Class 2: Marketing Profitability Analysis

Author

Affiliation

Dr Wei Miao

UCL School of Management

Published

October 1, 2025

1 Overview

1.1 Learning Objectives

How to conduct break-even analysis for a marketing campaign
How to conduct net present value analysis for a marketing campaign
Practise R basic calculations and vector operations in the case study

2 Break-Even Analysis

2.1 Decisions for Data Scientists

The ultimate goal of marketing (and other business activities) is to create value for and improve the profitability of firms.
As any marketing activity comes with a cost, data analysts need to correctly evaluate whether a campaign creates or destroys value for the company.
Such analyses are called cost-benefit analyses, sometimes referred to as profitability analysis or break-even analysis.

2.2 Break-Even Quantity

To evaluate the financial feasibility of a marketing campaign, we use break-even analyses. A key metric in marketing is the break-even quantity.
Break-even quantity is particularly useful when:
- Evaluating short-term marketing campaigns with fixed costs
- Comparing different marketing initiatives with similar time horizons
- Making quick go/no-go decisions for promotional activities
- Assessing campaigns where the primary goal is incremental sales volume

Definition

The break-even quantity (BEQ) calculates the number of incremental units the firm needs to sell to cover the cost of the marketing campaign.

The intuition behind BEQ is that, if the company sells less than the BEQ, it will lose money. If the company sells more than the BEQ, it will make money. The BEQ is the minimum quantity that the company needs to sell to cover the cost of the marketing campaign.

2.3 Compute BEQ: Contribution Margin

The difference between the price per unit and variable costs per unit is defined as the contribution margin per unit. That is,

Definition

Contribution Margin Per Unit = Price Per Unit - Variable Costs Per Unit

Price per unit: retail price customers pay
Variable costs per unit: Cost of Goods Sold (COGS)¹ + any other variable costs per unit

This gives the formula for BEQ:

Definition

BEQ = Marketing Expenditure / Contribution Margin Per Unit

2.4 Break-Even Quantity: Steps and Decision Rule

Steps to conduct break-even analysis
- Step 1: Compute the BEQ based on the product’s price and cost structure. This is the minimum quantity the company needs to sell to cover the costs of the marketing campaign.
- Step 2: Evaluate whether the campaign can generate an incremental quantity larger than the BEQ
The decision rule
- If the incremental sales quantity > BEQ, the company makes a profit, so the campaign should be accepted; otherwise, it should be rejected.

3 Case Study: Profitability Analysis for Apple Inc

3.1 Background

Tom, a senior marketing manager at Apple UK, is looking to launch a series of marketing campaigns to promote the just-released iPhone 17 series. Tom is a proud graduate of the UCL MSc BA programme in 2020. He remembers from the Marketing Analytics module that break-even analysis helps to evaluate different types of marketing decisions.

Code

price <- 799 # retail price of iPhone in £
quantity <- 10 # sales quantity in million units
endorsement_fee <- 100 # endorsement fee in million pounds
endorsement_sales_increase <- 0.025 # sales increase percentage due to endorsement
COGS <- 0.47 # cost of goods sold; 47% of retail price, i.e., 47% of £799
RD_costs <- 100 # R&D costs in million pounds
monthly_sales_increase_1stmonth <- 0.003 # sales increase percentage in the first month
monthly_sales_increase_after <- 0.002 # sales increase percentage in the following months
WACC <- 0.1 # weighted average cost of capital

Case objectives:

Practise situation analysis and compare with Uber’s case
Practise how to conduct break-even analyses for a marketing campaign
Practise R basic computations and vector operations

3.2 Apple Inc: Key Information

From the case: The marketing analytics team at Apple Inc had applied sales forecasting models to historical sales data and predicted that sales this year would reach 10 million units at the retail price of £799, without any additional marketing activities. The team had also collected information on the Cost of Goods Sold of the Apple 17, which is 47%. The Research and Development (R&D) costs for the iPhone 17 are 100 million pounds.

Open the .qmd answer sheet downloaded from Moodle for Week 1, and let’s solve this case using the R basics we have learned!
Question 1 (after class): Conduct a 5C analysis for Apple Inc. and compare it with Uber’s case.

3.3 Apple Inc: BEA Question 2

Question 2: Compute the contribution margin
- Do we need to consider R&D costs?

Code

contribution_margin <- (1 - COGS) * price
contribution_margin

[1] 423.47

3.4 Sunk Costs and Sunk Costs Fallacy

Sunk costs are costs that have already been incurred in the past and cannot be recovered. They should not be considered when making decisions.
However, behavioural economics research shows that people often fall victim to the sunk cost fallacy, where they consider sunk costs in their decision-making instead of focusing on future costs and benefits.
When making decisions, you should focus only on future costs and benefits. In our case, the R&D costs are sunk costs and should not be considered in the break-even analysis.

3.5 Apple Inc: BEA Question 3

Question 3: Based on the information at hand, should Tom approve the influencer marketing plan?

4 Net Present Value

4.1 Definition of NPV

When the effect of the marketing campaign is expected to have a long-term effect or when the time value of money is an important consideration, we need to take the future into account.

Definition

Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

4.2 Formula of NPV

\[ N P V=-I_{0}+\frac{CF_{1}}{(1+k)}+\frac{C F_{2}}{(1+k)^{2}}+\cdots+\frac{C F_{n}}{(1+k)^{n}} \]

$I_{0}$ is the initial marketing investment/expense
$C F_{n}$ is the incremental profit in period $n$: it must be the additional profit generated by the marketing campaign
$k$ (sometimes $r$ or $i$) is the discount rate, which reflects the value of time: £1 today is worth $£1 * (1+k)$ in the next period.
The decision rule
- If NPV > 0, the marketing campaign adds value to the company, so it should be accepted.
- If NPV < 0, the marketing campaign will decrease the company’s value, so it should be rejected.

4.3 Apple Inc: NPV Influencer Marketing I

Question 4: Based on the information at hand, should Tom approve the influencer marketing plan based on the Net Present Value method?

Compute the sequence of monthly cash flows
- Generate a sequence of incremental sales for 12 months (a vector with 12 elements)
  - Hint: use rep(), c(), and vector element-wise multiplication

Code

monthly_sales_increase_1stmonth <- 0.003
monthly_sales_increase_after <- 0.002
# incremental profit each month
monthly_incremental_sales <- c(
    monthly_sales_increase_1stmonth,
    rep(monthly_sales_increase_after, 11)
)

CF <- monthly_incremental_sales *
    quantity *
    contribution_margin

The resulting monthly CFs are: 12.7041, 8.4694, 8.4694, 8.4694, 8.4694, 8.4694, 8.4694, 8.4694, 8.4694, 8.4694, 8.4694, 8.4694

4.4 Apple Inc: NPV Influencer Marketing II

Compute the sequence of discount factors
- Generate a sequence of WACC for 12 months (a vector with 12 elements)
- Generate a sequence of discount rate for 12 months (a vector with 12 elements)
  - Hint: use seq() to generate geometric sequence with patterns

Code

monthly_WACC <- 0.1 / 12 # this is the discount rate
discount_factor <- (1 / (1 + monthly_WACC))^c(1:12) # this is the discount factor

The resulting monthly discount factors are: 0.9917355, 0.9835394, 0.975411, 0.9673497, 0.9593551, 0.9514265, 0.9435635, 0.9357654, 0.9280319, 0.9203622, 0.9127559, 0.9052124

4.5 Apple Inc: NPV Influencer Marketing III

Compute the NPV
- Generate a sequence of discounted CFs for 12 months
- Sum up all discounted CFs across the 12 months using sum()
- Subtract endorsement fee from the sum to get NPV

Code

NetPresentValue <- sum(CF * discount_factor) - endorsement_fee

The NPV is 0.5349641

4.6 After-class

Review the coding practice from today’s class and ensure you understand how to calculate NPV in R. Complete the R coding exercise for Week 1, and feel free to bring any questions to next week’s class.

Footnotes

Material and production labour costs for producing a unit of product, often represented in percentage terms, e.g., a COGS of 60% means the costs are 60% of retail prices. An iPhone with a retail price of £1,000 and a COGS of 30% means the COGS is £300.↩︎

--- title: "Class 2: Marketing Profitability Analysis" date: "`r (first_date + lubridate::dweeks(0))`" --- # Overview ## Learning Objectives ```{r} #| echo: false pacman::p_load(knitr) ``` - How to conduct break-even analysis for a marketing campaign - How to conduct net present value analysis for a marketing campaign - Practise R basic calculations and vector operations in the case study # Break-Even Analysis ## Decisions for Data Scientists - The ultimate goal of marketing (and other business activities) is to create value for and improve the profitability of firms. - As any marketing activity comes with a cost, data analysts need to correctly evaluate whether a campaign creates or destroys value for the company. - Such analyses are called *cost-benefit analyses*, sometimes referred to as *profitability analysis* or *break-even analysis*. ## Break-Even Quantity - To evaluate the financial feasibility of a marketing campaign, we use break-even analyses. A key metric in marketing is the **break-even quantity**. - Break-even quantity is particularly useful when: - Evaluating short-term marketing campaigns with fixed costs - Comparing different marketing initiatives with similar time horizons - Making quick go/no-go decisions for promotional activities - Assessing campaigns where the primary goal is incremental sales volume ::: {.callout-note icon="false"} ### Definition **The break-even quantity (BEQ)** calculates the number of ***incremental*** units the firm needs to sell to cover the cost of the marketing campaign. ::: - The intuition behind BEQ is that, if the company sells less than the BEQ, it will lose money. If the company sells more than the BEQ, it will make money. The BEQ is the minimum quantity that the company needs to sell to cover the cost of the marketing campaign. ## Compute BEQ: Contribution Margin - The difference between the **price per unit** and **variable costs per unit** is defined as the **contribution margin per unit**. That is, ::: {.callout-note icon="false"} ### Definition Contribution Margin Per Unit = Price Per Unit - Variable Costs Per Unit ::: - **Price per unit**: retail price customers pay - **Variable costs per unit:** Cost of Goods Sold (COGS)[^1] + any other variable costs per unit [^1]: Material and production labour costs for producing a unit of product, often represented in **percentage terms,** e.g., a COGS of 60% means the costs are 60% of retail prices. An iPhone with a retail price of £1,000 and a COGS of 30% means the COGS is £300. ::: {.content-visible when-format="pdf"} ## Compute BEQ: Formula ::: This gives the formula for BEQ: ::: {.callout-note icon="false"} ### Definition BEQ = Marketing Expenditure / Contribution Margin Per Unit ::: ## Break-Even Quantity: Steps and Decision Rule - Steps to conduct break-even analysis - *Step 1*: Compute the BEQ based on the product's price and cost structure. This is the minimum quantity the company needs to sell to cover the costs of the marketing campaign. - *Step 2*: Evaluate whether the campaign can generate an incremental quantity larger than the BEQ - The decision rule - If the incremental sales quantity > BEQ, the company makes a profit, so the campaign should be accepted; otherwise, it should be rejected. # Case Study: Profitability Analysis for Apple Inc ## Background ::: columns ::: {.column width="50%"} ```{r} #| echo: false #| fig-align: 'center' knitr::include_graphics("images/Week 1/iphone17.png") ``` ::: ::: {.column width="50%"} Tom, a senior marketing manager at Apple UK, is looking to launch a series of marketing campaigns to promote the just-released iPhone 17 series. Tom is a proud graduate of the UCL MSc BA programme in 2020. He remembers from the Marketing Analytics module that break-even analysis helps to evaluate different types of marketing decisions. ::: ::: ::: {.content-hidden when-format="beamer"} ```{r} price <- 799 # retail price of iPhone in £ quantity <- 10 # sales quantity in million units endorsement_fee <- 100 # endorsement fee in million pounds endorsement_sales_increase <- 0.025 # sales increase percentage due to endorsement COGS <- 0.47 # cost of goods sold; 47% of retail price, i.e., 47% of £799 RD_costs <- 100 # R&D costs in million pounds monthly_sales_increase_1stmonth <- 0.003 # sales increase percentage in the first month monthly_sales_increase_after <- 0.002 # sales increase percentage in the following months WACC <- 0.1 # weighted average cost of capital ``` ::: **Case objectives:** - Practise situation analysis and compare with Uber's case - Practise how to conduct break-even analyses for a marketing campaign - Practise R basic computations and vector operations ## Apple Inc: Key Information **From the case:** The marketing analytics team at Apple Inc had applied sales forecasting models to historical sales data and predicted that sales this year would reach **`r quantity`** million units at the retail price of **£`r price`**, without any additional marketing activities. The team had also collected information on the Cost of Goods Sold of the Apple 17, which is **`r COGS *100`%**. The Research and Development (R&D) costs for the iPhone 17 are **`r RD_costs`** million pounds. - Open the .qmd answer sheet downloaded from Moodle for Week 1, and let's solve this case using the R basics we have learned! - **Question 1 (after class):** Conduct a 5C analysis for Apple Inc. and compare it with Uber's case. ## Apple Inc: BEA Question 2 - **Question 2:** Compute the contribution margin - Do we need to consider R&D costs? ::: {.content-hidden when-format="beamer"} ```{r} contribution_margin <- (1 - COGS) * price contribution_margin ``` ::: ## Sunk Costs and Sunk Costs Fallacy - **Sunk costs** are costs that have already been incurred in the past and cannot be recovered. They should **not** be considered when making decisions. - However, behavioural economics research shows that people often fall victim to the **sunk cost fallacy**, where they consider sunk costs in their decision-making instead of focusing on future costs and benefits. - When making decisions, you should focus only on future costs and benefits. In our case, the R&D costs are sunk costs and should not be considered in the break-even analysis. ## Apple Inc: BEA Question 3 - **Question 3**: Based on the information at hand, should Tom approve the influencer marketing plan? # Net Present Value ## Definition of NPV - When the effect of the marketing campaign is expected to have a long-term effect or **when the time value of money is an important consideration**, we need to take the future into account. ::: {.callout-note icon="false"} ### Definition Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. ::: ## Formula of NPV $$ N P V=-I_{0}+\frac{CF_{1}}{(1+k)}+\frac{C F_{2}}{(1+k)^{2}}+\cdots+\frac{C F_{n}}{(1+k)^{n}} $$ - $I_{0}$ is the initial marketing investment/expense - $C F_{n}$ is the **incremental** profit in period $n$: it must be the additional profit generated by the marketing campaign - $k$ (sometimes $r$ or $i$) is the discount rate, which reflects the value of time: £1 today is worth $£1 * (1+k)$ in the next period. - The decision rule - If NPV > 0, the marketing campaign adds value to the company, so it should be accepted. - If NPV < 0, the marketing campaign will decrease the company's value, so it should be rejected. ## Apple Inc: NPV Influencer Marketing I **Question 4:** Based on the information at hand, should Tom approve the influencer marketing plan based on the Net Present Value method? 1. Compute the sequence of monthly cash flows - Generate a sequence of incremental sales for 12 months (a vector with 12 elements) - Hint: use `rep()`, `c()`, and vector element-wise multiplication ::: {.content-hidden when-format="beamer"} ```{r} monthly_sales_increase_1stmonth <- 0.003 monthly_sales_increase_after <- 0.002 # incremental profit each month monthly_incremental_sales <- c( monthly_sales_increase_1stmonth, rep(monthly_sales_increase_after, 11) ) CF <- monthly_incremental_sales * quantity * contribution_margin ``` ::: The resulting monthly CFs are: `r CF` ## Apple Inc: NPV Influencer Marketing II 2. Compute the sequence of discount factors - Generate a sequence of WACC for 12 months (a vector with 12 elements) - Generate a sequence of discount rate for 12 months (a vector with 12 elements) - Hint: use `seq()` to generate geometric sequence with patterns ::: {.content-hidden when-format="beamer"} ```{r} monthly_WACC <- 0.1 / 12 # this is the discount rate discount_factor <- (1 / (1 + monthly_WACC))^c(1:12) # this is the discount factor ``` ::: The resulting monthly discount factors are: `r discount_factor` ## Apple Inc: NPV Influencer Marketing III 3. Compute the NPV - Generate a sequence of discounted CFs for 12 months - Sum up all discounted CFs across the 12 months using `sum()` - Subtract endorsement fee from the sum to get NPV ::: {.content-hidden when-format="beamer"} ```{r} NetPresentValue <- sum(CF * discount_factor) - endorsement_fee ``` ::: - The NPV is `r NetPresentValue` ## After-class - Review the coding practice from today’s class and ensure you understand how to calculate NPV in R. Complete the R coding exercise for Week 1, and feel free to bring any questions to next week's class.