Question

CVP Analysis with Taxes (Single Product). Riviera Incorporated produces flat panel televisions. The company has annual fixed costs totaling $10,000,000 and variable costs of $600 per unit. Each unit of product is sold for $1,000. Riviera expects to sell 70,000 units this year (this is the same data as the previous problem). Assume a tax rate of 30 percent. Required: Round all calculations to the nearest dollar and nearest unit where appropriate. a. How many units must be sold to earn an annual profit of $2,000,000 after taxes? b. What amount of sales dollars is required to earn an annual profit of $500,000 after taxes? c. Refer to requirement a. What would happen to the number of units required to earn $2,000,000 in operating profit if the company were a non-profit organization that did not incur income taxes? Explain.

Answer 1

Ans.

Riviera Incorporation
Income Statement
Particulars		Amt.($)
Sales (70,000 @1,000 p.u.)		$   70,000,000
Less:
Variable cost @ 600 p.u.		42,000,000
Contribution Margin		28,000,000
Less: Fixed Cost		10,000,000
Earning before Tax		18,000,000
Less: Tax @30%		5,400,000
Net Profit		$   12,600,000

P/V Ratio =	(Contribution margin/Sales) x 100
=	(28,000,000/70,000,000) x 100
=	40%

Ans.(a)	Units to be sold to earn an annual profit of $2,000,000 after taxes is :
	Profit=	{ (Sales x P/V ratio) - Fixed Cost } x (1-Tax rate)
	Then,
	Sales ($) =	{ [Profit / (1-Tax rate)] + Fixed Cost } / P/V ratio
	=	{ [2,000,000 / (1 - .30) ]+ 10,000,000)/40%
	=	{ 2,857,143 + 10,000,000 }/40%
	=	12,857,143/40%
	=	32,142,858
	Sales (in units) =	Sales / Sale Price p.u.
	=	$ 32,142,858 / $ 1000
	=	32,143
Ans.(b)	Amount of sales to earn annual profit of $500,000 after taxes is :
	Profit =	{ (Sales x P/V ratio) - Fixed Cost } x (1-Tax rate)
	Then,
	Sales ($) =	{ [Profit / (1-Tax rate)] + Fixed Cost } / P/V ratio
	=	{ [500,000 / (1 - .30) ]+ 10,000,000)/40%
	=	{ 714,286 + 10,000,000 }/40%
	=	10,714,286/40%
	=	26,785,715
Ans.(c)	Number unitsrequired to earn $2,000,000 in operating profit if the if the company were a non profit organization that did not incur income taxes :
	Profit =	{ (Sales x P/V ratio) - Fixed Cost }
	Then,
	Sales ($) =	{ [Profit + Fixed Cost } / P/V ratio
	=	{ 2,000,000 + 10,000,000)/40%
	=	12,000,000 /40%
	=	$ 30,000,000
	Sales (in units) =	Sales / Sale Price p.u.
	=	$ 30,000,000 / $ 1000
	=	30,000