here, 1.36 against 1.00, and it is still the
wrong thing to research, because we already know the price and can change it on
a Tuesday. Attach rate has a smaller coefficient and a far wider error bar, and
you can only narrow that bar by going and measuring something. Leverage tells
you where the answer moves; evidence tells you where you are guessing, and the
next experiment belongs to the second question.
Every questionable number is labelled at the point of use. "Six of nine" is
stated as a weak basis rather than smoothed into sixty per cent and then treated
as a fact three lines later, which is how sizing models acquire false confidence.
Saying "this is the number I am least sure of" is a strength in this format, not a
hedge.
The two cost lines are what separate sizing from revenue fantasy. A model that
stops at £107k of ARR has not answered the question that was asked, because the
decision is whether to spend the quarter, and the quarter costs £110k. Volunteer
cost to serve in particular: per-unit vendor costs against a fixed subscription
price are the standard way a feature is revenue-positive and margin-negative.
The sensitivity block is also the answer to the follow-up about what you would do
with more time, and it is worth showing the arithmetic rather than asserting a
ranking. Each figure is one line: a one per cent price rise adds fifteen pence a
month across 594 accounts, which is £1,069 a year against a £78k contribution,
so 1.36 per cent. Doing that for three inputs takes a minute and stops you
claiming, as models of this kind routinely do, that the answer is insensitive to
something it is in fact most sensitive to.
The pay-back line deserves the same treatment. "It never pays back at 8%" is the
sort of sentence that sounds appropriately cautious and is simply false on the
model's own numbers, and an interviewer who checks it will conclude that you did
not. Halving the softest input and reporting the honest consequence — a year
later, not never — is both more useful and harder to argue with.