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

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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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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.