Chapter 13 In class - 13-21(20 min Cost-plus target return...

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Mathematics for Machine Technology
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Chapter 3 / Exercise 1
Mathematics for Machine Technology
Peterson/Smith
Expert Verified
13-21(20 min.)Cost-plus target return on investment pricing.John Branch is the managing partner of a business that has just finished building a 60-roommotel. Branch anticipates that he will rent these rooms for 16,000 nights next year (or 16,000room-nights). All rooms are similar and will rent for the same price. Branch estimates thefollowing operating costs for next year:The capital invested in the motel is $1,000,000. The partnership’s target return on investment is20%. Branch expects demand for rooms to be uniform throughout the year. He plans to price therooms at full cost plus a markup on full cost to earn the target return on investment.Required:1.What price should Branch charge for a room-night? What is the markup as a percentage ofthe full cost of a room-night?2.Branch’s market research indicates that if the price of a room-night determined inrequirement 1 is reduced by 10%, the expected number of room-nights Branch could rentwould increase by 10%. Should Branch reduce prices by 10%? Show your calculations.SOLUTION1.Target operating income = target return on investment invested capitalTarget operating income (20% of $1,000,000)$200,000Total fixed costs340,000Target contribution margin$540,000Target contribution per room-night, ($540,000 ÷ 16,000) $33.75Add variable costs per room-night4.00Price to be charged per room-night$37.75ProofTotal room revenues ($37.75 16,000 room-nights)$604,000Total costs:Variable costs ($4 16,000)$ 64,000Fixed costs340,000Total costs404,000
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Mathematics for Machine Technology
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Chapter 3 / Exercise 1
Mathematics for Machine Technology
Peterson/Smith
Expert Verified
Operating income$200,000The full cost of a room = variable cost per room + fixed cost per roomThe full cost of a room = $4 + ($340,000 ÷ 16,000) = $4 + $21.25 = $25.25Markup per room = Rental price per room – Full cost of a room= $37.75 – $25.25 = $12.50Markup percentage as a fraction of full cost = $12.50 ÷ $25.25 = 49.5%2.If price is reduced by 10%, the number of rooms Branch could rent would increase by 10%.The new price per room would be 90% of $37.75 $ 33.975The number of rooms Branch expects to rent is 110% of 16,000 17,600The contribution margin per room would be $33.975 – $4$ 29.975Contribution margin ($29.975 17,600)$527,560Because the contribution margin of $527,560 at the reduced price of $33.975 is less thanthe contribution margin of $540,000 at a price of $37.75, Branch should not reduce the price ofthe rooms. Note that the fixed costs of $340,000 will be the same under the $37.75 and the$33.975 price alternatives and hence, are irrelevant to the analysis.

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