# Solutions to Homework Problems for CVP! Cost Volume Profit by David Albrecht

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1 Solutions to Homework Problems for CVP! Cost Volume Profit by David Albrecht Solution to Problem #26 CVP analysis using CM per unit. The controller of Stardust Furniture Company has determined the following estimates for a new product: Sales price per unit \$175 Variable manufacturing cost per unit \$90 Variable sales cost per unit \$15 \$105 Fixed manufacturing costs \$310,000 Fixed sales costs \$40,000 \$350, Compute the projected break-even point in units. Prepare an income statement to prove your answer. SP*X! V*X! F = π \$70*X! \$350,000 = 0 X = \$350,000 \$70 X = 5,000 units Sales Revenue \$875,000 5,000*175 Variable costs \$525,000 5,000*105 Contribution margin \$350,000 5,000*70 Fixed cost \$350,000 Profit \$0 at the BE point, π = 0 2. Compute the number of units to be produced and sold to generate a before-tax profit of \$140,000. Prepare an income statement to prove your answer. \$70*X! \$350,000 = \$140,000 \$70*X = \$490,000 X = \$490,000 \$70 X = 7,000 units or, CM*ÎX = ªπ, given that X BE = 5,000 units \$70*ªX = \$140,000 ªX = \$140,000 \$70 ªX = 2,000 units X = 5, ,000 = 7,000 units 260

2 Sales Revenue \$1,225,000 7,000*175 Variable costs \$735,000 7,000*105 Contribution margin \$490,000 7,000*70 Fixed cost \$350,000 Profit \$140, Compute the number of units to be produced and sold to generate a before-tax profit of 10% of sales revenue. Prepare an income statement to prove your answer. \$70*X! \$350,000 = 0.10*(\$175*X) \$70*X! \$17.5*X = \$350,000 \$52.5*X = \$350,000 X = 6,667 units Sales Revenue \$1,166,667 6,667*175 Variable costs \$700,000 6,667*105 Contribution margin \$466,667 6,667*70 Fixed cost \$350,000 Profit \$116,667 1,166,667*10% 4. What is the profit at 10,000 units produced and sold above the break-even point? Prepare an income statement to prove your answer. CM*ÎX = ªπ, given that X BE = 5,000 units \$70*10,000= ªπ ªπ = \$700,000 Sales Revenue \$2,625,000 (5,000+10,000)*175 Variable costs \$1,575,000 15,000*105 Contribution margin \$1,050,000 15,000*70 Fixed cost \$350,000 Profit \$700, What is the amount of change in the before-tax profit going from 3,000 units below the breakeven point to 4,000 units above the break-even point? Change in profit from 2,000 (5,000! 3,000) units to 9,000 (5, ,000) The change in units is 7,000 = 9,000! 2,000 CM*ÎX = ªπ \$70*7,000 units = \$490,000 Proof: Profit at 2,000 units. \$70*2,000!\$350,000 =!210,000 Profit at 9,000 units: \$70*9,000!\$350,000 = +280, ,000! (!210,000) = + 490,

3 6. Stardust Furniture s average tax rate is 20%. Compute the number of units to be produced and sold to generate an after-tax profit of \$140,000. Prepare an income statement to prove your answer. (CM*X! F) = π (1) (CM*X! F)! (CM*X! F)*TR = ATNI (CM*X! F)*(1! TR) = ATNI (CM*X! F) = ATNI (1! TR) (2) π = ATNI (1! TR) substituting 1 into 2 π = \$140, π = \$175,000 70*X! \$350,000 = \$175,000 70*X = \$525,000 X = 7,500 Sales Revenue \$1,312,500 7,500*175 Variable costs \$787,500 7,500*105 Contribution margin \$525,000 7,500*70 Fixed cost \$350,000 Pre-tax profit (π) \$175,000 Tax \$ 35,000 After tax net income \$140, The tax rate is 20%. Compute the number of units to be produced and sold to generate an aftertax profit of \$100,000. Prepare a traditional/gross margin income statement to prove your answer. Proof coming later. 70*X! \$350,000 = \$100, *X = \$475,000 X = 6,

4 Solution to Problem #27 CVP analysis using CM per unit. The controller of Stardust Furniture Company has determined the following estimates for a new product: Sales price per unit \$71 Variable sales cost per unit \$32 Fixed manufacturing costs \$472,300 Required: 1. Compute the projected break-even point in units. Prepare an income statement to prove your answer. SP*X! V*X! F = π \$39*X! \$472,300 = 0 X = \$472,300 \$39 X = 12, units Sales Revenue \$859,828 12,110.26*71 Variable costs \$387,528 12,110.26*32 Contribution margin \$472,300 12,110.26*39 Fixed cost \$472,300 Profit \$0 at the BE point, π = 0 2. Compute the number of units to be produced and sold to generate a before-tax profit of \$58,500. Prepare an income statement to prove your answer. \$39*X! \$472,300 = \$58,500 \$39*X = \$530,800 X = \$530,800 \$39 X = 13, units or, CM*ÎX = ªπ, given that X BE = 12, units \$39*ªX = \$58,500 ªX = \$58,500 \$39 ªX = 1,500 units X = 12, ,500 = 13, units Sales Revenue \$966,328 13,610.26*71 Variable costs \$435,528 13,610.26*32 Contribution margin \$530,800 13,610.26*39 Fixed cost \$472,300 Profit \$58,

5 3. Compute the number of units to be produced and sold to generate a before-tax profit of 12% of sales revenue. Prepare an income statement to prove your answer. \$39*X! \$472,300 = 0.12*(\$71*X) \$39*X! \$8.52*X = \$472,300 \$30.48*X = \$472,300 X = 15, units Sales Revenue \$1,100,174 15,495.41*71 Variable costs \$495,853 15,495.41*32 Contribution margin \$604,321 15,495.41*39 Fixed cost \$472,300 Profit \$132,021 1,100,174*12% 4. What is the profit at 6,000 units produced and sold above the break-even point? Prepare an income statement to prove your answer. CM*ÎX = ªπ, given that X BE = 12, units \$39*6,000= ªπ ªπ = \$234,000 Or, (12, ,000)*39! 472,300 = 234,000 Sales Revenue \$1,285,828 (12, ,000)*71 Variable costs \$579,528 18,110.26*32 Contribution margin \$706,300 18,110.26*39 Fixed cost \$472,300 Profit \$234,

6 Solution to Problem #28 CVP analysis computing an indifference point. Under either process, the selling price for the product is \$20 per unit. h The first process requires fixed costs of \$120,000 and variable costs of \$15 per unit. h The second process requires fixed costs of \$960,000 and variable costs of \$8 per unit. 1. Calculate the break even point in units under the first process. (\$20! 15)*X = \$120,000 + \$0 \$5*X = \$120,000 X = \$120,000 \$5 X = 24,000 units 2. Calculate the break even point in units under the second process. (\$20! 8)*X = \$960,000 + \$0 \$12*X = \$960,000 X = \$960,000 \$12 X = 80,000 units 3. If production must take place, which process should be used if sales are projected to be 10,000 units? 25,000? 50,000? 160,000? 10,000 25,000 50, ,000 First (\$5*X! \$120,000)!\$70,000 +\$5,000 +\$130,000 +\$680,000 Second (\$12*X! \$960,000)!\$840,000!\$660,000!\$360,000 +\$960, At what volume is the company indifferent between the two methods? Prepare an income statement for each process at this volume level. Equating the profit equation for each process, \$5*X! \$120,000 = \$12*X! \$960,000 +\$960,000! \$120,000 = \$12*X! \$5*X +\$840,000 = \$7*X X = 120,000 units Sales Revenue \$2,400, ,000*20 \$2,400, ,000*20 Variable costs \$1,800, ,000*15 \$960, ,000*8 Contribution margin \$600, ,000*6 \$1,440, ,000*12 Fixed cost \$120,000 \$960,000 Profit \$480,000 \$480,

7 5. Identify which process should be used for all portions of the range from 0 units to 4 units. For 0 to 120,000 units, the first process is more profitable than the second. For 120,000 units to 4 units the second process is more profitable. Solution to Problem #29 CVP analysis computing an indifference point. Under all processes, the selling price for the product is \$25 per unit. h The first process requires fixed costs of \$35,000 and variable costs of \$21 per unit. h The second process requires fixed costs of \$145,000 and variable costs of \$18 per unit. h The third process requires fixed costs of \$1,200,000 and variable costs of \$10 per unit. 1. Calculate the break even point in units under the first process. (\$25! 21)*X = \$35,000 + \$0 \$4*X = \$35,000 X = \$35,000 \$4 X = 8,750 units 2. Calculate the break even point in units under the second process. (\$25! 18)*X = \$145,000 + \$0 \$7*X = \$145,000 X = \$145,000 \$7 X = 20,714 units 3. Calculate the break even point in units under the third process. (\$25! 10)*X = \$1,200,000 + \$0 \$15*X = \$1,200,000 X = \$1,200,000 \$15 X = 80,000 units 4. If production must take place, which process should be used if sales are projected to be 10,000 units? 25,000? 50,000? 100,000? 160,000? 10,000 25,000 50, , ,000 First (4*X! 35,000) +5, , , , ,000 Second (7*X! 145,000)!75, , , , ,000 Third (15*X! 1,200,000)!1,050,000!825,000!\$450, ,000 +1,200,

8 5. At what volume is the company indifferent between the first and second methods? first and third? second and third? Between first and second: \$4*X! \$35,000 = \$7*X! \$145,000 +\$145,000! \$35,000 = \$7*X! \$4*X +\$110,000 = \$3*X X = 36,667 units first is preferred below this, second is preferred above this Between first and third: \$4*X! \$35,000 = \$15*X! \$1,200,000 +\$1,200,000! \$35,000 = \$15*X! \$4*X +\$1,165,000 = \$11*X X = 105,909 units first is preferred below this, third is preferred above this Between second and third: \$7*X! \$145,000 = \$15*X! \$1,200,000 +\$1,200,000! \$145,000 = \$15*X! \$7*X +\$1,055,000 = \$8*X X = 131,875 units second is preferred below this, third is preferred above this 6. Please state which method is preferable for any volume? 0 < 1 st # 36,667 # 2 nd # 131,875 # 3 rd 267

9 Solution to Problem #30 CVP analysis break even point with changing cost structures. The Jones Company is contemplating a new product, to be sold for \$10 per unit. The projected cost structure varies depending on the relevant range. h For the range from 1 to 25,000 units, the cost structure for units produced and sold is expected to be \$6 per unit variable, \$200,000 fixed. h For the range above 25,000, the cost structure for units produced and sold is expected to be \$5 per unit variable Compute the projected break even point for the Jones Company. CM1*X + CM2*Y! F = π No break even at 25,000, so X=25,000 units 4*25, *Y! 200,000 = 0 4*25, *Y! 200,000 = 0 100, *Y = 200, *Y = 100,000 Y = 20,000 X + Y = 25, ,000 = 45,000 Sales Revenue \$450,000 45,000*10 Variable 6! \$150,000 25,000*6 Variable 5! \$100,000 20,000*5 Contribution margin \$200,000 Fixed cost! \$200,000 Profit \$0 268

10 Solution to Problem #31 CVP analysis break even point with changing cost structures. The Jones Company is contemplating a new product, to be sold for \$10 per unit. The projected cost structure varies depending on the relevant range. h h h For the range from 1 to 25,000 units, the cost structure for units produced and sold is expected to be \$6 per unit variable, \$200,000 fixed. For the range from 25,001 to 35,000, the cost structure for units produced and sold is expected to be \$5 per unit variable (a reduction of \$1 per unit) in addition to all costs previously incurred. For the range above 35,000, the cost structure for units produced and sold is expected to be \$4 per unit variable (a further decrease of \$1 per unit) in addition to all costs previously incurred Compute the projected break even point for the Jones Company. 4*X + 5*Y + 6*Z = 200, *25, *Y + 6*Z = 200, , *Y + 6*Z = 200,000 5*Y + 6*Z = 100,000 5*10, *Z = 100,000 6*Z = 50,000 Z = 8,333 X + Y + Z = 25, , ,333 = 43,333 What will be the profit/loss at 31,000 units? What will be the profit/loss at 42,000 units? 4*25, *6, *0! 200,000 = π 100, ,000! 200,000 = π! 70,000 = π 4*25, *10, *7,000! 200,000 = π 100, , ,000! 200,000 = π! 8,000 = π 269

11 Solution to Problem #32 Complex CVP analysis. During 2001 Hartig sold 75,000 units for \$60 million and realized a loss of \$10 million. The breakeven point was 100,000 units. Required: Compute the: 1. Contribution margin per unit. cm*75,000! F =!\$10,000,000 cm*100,000! F = \$0 subtracting eq2 from eq1 cm*25,000 = \$10,000,000 cm = \$400/unit 2. Total fixed costs. Using either eq1 or eq2 \$400*100,000! F = \$0 F = \$40,000, Profits if sales would have been twice as large. 400*X! \$40,000,000 = π 400*150,000! \$40,000,000 = π \$20,000,000 = π or units above BE point * cm - prifit 50,000*400 = \$20,000,

12 Solution to Problem #33 Complex CVP analysis. In 2000, the Peter Vandervort Company was in financial distress, losing lots of money. One of his students took over and trimmed fixed costs by \$2 million to reduce the breakeven point from 35,000 units in 2000 to 25,000 units in Contribution margin per unit (assumed constant for 2000 and 2001). cm*35,000! F = \$0 cm*25,000! (F!2,000,000) = \$0 cm*10,000! 2,000,000 = 0 cm = \$200 per unit 2. Fixed costs for 2000 and *35,000! F = 0 F = \$7,000,000 in 2000 F = \$7,000,000! \$2,000,000 = \$5,000,000 in losses assuming sales of 30,000 units. \$200*30,000! \$7,000,000 =!\$1,000, profits assuming sales of 40,000 units. \$200*40,000! \$5,000,000 = +\$3,000,000 Solution to Problem #34 Complex CVP analysis. At 30,000 units, the XYZ company experiences a pre-tax loss of \$2,000. With a contribution margin of \$4 per unit, how many units must be produced and sold to generate a profit of \$10,000? What is the amount of fixed costs? CM*ªX = ªπ 4*ªX = 12,000 ªX = 3,000 X = 30, ,000 = 33,000 \$4*30,000! F =!2,000 F = \$122,

13 Solution to Problem #35 Difficult CVP analysis. At 50,000 units, the XYZ company loses \$45,000. If it produces 10,000 additional units, it will do \$13,000 better. What is the contribution margin per unit, the total fixed costs, and the breakeven point in units? cm*50,000! F =!45,000 cm*60,000! F =!32,000 CM*ªX = ªπ CM*10,000 = 13,000 CM = *50,000! F =!45,000 F = 110,000 \$1.3*X! 110,000 = 0 F = \$84,

14 Solution to Problem #36 CVP Graph 1. Dollars of revenue 2. Units or volume 3. Total cost 4. Total variable cost 5. Total fixed cost 6. Break-even point 7. Amount of loss 8. Amount of profit 9. Total revenue 273

15 Solution to Problem #37 CVP With Uncertainty The XYZ Company has a new product that it can produce and sell with unit variable costs of \$16 and fixed costs of \$350,000. It believes that it can sell up to 15,000 units at \$35 per unit. If it sells any more than this, the additional sales will need to be discounted to a sales price of \$28 per unit. The marketing department estimates that there is a 10% chance of selling only 5,000 units, a 20% chance of selling 5,001 to 12,000 units, a 20% chance of selling 12,001 to 15,000 units, a 30% chance of selling 15,001 to 20,000 units, and a 15% chance of selling 20,001 to 30,000 units and a 5% chance of selling 30,000 to 35,000 units. Do you think XYZ will be able to break even with this new product? Why or why not? BE point º (35! 16)*X + (28! 16)*Y! \$350,000 = 0 \$19*(X=15,000) + \$12*Y = \$350,000 \$12*Y = \$65,000 Y = 5,417 BE point = X + Y = 15, ,417 = 20,417 units There is a 15% chance of selling 20,001 to 30,000 units, with a 5% chance of selling more. I conclude that there is at least 80% chance of failing to break even. I wouldn t proceed. How would your answer change if fixed costs were only \$250,000 but variable costs increased to \$18 per unit? BE point º (35! 18)*X + (28! 18)*Y! \$550,000 = 0 \$17*X + \$10*(Y=0) = \$250,000 X = 14,706 units There is a 20% chance of selling 12,001 to 15,000 units and a 50% chance ( ) chance of selling more. 14,706 is just below 15,000. There is a chance of reaching 15,000 units. I conclude that chances are a bit better than least of making a profit. 274

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