Paid media basics
Size a paid channel from CPM to paying customer, find the input its profit is most sensitive to, and price the next $20,000 rather than the average.
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A paid channel is a chain of rates whose first link is bought at auction. Sizing one takes ten minutes: multiply the chain to the paying customer, subtract the spend, then ask which rate the answer is most sensitive to and what the next dollar buys. Most money lost in paid media is lost on the last two questions, because the platform's report answers neither.
The auction prices the first link
Every ad slot is auctioned as the page loads. On most search and social platforms the bid is ranked by the bid multiplied by the platform's predicted chance that the ad earns the click or action, and the winner often pays less than its bid, roughly what it needed to hold its rank. A more clickable ad therefore pays less for the same slot: relevance works as a discount.
There are three ways to buy, and the unit you buy decides who carries which risk.
- CPM, cost per thousand impressions. You carry the click rate and every rate after it.
- CPC, cost per click. The platform carries the click rate; you carry everything after the click.
- CPA, cost per action. The platform carries the rates up to the event it can see, usually the sign-up, and you still carry every rate after that.
No buying unit moves the risk past the event the platform observes. The payment happens in your billing system, weeks later, and unless you send it back to the platform, nothing it optimises knows whether the customer paid. The units convert into each other through the rates: CPC = CPM ÷ (1,000 × CTR), so $20 ÷ (1,000 × 1%) = $2, and CPA = CPC ÷ conversion, so $2 ÷ 3% = $67.
One month of the channel, sized
The course's paid rates from the arithmetic a marketer carries, run through a $20,000 month:
spend $20,000 at a $20 CPM -> 1,000,000 impressions
clicks x 1% CTR -> 10,000 clicks $2 each
sign-ups x 3% -> 300 sign-ups $67 each
customers x 20% who pay -> 60 customers $333 each
value x $368 of 12-month margin -> $22,080
profit $22,080 - $20,000 -> $2,080
The value per customer is the 12-month margin, not the lifetime $800, because the course's payback target is 12 months. The default customer's $40 a month, cumulated with 5% monthly churn, is 800 × (1 − 0.95¹²) ≈ $368 by month 12, which is also the most a customer may cost; CAC, LTV and payback derives both figures. The month clears that ceiling by $35 a customer, $2,080 in all.
Stopping at the platform's $67 CPA is the error module 0 covers. The two errors this lesson covers come after the chain is complete.
Which input the profit is most sensitive to
Every rate multiplies the value, and the spend stays fixed, so a 10% shortfall in any one rate removes 10% of $22,080: $2,208, which is 106% of the profit. In general:
profit multiplier = value / (value - cost) = 22,080 / 2,080 ≈ 10.6
A 1% error in any rate is a 10.6% error in profit. The multiplier is large whenever value sits close to cost, which is exactly where a channel at its ceiling sits. Turned round, the profit is gone when value falls to $20,000, a factor of 20,000 ÷ 22,080 = 0.906, so a 9.4% shortfall in any single rate wipes it out:
| Input | Base | Break-even | Plausible range before data | Known from |
|---|---|---|---|---|
| CPM | $20 | $22.08 | $16 to $24 | the platform, on day one |
| Click rate | 1% | 0.91% | 0.6% to 1.4% | the platform, in a week |
| Click to sign-up | 3% | 2.72% | 2% to 4% | your analytics, in two weeks |
| Sign-up to paying | 20% | 18.1% | 10% to 30% | your billing, after the trial |
| 12-month margin | $368 | $333 | $316 to $408 | your cohorts, in a year |
Every rate has the same multiplier, so the multiplier alone cannot say which input matters most. The range does. The input the decision is most sensitive to is the one whose plausible range reaches furthest past its break-even, and here that is sign-up to paying: the rate measured last, off the platform, and the one most likely to differ for a new audience.
The margin row is the surprise: churn anywhere from 8% to 3% moves 12-month margin only between $316 and $408, because most first-year margin arrives before churn compounds. Over a lifetime the same range moves value from $500 to $1,333.
Naming the input is half the job; the other half is admitting what a test can settle. A $20,000 month produces 300 sign-ups and about 60 payers, give or take 7, since √(300 × 0.2 × 0.8) ≈ 6.9. The measured rate lands somewhere between about 18% and 22%, which still straddles the 18.1% break-even. A channel that clears its ceiling by 10% cannot be confirmed by one month of data; it is a break-even channel until a larger margin shows up. The cheaper way to widen that margin is usually the stretch every channel shares, from sign-up to paying, where the funnel and AARRR finds activation the cheapest lift.
Frequency and saturation: why the second $20,000 costs more
The chain is linear only for the first dollars. Double the spend against the same audience and two rates move against you. To win more auctions you have to outbid advertisers you lost to before, so the CPM rises. The platform has already shown the first $20,000 of ads to the people likeliest to click, so the next impressions go to less likely people and to the same people again, and the click rate falls as frequency climbs. A channel's second $100,000 costs more than its first for the same two reasons. Assume the second $20,000 runs at a $25 CPM and a 0.8% click rate:
second $20,000 at a $25 CPM -> 800,000 impressions
x 0.8% CTR -> 6,400 clicks $3.13 each
x 3% x 20% -> 38.4 customers $521 each
x $368 -> $14,131 of 12-month margin
profit on the increment -> -$5,869
The platform reports the blend: $40,000 for 98.4 customers, $406 each. That is 10% over the $368 ceiling and reads like something a bid adjustment could fix. The increment is the real number. Its customers cost $521, the same figure as the invoicing app's paid CAC in module 2, and pay back only in month 21. The second $20,000 loses $5,869 inside the payback window while the first $20,000 makes $2,080. The whole $40,000 month loses $3,789, and the report never shows the line that loses it. It is why the five decisions says a channel is chosen at the margin.
The fix is to price every budget increase as its own chain: marginal customers ÷ marginal spend. Raise the budget in steps, say 25% for two weeks, and read the change in paying customers against the change in spend, never the new average. The exercise size a channel runs the same ten-minute model on a search channel, where the audience is capped by how many people search.
In practice
To the channel owner or the agency: report every budget change as an increment with the paying customers it bought, and send the payment event back to the platform so its bidding optimises for payers, not sign-ups. Ask "what did the last $5,000 buy?" before "what is our CPA?" To the team: mark every rate as measured or assumed, name the input whose range reaches furthest past its break-even, and say what result would stop the spend.
The mistake that costs money is scaling a channel on its average cost per customer. A $406 blend looks like tuning; underneath it is a $521 increment that loses $5,869 a month inside the payback window.
Check yourself
1. A creative refresh lifts the click rate from 1% to 1.2% on both tiers, and the platform suggests doubling the budget to $40,000. Do you?
The first $20,000 now buys 72 customers at $278. The second, at a $25 CPM and 0.8% × 1.2 = 0.96%, buys 800,000 × 0.96% × 3% × 20% ≈ 46 customers at $434, and loses about $3,040 against $368 of margin each. The blend is $339, under the ceiling, which is why the suggestion sounds right. Stay at $20,000 and bank the better creative as profit; the increment pays only if its click rate reaches about 1.13%.
2. An agency offers to buy sign-ups on a CPA basis at a guaranteed $60 each. Do you take it?
Only with a condition on the paying rate. At 20% paid, $60 a sign-up is $300 a customer, under the $368 ceiling; the break-even paying rate is 60 ÷ 368 ≈ 16.3%. But on CPA pricing the agency is paid for sign-ups and will buy the cheapest ones, which are the likeliest to pay at less than 20%. Take it with the paying rate of its sign-ups measured weekly, and stop if it falls below 16%.