Exam 5: Applications of Linear Equations

Solve the following problem using the Contribution Margin Approach. In the past year, the Greenwood Corporation had sales of $1,200,000, fixed costs of $400,000, and total variable costs of $600,000. a) At what sales figure would Greenwood have broken even last year? b) If sales increase by 15% in the year ahead (but all prices remain the same), how much (in $) will the net income increase? c) If fixed costs are 10% lower in the year ahead (but sales and variable costs remain the same as last year), how much (in $) will the net income increase? d) If variable costs are 10% higher in the year ahead (but sales and fixed costs remain the same as last year), how much (in $) will the net income decrease?

Use the Interactive break-even Chart in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text. Leaving other variables unchanged, what effect does increasing the value of S have on: a. The Fixed Cost (FC) line? b. The Total Cost (TC) line? c. The Total Revenue (TR) line? d. The break-even point?

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem: ChildCare Industries manufactures infant car seats that it sells to retailers for $155 each. The costs to manufacture each additional seat are $65, and the monthly fixed costs are $18,000. a) To just break even, how many CDs must be sold per month if the fixed costs are $60,000 per month? b) What must sales be in order to have a profit of $7500 per month?

Solve the following problem using the Contribution Margin Approach. Reflex Manufacturing Corp. manufactures composters at a unit variable cost of $43. It sells them for $70 each. It can produce a maximum of 3200 composters per month. Annual fixed costs total $648,000. a) What is the break-even volume per month? b) What is the monthly net income at a volume of 2500 composters per month? c) What is the monthly net income if Reflex operates at 50% of capacity during a recession? d) At what percent utilization would the annual net income be $226,800? e) If fixed and variable costs remain the same, how much do the monthly break-even unit sales change for a $1 increase in the selling price?

Enrique is studying the feasibility of producing a new product. His existing facilities could be expanded to manufacture 2000 new units per month. The unit cost is $75. Estimated fixed costs are $3.36 mil per year and variable costs are $25 per unit. Competitors sell a similar product for $350 each. Use the graphical approach to CVP analysis to solve the following: a) What would the net income be at 80% capacity? b) What would unit sales have to be to attain a net income of $100,000? c) If sales dropped to 60% of capacity, what would the resulting net income be?

Determine the slope and y-intercept of each of the following equations: -2x = 3y + 4

Solve the following problem using the Contribution Margin Approach. The Kelowna division of Windstream RVs builds the Wanderer model. The division had total revenue of $4,785,000 and a profit of $520,000 on the sale of 165 units in the first half of its financial year. Sales declined to 117 units in the second half of the year, resulting in a profit of only $136,000. Determine the selling price per unit, the total revenue in the second half, the unit variable costs, and the annual fixed costs.

Solve the following problem using the Contribution Margin Approach. Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month. a) How many Home Office Systems must be sold each month to break even on this product line? b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

A company makes gadgets selling for $15 each. For 20,000 gadgets, the cost is $3 each, and the estimated fixed costs are $150,000. What is the break-even volume and revenue? Use the graphical approach to CVP analysis to solve.

Go to the textbook's OLC (www.mcgrawhill.ca/olc/jerome/) and work your way to the Student Edition. In the navigation bar, select "Chapter 5" in the dropdown box. In the list of resources for Chapter 5, select "Links in Textbook" and then click on the link named "Contribution Margin Chart". Use the chart to solve the following problem: Jordan is developing a business plan for a residential building inspection service he may start. Rent and utilities for an office would cost $1000 per month. The fixed costs for a vehicle would be $450 per month. He estimates that the variable office costs (word processing and supplies) will be $50 per inspection and variable vehicle costs will be $25 per inspection. Jordan would also spend $200 per month to lease a computer, and $350 per month for advertising. a) If he charges $275 per inspection, how many inspections per month are required before he can "pay himself?" b) How many inspections per month are required for Jordan to be able to draw a salary of $4000 per month?

Determine the slope and y-intercept of each of the following equations: -3a - 4b = 12

Solve the following problem using the Contribution Margin Approach. This problem is designed to illustrate how the relative proportions of fixed and variable costs affect a firm's net income when the sales volume changes. Two hypothetical firms, A and B, manufacture and sell the same product at the same price of $50. Firm A is highly mechanized with monthly fixed costs of $4000 and unit variable costs of $10. Firm B is labour-intensive and can readily lay off or take on more workers as production requirements warrant. B's monthly fixed costs are $1000, and its unit variable costs are $40. a) Calculate the break-even volume for both firms. b) At each firm's break-even point, calculate the proportion of the firm's total costs that are fixed and the proportion that are variable. c) For a 10% increase in sales above the break-even point, calculate the dollar increase in each firm's net income. Explain the differing results. d) For a 10% decrease in sales below the break-even point, calculate the dollar decrease in each firm's net income. Explain the differing results. e) What is each firm's net income at sales of 150 units per month and each firm's loss at sales of 50 units per month?

Dynacan Ltd. manufactured 10,000 units of product last year and identified the following manufacturing and overhead costs. (V denotes "variable cost" and F denotes "fixed cost.") If unit variable costs and fixed costs remain unchanged, calculate the total cost to produce 9700 units this year.

Kuldip's factory manufactures toys that sell for $29.95 each. The variable cost per toy is $11, and the total fixed costs for the month are $45,000. What is the break-even point in revenue per month?

Sam manufactures a product that is selling so well, he has decided to expand his operation to 50,000 units per month. The unit cost is $7, estimated fixed costs are $1.8 mil per year and variable costs are $5 per unit. The product currently sells for $20. Use the graphical approach to CVP analysis to solve the following: a) What is the break-even point as a percent of capacity? b) What would the net income be at 75% capacity? c) What would unit sales have to be to attain a net income of $100,000? d) If sales dropped to 50% of capacity, what would the resulting net income be?

Use the graphical method to solve the following pair of equations.

Use the Interactive break-even Chart and its accompanying in the textbook's OLC to answer the following problem. To access the chart, follow the instructions given in the NET @ssets box at the beginning of section 5.4 in the text. Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month. a) How many Home Office Systems must be sold each month to break even on this product line? b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?

This problem is designed to illustrate how the relative proportions of fixed and variable costs affect a firm's net income when the sales volume changes. Two hypothetical firms, A and B, manufacture and sell the same product at the same price of $50. Firm A is highly mechanized with monthly fixed costs of $4000 and unit variable costs of $10. Firm B is labour-intensive and can readily lay off or take on more workers as production requirements warrant. B's monthly fixed costs are $1000, and its unit variable costs are $40. a) Calculate the break-even volume for both firms. b) At each firm's break-even point, calculate the proportion of the firm's total costs that are fixed and the proportion that are variable. c) For a 10% increase in sales above the break-even point, calculate the dollar increase in each firm's net income. Explain the differing results. d) For a 10% decrease in sales below the break-even point, calculate the dollar decrease in each firm's net income. Explain the differing results. e) What is each firm's net income at sales of 150 units per month and each firm's loss at sales of 50 units per month?

Solve the following problem using the Contribution Margin Approach. Beta Inc. has based its budget forecast for next year on the assumption it will operate at 90% of capacity. The budget is a) At what percentage of capacity would Beta break even? b) What would be Beta's net income if it operates at 70% of capacity?

Clone Computers assembles and packages personal computer systems from brand-name components. Its Home Office PC System is assembled from components costing $1400 per system and sells for $2000. Labour costs for assembly are $100 per system. This product line's share of overhead costs is $10,000 per month. a) How many Home Office Systems must be sold each month to break even on this product line? b) What will be the profit or loss for a month in which 15 Home Office Systems are sold?