Calculating breakeven sales and sales to earn a target profit;preparing a contribution margin income statement

Famous Productions performs London shows. The average show sells 1,000 ticketsat \(60 per ticket. There are 175 shows a year. No additional shows can be held as thetheater is also used by other production companies. The average show has a cast of60, each earning a net average of \)320 per show. The cast is paid after each show. Theother variable cost is a program-printing cost of \(8 per guest. Annual fixed costs total\)459,200.

Requirements

1. Compute revenue and variable costs for each show.

2. Use the equation approach to compute the number of shows Famous Productionsmust perform each year to break even.

3. Use the contribution margin ratio approach to compute the number of showsneeded each year to earn a profit of $4,264,000. Is this profit goal realistic? Giveyour reasoning.

4. Prepare Famous Productions’s contribution margin income statement for 175shows performed in 2018. Report only two categories of costs: variable andfixed.

Step by step solution

01

Step 1:1. Computation of revenue for each show-

$\begin{array}{rcl}\mathbf{Sales}\mathbf{}\mathbf{revenue}\mathbf{}\mathbf{per}\mathbf{}\mathbf{show}& \mathbf{=}& \mathbf{Tickets}\mathbf{\times }\mathbf{Selling}\mathbf{}\mathbf{price}\mathbf{}\mathbf{per}\mathbf{}\mathbf{ticket}\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{\$}\mathbf{60}\\ & \mathbf{=}& \mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}\end{array}$

02

1. Computation of variable cost for each show-

$\begin{array}{rcl}\mathbf{Variable}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{of}\mathbf{}\mathbf{performance}& \mathbf{=}& \mathbf{Cast}\mathbf{\times }\mathbf{Net}\mathbf{}\mathbf{average}\mathbf{}\mathbf{per}\mathbf{}\mathbf{show}\\ & \mathbf{=}& \mathbf{\$}\mathbf{60}\mathbf{\times }\mathbf{320}\\ & \mathbf{=}& \mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{200}\end{array}$

$\begin{array}{rcl}\mathbf{Variable}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{of}\mathbf{}\mathbf{ticket}\mathbf{}\mathbf{printing}& \mathbf{=}& \mathbf{Tickets}\mathbf{\times }\mathbf{Program}\mathbf{}\mathbf{printing}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{per}\mathbf{}\mathbf{guest}\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{\$}\mathbf{8}\\ & \mathbf{=}& \mathbf{\$}\mathbf{8000}\end{array}$

$\begin{array}{rcl}\mathbf{Total}\mathbf{}\mathbf{variable}\mathbf{}\mathbf{cost}& \mathbf{=}& \mathbf{Variable}\mathbf{}\mathbf{Cost}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Performance}\mathbf{+}\mathbf{Variable}\mathbf{}\mathbf{Cost}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Printing}\\ & \mathbf{=}& \mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{200}\mathbf{+}\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{27}\mathbf{,}\mathbf{200}\end{array}$

03

Step 3:2.Computation of number of show in Break even point-

Let number of show be ‘x’

$\begin{array}{rcl}\mathbf{Target}\mathbf{}\mathbf{profit}& \mathbf{=}& \mathbf{Revenue}\mathbf{-}\mathbf{Variable}\mathbf{}\mathbf{cost}\mathbf{-}\mathbf{Fixed}\mathbf{}\mathbf{cost}\\ \mathbf{\$}\mathbf{0}& \mathbf{=}& \left(\$60,000\times x\right)\mathbf{-}\left(\$27,200\times x\right)\mathbf{-}\mathbf{\$}\mathbf{459}\mathbf{,}\mathbf{200}\\ \mathbf{\$}\mathbf{32}\mathbf{,}\mathbf{800}\mathbf{\times }\mathbf{x}& \mathbf{=}& \mathbf{\$}\mathbf{459}\mathbf{,}\mathbf{200}\\ \mathbf{x}& \mathbf{=}& \mathbf{14}\end{array}$

04

Step 4:3 Computation of contribution margin ratio-

$\begin{array}{rcl}\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{ratio}& \mathbf{=}& \frac{\mathbf{Sales}\mathbf{-}\mathbf{Revenue}}{\mathbf{Sales}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{27}\mathbf{,}\mathbf{200}}{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{32}\mathbf{,}\mathbf{800}}{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}\\ & \mathbf{=}& \mathbf{54}\mathbf{.}\mathbf{67}\mathbf{\%}\end{array}$

05

3. Computation of Break even point-

$\begin{array}{rcl}\mathbf{Break}\mathbf{}\mathbf{even}\mathbf{}\mathbf{Sales}& \mathbf{=}& \frac{\mathbf{Fixed}\mathbf{}\mathbf{cost}\mathbf{+}\mathbf{Target}\mathbf{}\mathbf{profit}}{\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{ratio}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{459}\mathbf{,}\mathbf{200}\mathbf{+}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{264}\mathbf{,}\mathbf{000}}{\mathbf{54}\mathbf{.}\mathbf{67}\mathbf{\%}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{639}\mathbf{,}\mathbf{473}\end{array}$

$\begin{array}{rcl}\mathbf{Break}\mathbf{}\mathbf{even}\mathbf{}\mathbf{point}\left(\mathrm{in}\mathrm{show}\right)& \mathbf{=}& \frac{\mathbf{Break}\mathbf{}\mathbf{even}\mathbf{}\mathbf{point}}{\mathbf{Revenue}\mathbf{}\mathbf{per}\mathbf{}\mathbf{show}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{639}\mathbf{,}\mathbf{473}}{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}\\ & \mathbf{=}& \mathbf{144}\mathbf{}\mathbf{shows}\end{array}$

06

Step 6:4.Contribution margin income statement-

Contribution margin Income Statement

For the year ended 2016

Revenue	$10,500,000
Less: Variable cost	($4,760,000)
Contribution	$5,740,000
Less: Fixed Costs	($459,200)
Net Operating Profit	$5,280,800

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