Break-Even Analysis Example

Scenario

A company produces and sells a product for $20 per unit. the fixed costs(FC) are $5,000, and the variable cost(VC) per unit is 10. ### Formulas: 1. Total Revenue(TR) = Price×Quantity sold \[TR=P\times Q\] 2. Total Cost(TC) = Fixed + (Variable Cost×Quantity sold) \[TC=FC+(VC\times Q)\] 3. Break-even point(BEP) in units: \[BEP=\frac{FC}{P-VC}\] Calculating the Break-Even Point

# Import libraries
library(mosaic)
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library(mosaicCalc)
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library(ggplot2)
library(dplyr)
library(Matrix)
# Define given values 
price_per_unit <- 20
fixed_costs <- 5000
variable_cost_per_unit <- 10
break_even_units<- fixed_costs/(price_per_unit-variable_cost_per_unit)
# Display result
break_even_units
## [1] 500

So, the company needs to sell **500 units to break even. ## Break-Even Table {r} # Create table for different quantity values quantity <- seq(0,1000,100) total_revenue <- price_per_unitquantity total_cost <- fixed_costs+(variable_cost_per_unitquantity) profit_loss <- total_revenue-total_cost # Create a data frame data.frame(Quantity=quantity, Total_Revenue=total_revenue, Total_Cost=total_cost, Profit_Loss=profit_loss) At 500 units, TR=TC, meaning no profit, no loss (break-even-point). Beyond 500 units, the company starts making a profit. # create graphic — title: “Break-Even Analysis Example” output: html_document —

knitr::opts_chunk$set(echo = TRUE, error = TRUE) ## Scenario A company produces and sells a product for $20 per unit. The fixed costs (FC) are $5,000, and the variable cost (VC) per unit is $10.

Formulas

  1. Total Revenue (TR) = Price per unit × Quantity sold  \[ TR = P \times Q \]

  2. Total Cost (TC) = Fixed Cost + (Variable Cost × Quantity sold)  \[ TC = FC + (VC \times Q) \]

  3. Break-even point (BEP) in units: \[ BEP = \frac{FC}{P - VC} \]

Calculating the Break-Even Point

Define given values

price_per_unit <- 20 fixed_costs <- 5000 variable_cost_per_unit <- 10

Compute Break-Even Point (BEP)

break_even_units <- fixed_costs / (price_per_unit - variable_cost_per_unit)

Display result

break_even_units So, the company needs to sell 500 units to break even.

Break-Even Table

Create a table for different quantity values

quantity <- seq(0, 1000, 100) total_revenue <- price_per_unit * quantity total_cost <- fixed_costs + (variable_cost_per_unit * quantity) profit_loss <- total_revenue - total_cost library(ggplot2)

Define parameters

price_per_unit <- 20 fixed_costs <- 5000 variable_cost_per_unit <- 10

Create a table for different quantity values

quantity <- seq(0, 1000, 100) total_revenue <- price_per_unit * quantity total_cost <- fixed_costs + (variable_cost_per_unit * quantity)

{r} # Create a data frame data <- data.frame(Quantity = quantity, Total_Revenue = total_revenue, Total_Cost = total_cost)

Create ggplot object

p <- ggplot(data, aes(x = Quantity)) + geom_line(aes(y = Total_Cost, color = “Total Cost”), size = 1) + geom_line(aes(y = Total_Revenue, color = “Total Revenue”), size = 1) + geom_vline(xintercept = fixed_costs / (price_per_unit - variable_cost_per_unit), linetype = “dashed”, color = “red”) + labs(title = “Break-Even Analysis”, x = “Quantity”, y = “Amount ($)”) + scale_color_manual(values = c(“Total Cost” = “red”, “Total Revenue” = “cyan”)) + theme_minimal()