Chapter 7 Solutions to Problems. 1. Selling price - Variable cost per unit = Contribution margin \$ \$8.00 = \$4.00

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1 Problem 1: Solution 1. Selling price - Variable cost per unit = Contribution margin \$ \$8.00 = \$4.00 Contribution margin / Selling price = Contribution margin ratio \$4.00 \$12.00 = Selling price - Variable cost per unit = Contribution margin \$ \$7.75 = \$3.25 Contribution margin Selling price = Contribution margin ratio \$3.25 / \$11.00 = Total fixed cost (Selling price - Variable cost per unit) = Units sold \$ (\$ \$7.75) = 62 lunch covers Problem 2: Solution 1. Total fixed cost (Selling price - Variable cost per unit) = Units sold at breakeven \$100,000 (\$80 - \$15) = 1,539 rooms 2. Rooms sold to break even Rooms sold per day = Day breakeven occurs 1, = or the 26th day 3. Annual fixed costs increase 12 months = Monthly fixed costs increase \$72, = \$6,000 Total fixed costs (Selling price - Variable cost per unit) = Units sold at breakeven \$106,000 (\$80 - \$12) = 1,559 rooms Units sold at breakeven Selling price = Breakeven revenues 1,559 \$80 = \$124,720

2 Problem 3: Solution Transportation costs are fixed only on a daily basis. Treat this as a variable cost at \$.02 per glass. 1. Cost per drink + Other variable costs = Total variable cost per unit \$.20 + \$.05 + \$.02 = \$.27 Selling price - Variable cost per unit = Contribution margin \$.75 - \$.27 = \$ Total fixed cost (Selling price - Variable cost per unit) = Units sold at breakeven \$750 (\$.75 - \$.27) = 1,563 lemonades 3. Lemonades sold to break even Lemonades sold per day = Day breakeven occurs 1, = or the 16th day or Monday, June 22. Problem 4: Solution 1.Mixed Low Month High Month Variable Costs Variable Costs Fixed Costs 60% Occ. 80% Occ. per 1% Occ. Per Room Costs Repairs \$3,000 \$3,500 \$25 \$0.83 \$1,500 Utilities \$4,000 \$5,000 \$50 \$1.67 \$1,000 Variable cost per room: \$20 + \$.83 + \$1.67 = \$ Monthly fixed costs: \$100,000 + \$1,500 + \$1,000 = \$102, Day breakeven occurs = Rooms sold to break even Rooms sold per day 25 = X 75 X = 1,875 rooms sold to break even (Total fixed costs Units sold) + Variable cost per unit = Selling price at breakeven (\$102,500 1,875) + \$22.50 = \$77.17

3 Problem 5: Solution 1. CMR for the rooms operation: Rooms CMR = 1 variable cost percentage = 1.25 = CMR for the food operation: Food CMR = 1 variable cost percentage = 1.6 =.4 3. Weighted average CMR: Weighted avg. CMR = (rooms sales mix % rooms CMR)+ (food sales mix % food CMR) = (.65.75) + (.35.4) = Breakeven point: BE = Fixed costs weighted average CMR = \$300, = \$478, Revenue when net income equals \$100,000: Pretax income = net income (1 - tax rate) = \$100,000 (1 -.2) = \$125,000 Revenue = (FC + Pretax income) weighted avg. CMR = (\$300,000 + \$125,000).6275 = \$677, Problem 6: Solution 1. Fixed costs = (1 Variable cost percentage) Sales 550,000 =.8 Sales Sales = 687, Required return = investment ROI = 1,500,000.2 = 300,000

4 Problem 7: Solutions 1. a. Breakeven Point CMRw = ((60/100) ((60-12)/60)) + ((40/100) ((40-20)/40)) CMRw = 0.68 R = \$410,000/.68 Breakeven Point = \$602, b. NI Variable Expense % Rooms = \$120,000/\$600,000 = 0.2 Variable Expense % Coffee Shop = \$200,000/\$400,000 = 0.5 Calculations Rooms Sales \$720,000.6(1,200,000) Coffee Shop Sales 480,000.4(1,200,000) Variable Expense Rooms 144,000.2(720,000) Variable Expense C.S. 240,000.5(480,000) Total Contrib. Margin 816,000 Fixed Costs: Rooms 50,000 Coffee Shop 60,000 Overhead 300,000 Pre-tax earnings 406,000 Taxes 81,200.2(406,000) Net Income \$324,800 c. Net Income \$200,000 Fixed Costs: Rooms 50,000 Coffee Shop 60,000 Overhead 300,000 \$610,000 NI + Fixed costs = annual revenue CMRw 610,000/0.68 = \$ 897,058.82

5 Problem 7: Solutions (continued) 2. a. Breakeven Point CMRw = ((75/100) (.8) + ((25/100 (.5)) CMRw =.725 R = \$410,000/0.725 Breakeven Point = \$565, b. Net Income Calculations Total Revenue \$1,200,000 Fixed Costs: Rooms 50,000 Coffee Shop 60,000 Overhead 300,000 Variable Costs: Rooms 180,000.2(.75 1,200,000) Coffee Shop 150,000.5(.25 1,200,000) Pre-tax earnings 460,000 Taxes 92,000.2(460,000) Net Income \$368,000 c. Net Income \$200,000 Fixed Costs: Rooms 50,000 Coffee Shop 60,000 Overhead 300,000 \$610,000 (NI + Fixed costs)/cmrw = annual revenue \$610,000/0.725 = \$841,379.31

6 Problem 8: Solution 1. Revenue at breakeven point: B = F = 20,000 = 1,000 rooms CM 20 Revenue = rooms sold selling price = 1,000 \$30 = \$30, Margin of safety: Stated revenues \$450,000 Breakeven (\$30,000 12) 360,000 Margin of safety revenue \$ 90,000 Margin of safety rooms: \$90,000/30 = 3,000 rooms 3. Rooms sold when pretax profit is \$100,000 x = F + I b = \$240,000 + \$100,000 = 17,000 CM \$20 4. Paid occupancy percentage: rooms sold = 17,000 = 93.15% rooms available Problem 9: Solution Part 1 Revenue Var. Cost Dept. Income Rooms \$2,500,000 \$ 750,000 \$1,750,000 Coffee Shop 750, , ,000 Restaurant 1,200, , ,000 \$4,450,000 \$1,800,000 \$2,650,000 CMR w = Total Dept. Income = 2,650,000 = 59.55% Total Sales 4,450,000 Part 2 (I n + F)/CMR w = Sales \$500,000 + \$1,000,000 = \$2,518, Part 3 I b = I n /(1 t) = \$500,000 = \$714, (I b + F)/CMR w = Sales \$1,000,000 + \$714, = \$2,878,

7 Problem 10: Solution Required annual profit = ROI(investment) =.18(\$1,500,000)= \$270,000 Pretax income (I b ) = I n /(1 t) = \$270,000/0.7 = \$385, CMR w =.8(.76) +.2(.55) = =.718 Revenue = (F + I b )/CMR w = \$240,000 + \$385, = \$871, Problem 11: Solution 1. Total Revenues - Total Variable Costs = Contribution Margin \$2,000,000 - \$700,000 = \$1,300,000 Contribution Margin Percentage \$1,300,000 \$2,000,000 = 0.65 Breakeven Point \$1,000, = \$1,538, \$520, = \$1,155,556 Problem 12: Solution 1) CMR (\$60 \$20)/\$60 = ) Breakeven Point \$20, = \$29, \$29, \$60 = 500 rooms 3) Total Revenue Net Income \$10, Pretax Income \$10,000 (1 -.2) = \$12, Total Revenue (\$12,500 + \$20,000) = \$48, ) June breakeven point Total Revenue \$48, Rooms sold per day (\$48, ) 30 = Daily Revenue \$ = \$1, Breakeven point \$29, Days to break even \$29, / \$1, = The Meyer Motel will break even on: June 19th 5) Increase in ADR Revised variable costs \$ = \$30 To maintain the CM of \$40, ADR must increase by: \$10

8 Problem 13: Solution 1. Mackinaw Hotel Minier Hotel B = F \$1,200,000 = \$2,000,000 \$1,000,000 = \$2,000,000 CMR w Profit-volume graph: 3. The Mackinaw Hotel is riskier because it has a higher level of fixed costs and a lower variable cost percentage than the Minier Hotel. With zero sales, the Mackinaw Hotel would lose \$1,200,000 (its fixed costs). With zero sales, the Minier Hotel would lose only \$1,000,000.

9 Problem 14: Solution 1. Level of sales under each lease option Var.: X =.3X +.2X +.1X +.06X + \$100,000 = \$294, Mixed: X =.3X +.2X +.1X +.02X + 12(\$1,500) + \$100,000 = \$310,526 Fixed: X =.3X +.2X +.1X + 12(2,500) + \$100,000 = \$325, Net Income Var.: \$700,000 ((.66 \$700,000) + \$100,000)) NI = \$138,000 Mixed: \$700,000 (.62(\$700,000) + 12(\$1,500) + \$100,000) NI = \$148,000 Fixed: \$700,000 (.6(\$700,000) + 12(\$2,500) + \$100,000) NI = \$150, Recommendation Var.: \$400,000 (.66(\$400,000) + \$100,000) NI = \$36,000 Mixed: \$400,000 (.62(\$400,000) + 12(\$1,500) + \$100,000) NI = \$34,000 Fixed: \$400,000 (.6(\$400,000) + 12(\$2,500) + \$100,000) NI = \$30,000 The variable lease is the better option at the given level of sales.

10 Problem 15: Solution 1. Breakeven point for the Hazen: BE = (\$300,000 + \$800,000).675 = \$1,629,630 CMR w = (\$2,000,000 \$ 500,000 \$150,000) \$2,000,000 = If the sales mix changes, what is the breakeven point? Rev. CMR w = (((\$1,500,000 \$200,000 \$150,000) \$1,500,000).6) + (((\$500,000 \$300,000) \$500,000).4) =.62 Breakeven = \$1,100, = \$1,774, What is the level of revenue where the Hazen's cash flow is zero? Rev = (cash flow + FC NCE sale of cap stock + NECD)/CMR w = 0 + \$1,100,000 - \$500,000 + \$50,000 - \$100,000)/.675 = \$814, Note: this is based on the problem independent of part How many meals must be sold to make \$200 in profit based on the proposal? Increase in pretax profits = \$200 (1.4) = \$333 SP - variable costs per cover = CM CM = \$12 - (\$12.6) = \$4.80 Number of meals = ( ) \$4.80 = , therefore, 132

11 Problem 16: Solution 1. Breakeven point: B = F = \$1,000, = \$1,538, CMR w Revised breakeven point: Revised CMR w = =.45 B = F = \$520,000 = \$1,155, CMR w Increase in sales required to cover an increase in variable costs: Revised revenue = I b + F Revised CMR w = CMR w =.615 = \$300,000 + \$1,000, = \$2,113, Original revenue = \$2,000, Increase in revenue = \$113, Percentage increase = 5.69% in sales 4. Room sales when net income equals \$300,000: Revenue = I b + F I b = I n CMR w 1 - t = \$400,000 + \$1,000,000 = \$300, = \$1,400,000 = \$400, = \$2,153, Room sales =.75(total sales) =.75(\$2,153,846.15) = \$1,615,384.62

12 Problem 17: Solution Part 1 Revenue = (I b + F)/CMR w I b = I n /(1 t) = \$40,000 = \$53, CMR w = Contribution Margin = \$100,000 = 71.43% Total Revenue \$140,000 Revenue = \$53,333 + \$80,000 = \$186, Part 2 CF b = CF d + NECD - NCE 1 - t - NECD + NCE = \$20,000 + \$5,000 - \$20,000 - \$5,000 + \$20, = \$5,000 + \$15, = \$21, R = CF b + F - NCE + NECD CMR w = \$21, \$80,000 - \$20,000 + \$5, = \$121, *depreciation **reduction of mortgage: mortgage payment \$15,000 less: interest exp. 10,000 \$ 5,000 Note: The cash flow calculation assumes income taxes are based on cash flows.

13 Problem 18: Solution 1. CMR w = (\$7,600,000 - \$3,100,000) \$7,600,000 = 59.21% 2. Breakeven point = \$4,000, = \$6,755, Food sales when the Allen Hotel earns \$500,000: Required pretax income = \$500,000 (1 -.2) = \$625,000 Revenue = Fixed costs CMR w = (\$4,000,000 + \$625,000).5921 = \$7,811, Food revenue = Total rev. (% of food rev. to total rev.) = \$7,811, (\$2,000,000 \$7,600,000) = \$2,055, Total revenue when AH earns pretax cash flow of \$500,000: Rev. = (CF + FC - NCE + NECD) CMR w = (800, ,000, , ,000).5921 = \$7,431, Revised CMR w = (\$5,000,000 - \$1,950,000).6 + (\$2,000,000 - \$800,000).3 + (\$400,000 - \$150,000).05 = or % Problem 19: Solution 1. Contribution Margin Ratio 5,000,000-1,000,000 = 0.8 5,000, Weighted Ave. CMR 8,500,000-2,700,000 = ,500, Breakeven Point 3,600,000 = \$5,275, R = F / CMR w Room sales when NI= 1.5M Ib = In 1,500,000 = \$2,062,500 (1 - t) (1-6/22)

14 Problem 19: Solution (continued) R = (Ib + F) (3,600, ,062,500) = \$8,297, CMRw Room Sales = R Room Sales 8,297, ,000,000 \$4,881, Problem 20: Solution Total Sales 8,500,000 Part 1 Food department's CMR: \$50,000 \$200,000 = 25% Part 2 CMR w : \$401,000 \$705,000 = 56.88% Part 3 Breakeven point: \$151, = \$265, Part 4 Increase in room sales to yield a \$30,000 increase in net income: I n \$30,000 I b = = = \$60, CMR rooms = \$350,000 \$500,000=.7 Increased room sales = I b \$60,000 = = \$85, CMR rooms.7 Part 5 Stable sales to cover increase in fixed costs of \$500: CMR stables = \$1,000 =.2 \$5,000 Increase in stable sales = F = \$500 = \$2,500 CMR stables.20 Part 6 Total revenue to cover increase in fixed costs of \$1,500: Increase in total sales = F = \$1,500 = \$2, CMR w.5688

15 Problem 21: Solution 1. (\$7,000,000 - \$2,850,000) = ,000, (\$200,000 + \$400,000 + \$100,000 + \$100,000 + \$2,800,000) = \$6,071, (\$2,000,000 - \$1,000,000 + \$200,000 + \$100,000 + \$200,000 + \$400,000 + \$100,000 + \$100,000 + \$2,800,000) = \$8,264, CMR = (\$300,000 - \$150,000) =.5 +.1* =.6 \$300,000 *Management Fee (\$2,000 + \$4,000 + \$3,143**) = \$22, **\$2,000/( ) = \$3, CM Weight CMR Rooms (\$4,000,000 - \$800,000) = % 0.4 \$4,000,000 Food (\$2,400,000 - \$1,000,000) = % \$2,400,000 Other (\$300,000 - \$200,000) = % \$300,000 Gift (\$300,000 - \$150,000) = % 0.05 Shop \$300,000 Problem 22: Solution CMR Management Fee -0.1 CMR = Expected net income during June. Expected number of room sales: = 2,400 Sales 2,400 \$35 \$84,000 Variable costs 2,400 \$9 21,600 Monthly fixed costs 21,500 Pre-tax income 40,900 Income taxes 12,270 Net income \$28,630

16 Problem 22: Solution (continued) 2. Breakeven point in rooms sold in June \$21,500/\$26 = rooms, on June Net income expected to be earned during November. Expected number of room sales: = 2,100 Sales 2,100 \$35 \$73,500 Variable costs 2,100 \$10 21,000 Fixed costs 19,500 Pre-tax income 33,000 Income taxes 9,900 Net income \$23, Breakeven point during November: \$19,500/\$25 = 780 rooms, on November 12 Problem 23: Solution 1. (\$5,000,000 - \$1,000,000) = 0.8 \$5,000, (\$8,500,000 - \$2,700,000) = \$8,500, (\$1,000,000 + \$500,000 + \$100,000 + \$2,000,000) = \$5,275, Desired pretax income: \$1,500,000 = \$2,062, Total revenue: (\$2,062,706 + \$3,600,000) = \$8,298, Room sales: \$5,000,000 8,298,221 = \$4,881,307 \$8,500,000

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