Exam 5: Applications of Linear Equations

Solve the following set of equations graphically:

Bentley Plastics Ltd. has annual fixed costs of $450,000 and variable costs of $15 per unit. The selling price per unit is $25. a) What annual revenue is required to break even? b) What annual unit sales are required to break even? c) What will be the annual net income at annual sales of: (i) 50,000 units? (ii) $1,000,000? d) What minimum annual unit sales are required to limit the annual loss to $20,000? e) If the unit selling price and fixed costs remain the same, what are the changes in break-even unit sales and break-even revenue for a $1 increase in variable costs?

Solve the following problem using the Contribution Margin Approach. Bentley Plastics Ltd. has annual fixed costs of $450,000 and variable costs of $15 per unit. The selling price per unit is $25. a) What annual revenue is required to break even? b) What annual unit sales are required to break even? c) What will be the annual net income at annual sales of: (i) 50,000 units? (ii) $1,000,000? d) What minimum annual unit sales are required to limit the annual loss to $20,000? e) If the unit selling price and fixed costs remain the same, what are the changes in break-even unit sales and break-even revenue for a $1 increase in variable costs?

The social committee of a college's student government is planning the annual graduation dinner and dance. The preferred band can be signed for $1000 plus 10% of ticket revenues. A hall can be rented for $4400. Fire regulations limit the hall to 400 guests plus the band and caterers. A food caterer has quoted a price of $24 per person for the dinner. The committee thinks that the event will be a sellout if ticket prices are set at $46 per person. Some on the committee are in favour of less crowding at the dance and argue for a ticket price of $56. They estimate that 300 will attend at the higher price. a) Calculate the number of tickets that need to be sold at each price to break even. b) What will the profit be at the predicted sales at each ticket price?

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: Valley Peat Ltd. sells peat moss for $10 per bag. Variable costs are $7.50 per bag and annual fixed costs are $100,000. a) How many bags of peat must be sold to break even? b) What will be the net income for a year in which 60,000 bags of peat are sold? c) How many bags must be sold for a net income of $60,000 in a year? d) What annual sales in terms of bags and in terms of dollars would produce a loss of $10,000? e) How much do the break-even unit sales and break-even revenue increase per $1000 increase in annual fixed costs?

Solve the following problem using the Contribution Margin Approach. The Morgan Company produces two products, G and H, with the following characteristics: Total fixed costs for the year are expected to be $700,000. a) What will be the net income if the forecast sales are realized? b) Determine the break-even volumes of the two products. Assume that the product mix (that is, the ratio of the unit sales for the two products) remains the same at the break-even point. c) If it turns out that Morgan sells twice as many units of H as of G, what will be the break-even volumes of the two products?

Solve the following set of equations graphically:

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 VC 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?

A company expects to sell 30,000 hats at $35 each. The estimated variable cost of each hat is $12.50, and the fixed costs are estimated to be $450,000. Calculate the breakeven point in units and revenue. Use the graphical approach to CVP analysis to solve.

Alpha Corp. expects to operate at 80% of capacity next year. Its forecast operating budget is: a) What is Alpha's break-even revenue? b) What would be Alpha's net income if it operates at full capacity?

Solve the following set of equations graphically:

A farmer is trying to decide whether to rent his neighbour's land to grow additional hay for sale to feedlots at $180 per delivered tonne. The land can be rented at $400 per hectare for the season. Cultivation and planting will cost $600 per hectare; spraying and fertilizer will cost $450 per hectare. It will cost $42 per tonne to cut, condition, and bale the hay, and $24 per tonne to transport it to the feedlots. a) How many tonnes per hectare must be produced to break even? b) How much is the break-even tonnage lowered if the selling price is $10 per tonne higher? c) What is the profit or loss at the $180 per tonne price if the crop yield is: (i) 15 tonnes per hectare? (ii) 10 tonnes per hectare?

The Morgan Company produces two products, G and H, with the following characteristics: Total fixed costs for the year are expected to be $700,000. a) What will be the net income if the forecast sales are realized? b) Determine the break-even volumes of the two products. Assume that the product mix (that is, the ratio of the unit sales for the two products) remains the same at the break-even point. c) If it turns out that Morgan sells twice as many units of H as of G, what will be the break-even volumes of the two products?

Solve the following problem using the Contribution Margin Approach. The social committee of a college's student government is planning the annual graduation dinner and dance. The preferred band can be signed for $1000 plus 10% of ticket revenues. A hall can be rented for $4400. Fire regulations limit the hall to 400 guests plus the band and caterers. A food caterer has quoted a price of $24 per person for the dinner. The committee thinks that the event will be a sellout if ticket prices are set at $46 per person. Some on the committee are in favour of less crowding at the dance and argue for a ticket price of $56. They estimate that 300 will attend at the higher price. a) Calculate the number of tickets that need to be sold at each price to break even. b) What will the profit be at the predicted sales at each ticket price?

Solve the following problem using the Contribution Margin Approach. 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?

Use the graphical approach to CVP analysis to solve the following problem. CD Solutions Ltd. manufactures and replicates CDs for software and music recording companies. CD Solutions sells each disc for $2.50. The variable costs per disc are $1.00. 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?

Determine the slope and y-intercept of each of the following equations: -8x - 2y - 3 = 0

The current annual budget for Armstrong Ltd. indicates total revenue of $8,000,000. The total variable costs are $1,600,000 and fixed costs are $5,600,000. Calculate the budgeted net income.

Solve the following problem using the Contribution Margin Approach. A farmer is trying to decide whether to rent his neighbour's land to grow additional hay for sale to feedlots at $180 per delivered tonne. The land can be rented at $400 per hectare for the season. Cultivation and planting will cost $600 per hectare; spraying and fertilizer will cost $450 per hectare. It will cost $42 per tonne to cut, condition, and bale the hay, and $24 per tonne to transport it to the feedlots. a) How many tonnes per hectare must be produced to break even? b) How much is the break-even tonnage lowered if the selling price is $10 per tonne higher? c) What is the profit or loss at the $180 per tonne price if the crop yield is: (i) 15 tonnes per hectare? (ii) 10 tonnes per hectare?

Ace Corporation's variable costs are equal to 43% of sales revenue. Their fixed costs per month are $600,000. Calculate total revenue at the break-even point.