Marketing Science + Capital Allocation

NPVROAS

The Complete Formula Map: From Raw Spend to Capital Allocation Decisions

"A junior marketer worries about ROAS. A better marketer worries about ROI. A serious capital allocator thinks in NPV. NPVROAS bridges the gap."

The Evolution

Why existing metrics fail at capital allocation

Junior Marketer

ROAS

Revenue / Ad Spend

Misses: time value, churn, margins, LTV

Better Marketer

ROI

(Revenue - Cost) / Cost

Misses: discounting, expansion, saturation

Capital Allocator

NPVROAS

NPV(Cashflows) / Investment

Captures: TVM, churn, expansion, saturation, margins

Raw Spend

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Adstock

→

Response Curve

→

Customers

→

T-Horizon Cashflows

→

NPV

→

Capital Decision

Spend & Adstock Modeling

Marketing impressions don't vanish instantly. Adstock captures memory decay.

Monthly Spend with Seasonality

Budget allocation over time

S(c,t) = Base_Spend(c) × Seasonality(t)

// Seasonality multipliers by month:
// Jan=0.8, Feb=0.85, Mar=0.95, Apr=1.0,
// May=1.05, Jun=0.9, Jul=0.7, Aug=0.6,
// Sep=1.1, Oct=1.2, Nov=1.5, Dec=1.8

S(c,t) spend for channel c, month t

Base_Spend annual budget / 12

Seasonality monthly multiplier

∿

Adstock (Exponential Decay)

Carryover effect of past spend

A(t) = S(t) + θ × A(t-1)

θ decay rate (0 = no memory, 1 = perfect memory)

A(t) adstocked spend at time t

Why it matters: TV and content have high θ because brand impressions linger. Paid Search has low θ because intent fades quickly. Ignoring adstock misattributes long-memory channels' contributions.

Channel-Specific Decay Parameters

Calibrated adstock rates by channel type

Paid_Search: θ = 0.20
Display: θ = 0.30
LinkedIn_Ads: θ = 0.45
Organic: θ = 0.50
Account_Based: θ = 0.55
Content: θ = 0.60

Response Curves (Saturation)

More spend doesn't mean proportionally more customers. Diminishing returns are the law.

log

Log Response Curve

Most channels — concave saturation

R(x) = β × log(1 + k × x)

β scale (max response)

k sensitivity (how fast it saturates)

x adstocked spend

Why log: Doubling spend does not double output. The marginal customer costs more than the average customer. This is why average ROAS misleads.

⇑

Hill Response Curve

Account-Based Marketing — S-curve with threshold

R(x) = β × x^α / (x^α + λ)

α steepness of S-curve

λ half-max spend

β max response ceiling

Why Hill for ABM: Enterprise ABM often requires minimum investment before returns appear. Below-threshold spend is wasted.

⚠

The Core Insight: Average Returns ≠ Marginal Returns

Channels with the strongest average performance are often not the best place to allocate the next dollar. A capital allocator who invests on marginals creates value; one who invests on averages can destroy it.

Customer Acquisition

Converting response curve output into actual customer arrivals

👥

Expected Customers per Channel

Response to customer conversion

E[Customers(c,t)] = R(Adstock(c,t))

Actual ~ Poisson(λ = E[Customers])

R() response curve output

Poisson discrete random arrivals

🎯

Persona Assignment

Channel-persona affinity matrix

P(persona | channel) = Affinity_Matrix[c,p]

ACV contract value by persona

Retention monthly survival rate

Expansion annual growth rate

Customer Lifetime Value (NPV)

The heart of NPVROAS: discounted, risk-adjusted cashflows over the customer lifetime

The NPVROAS Master Formula

NPV_customer = Σ_t=0^T CF(t) / (1 + r)^t

CF(t)

cashflow at time t

Rev(t)

revenue at time t

gross margin

Alive(t)

survival at time t

discount rate

economic horizon in months

💰

Cashflow Definition

Finance-native decomposition

CF_i,c(t) = Rev_i(t) × GM × Alive_i(t)

💰

Monthly Revenue per Customer

Base + expansion, pre-churn

Rev_i(t) = (ACV_i / 12) × (1 + g_i)^t/12

ACV annual contract value

g expansion rate

☠

Churn / Survival Function

Stochastic customer lifetime

E[Alive_i(t)] = retention_i^t

Why stochastic: expected survival gives the mean, but simulation reveals the variance and risk profile of each channel’s customer base.

Discount Rate

Time value of money conversion

r_monthly = (1 + r_annual)^1/12 - 1

DF(t) = 1 / (1 + r_monthly)^t

⏱

Sales Cycle Delay

Time from acquisition to first revenue

Revenue starts at: t = ceil(sales_cycle_days / 30)

Cost & Efficiency Metrics

What you actually paid vs. what you actually got

📊

Customer Acquisition Cost (CAC)

True fully-loaded cost per customer

CAC(c) = Total_Spend(c) / Customers(c)

Fully_Loaded_CAC = CAC × Sales_Multiplier

⚖

LTV:CAC Ratio

The classic — but incomplete — efficiency metric

LTV:CAC = NPV(Customer Cashflows) / CAC

The trap: LTV:CAC is an average metric. Marginal NPV tells you where to allocate the next dollar.

Marginal NPV & Capital Allocation

The decision that matters: where does the NEXT dollar go?

Marginal NPV per Channel

Monte Carlo incremental testing

ΔNPV(c) = E[NPV(budget + δ)] - E[NPV(budget)]

δ marginal spend increment

N simulation count

⇄

Budget Reallocation

Moving capital from saturated to hungry channels

New_Budget(c) = Old_Budget(c) + Reallocation(c)

ΔPortfolio_NPV = NPV(new) - NPV(old)

A/B Testing & Bayesian Updating

Continuous learning: updating beliefs about channel performance with new data

A|B

Frequentist A/B Test

Standard significance testing

z = (μ_B - μ_A) / √(s_A²/n_A + s_B²/n_B)

MDE = z_α × √(2σ²/n)

𝒫

Bayesian Posterior Update

Updating channel beliefs with new evidence

P(θ|data) ∝ P(data|θ) × P(θ)

P(B > A) = ∫ P(θ_B > θ_A) dθ

Why Bayesian: it answers the capital allocator’s question: how confident am I, and what should I do next?

Putting It All Together: NPVROAS

NPVROAS(c) = [ Σ_{i in Customers(c)} Σ_t=0^T CF_i,c(t) / (1+r)^t ] / Total_Spend(c)

T is a flexible economic horizon, not an arbitrary fixed month count. This makes the framework more generalizable and more finance-native.