Professional Development Programme on Enriching Knowledge of the Business, Accounting and Financial Studies (BAFS) Curriculum Course 1 : Contemporary Perspectives on Accounting Unit 8 : Cost Accounting for Decision Making 1 Technology Education Section, Curriculum Development Institute Education Bureau, HKSARG August 2008 1 Learning objectives On completion of this unit, you should be able to: Explain the objective and assumptions of cost-volume volume- profit (CVP) analysis. Calculate and explain the break-even even point (BEP) and revenue, contribution/sales (CS) ratio, margin of safety (MOS) and target profit. Construct break-even even chart, contribution chart and profit- volume chart. Assess the effects of changes in costs, selling price and units sold on the break-even even point and target profit. Explain the limitations of CVP analysis. 2
Organisation of Unit 8 Cost-volume-profit (CVP) analysis Introduction and objective Assumptions Mathematical approach: - break-even point - contribution to sales ratio - margin of safety - target profit Graphical approach: - break-even chart - contribution chart - profit-volume chart Effects of changes in cost, selling price and units sold on the break-even point and target profit Example 1 Example 2 Example 3 Example 4 Limitations of CVP analysis 3 Introduction and objective (1) CVP analysis uses basically the principles of marginal costing and is an important short-term planning tool. It explores the relationship, which exists between costs, revenue, output levels and resulting profit. 4
Introduction and objective (2) CVP analysis is useful for short-term decision making in that it can assist managers to predict the profits by incorporating changes in total fixed costs, selling price per unit, unit variable cost and units sold. 5 Assumptions of CVP analysis (1) Total costs can be separated into variable costs and fixed costs. Total revenues and total costs are linear within the relevant range. Unit selling price, unit variable costs and fixed costs are known and constant. Volume is the only determinant of cost and revenue changes. 6
Assumptions of CVP analysis (2) The technology and efficiency remain unchanged. The company sells only single product or there is a constant sales mix. The time value of money is ignored. 7 BEP, C/S ratio, MOS and target profit (1) CVP analysis is also known as break-even even analysis. Break-even even point (BEP) means the level of sales in units or in dollars that produces neither profit nor loss. Margin of safety (MOS) is the extent to which the planned volume of sales lies above the breakeven point. MOS can be expressed in %, units or sales in dollars. 8
BEP, C/S ratio, MOS and target profit (2) CVP analysis can be undertaken by simple formulas, which are listed below: Break-even even point (in units) = Fixed costs Contribution per unit 9 BEP, C/S ratio, MOS and target profit (3) Break-even even revenue = Fixed costs Contribution per unit x Sales price per unit, OR = Fixed costs Contribution/sales (C/S) ratio = Contribution per unit Sales price per unit x 100% 10
BEP, C/S ratio, MOS and target profit (4) Margin of safety (in units or in %) = Planned sales (in units) Break-even even point (in units), OR = [Planned sales (in units) Break-even even point (in units)] Planned sales (in units) x 100% 11 BEP, C/S ratio, MOS and target profit (5) Margin of safety (in $ or in %) = Planned sales (in $) Break-even even point (in $), OR = [Planned sales (in $) Break- even point (in $)] Planned sales ($) x 100% 12
BEP, C/S ratio, MOS and target profit (6) Level of sales to result in target profit (in units) = (Fixed costs + Target profit) Contribution per unit Level of sales to result in target profit (in $) = (Fixed costs + Target profit) x Sales price per unit Contribution per unit 13 Example 1 (1) Chai Wan Limited makes and sells wooden chairs with sales price of $30 and variable cost of $18 per unit. The fixed costs for a month are $360,000. Required: Calculate: a. Break-even point (in units), b. Break-even point (in $ sales), and c. Contribution/sales (C/S) ratio. 14
Example 1 (2) Solution: Contribution per unit = Selling price variable cost 15 Example 1 (3) Solution: Contribution per unit = Selling price variable cost = $30 - $18 = $12 16
Example 1 (4) Solution: a. Break-even even point (in units) = Fixed costs Contribution per unit 17 Example 1 (5) Solution: a. Break-even even point (in units) = Fixed costs Contribution per unit = $360,000 $12 = 30,000 units per month 18
Example 1 (6) b. Break-even even point (in $ sales) = BE units x unit selling price 19 Example 1 (7) b. Break-even even point (in $ sales) = BE units x unit selling price = 30,000 x $30 = $900,000 20
Example 1 (8) c. C/S ratio = Unit contribution unit selling price x 100% 21 Example 1 (9) c. C/S ratio = Unit contribution unit selling price x 100% = $(12 30) x100% = 40% 22
Example 2 (1) Use the information in Example 1. The general manager of Chai Wan Limited plans to make and sell 40,000 wooden chairs next month. 23 Required: a. Calculate and explain the margin of safety (in units, in dollar sales and in %) for next month. b. If the general manager wants to achieve a profit of $300,000 next month, what number of units will need to be sold? c. What level of sales will achieve a profit of $300,000 next month? Solution: Example 2 (2) a. Margin of safety (in units) = Planned sales (in units) Break-even even point (in units) 24
Solution: Example 2 (3) a. Margin of safety (in units) = Planned sales (in units) Break-even even point (in units) = (40,000 30,000) units = 10,000 units 25 Solution: Example 2 (4) a. Margin of safety (in sales) = Planned sales (in $) Break-even even point (in $) 26
Solution: Example 2 (5) a. Margin of safety (in $ sales) = Planned sales (in $) Break-even even point (in $) = $1,200,000 - $900,000 = $300,000 27 Example 2 (6) Solution: a. Margin of safety (in %) = [Planned sales (in units/$) Break-even even point (in units/$)] Planned sales (in units/$) x 100% 28
Example 2 (7) Solution: a. Margin of safety (in %) = [Planned sales (in units/$) Break-even even point (in units/$)] Planned sales (in units/$) x 100% =(10,000 40,000) units x 100% = 25%, OR = $(300,000 1,200,000) x 100% = 25% 29 Example 2 (8) The margin of safety in next month is 10,000 units (or sales value $300,000) or 25%. It means that if the actual volume of sales drop more than 10,000 units (or sales value $300,000) or 25% from its planned sales of 40,000 units, the company will suffer a loss. 30
Example 2 (9) b. Number of units for target profit = (Fixed costs + target profit) unit contribution 31 Example 2 (10) b. Number of units for target profit = (Fixed costs + target profit) unit contribution = $(360,000 + 300,000) $12 = 55,000 units 32
Example 2 (11) c. Sales for units for target profit = (Fixed costs + target profit) unit contribution x unit selling price 33 Example 2 (12) c. Sales for units for target profit = (Fixed costs + target profit) unit contribution x unit selling price = $(360,000 + 300,000) $12 x $30 = $1,650,000 34
Break-even even chart, contribution chart and profit-volume chart Alternatively, CVP analysis can be conducted by the graphical approach. The graphical approach may be preferable where a simple overview is sufficient or where there is a need to avoid a detailed numerical approach that may not easily be understood by non-financial users. 35 Break-even even chart (1) Break-even even chart A break-even even chart can be drawn in the following steps: a. Draw the horizontal and vertical axes. The horizontal axis shows the levels of activity expressed as sales units and the vertical axis shows the values in dollars for costs and revenue. 36
Break-even even chart (2) Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 300 37 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) Break-even even chart (3) b. Draw the fixed costs line and then the total costs line. The fixed costs line will be a straight line parallel to the horizontal axis at the level of the fixed costs. The total costs line, which comprises both fixed and variable costs, will start where the fixed costs line intersects the vertical axis and will be a straight line sloping upward at an angle depending on the proportion of variable costs in total costs. 38
Break-even even chart (4) Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Total costs Fixed costs Variable costs 300 Fixed costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 39 Break-even even chart (5) c. Draw the revenue line, which will be a straight line from the point of origin sloping upwards at an angle determined by the selling price. 40
Break-even even chart (6) Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 Sales 900 600 Total costs Fixed costs Variable costs 300 Fixed costs 41 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) Break-even even chart (7) d. The break-even even point (in units and in $ sales) can be determined as the inter-section of the total cost line and the revenue line. The profit generated from sales above the break- even point and the loss suffered from sales below the break-even even point can easily be determined in the chart. 42
Break-even even chart (8) Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 Break-even point Sales Profit Profit 900 600 Total costs Fixed costs Variable costs 300 Loss Fixed costs 43 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) Break-even even chart (9) e. The margin of safety (in units and in $ sales) can be determined as the difference between the budgeted sales (in units and in $) and the break- even (in units and in $). 44
Break-even even chart (10) Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 Margin of safety Break-even point Sales Profit Profit 900 600 Total costs Fixed costs Variable costs 300 Loss Margin of safety Fixed costs 45 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) Contribution chart (1) Contribution chart A contribution chart is an alternative form of presenting the break-even even chart in that the variable costs line is drawn first instead of the fixed costs line. The contribution chart can show clearly the contribution for different level of activity and the effect on profit for different level of sales. 46
Contribution chart (2) Contribution chart A contribution chart can be drawn in the following steps: a. Draw the horizontal and vertical axes. The horizontal axis shows the levels of activity expressed as sales units and the vertical axis shows the values in dollars for costs and revenue. 47 Contribution chart (3) Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 300 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 48
Contribution chart (4) b. Draw the variable costs line and then the total costs line. The variable costs line start at the origin and will be a straight line sloping upward at an angle depending on the level of the variable costs. The total costs line, which comprises both variable and fixed costs, will be a straight line parallel to the variable costs line at the level of the fixed costs starting from the vertical axis. 49 Contribution chart (5) Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 300 Variable costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 50
Contribution chart (6) Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Total costs Fixed costs 300 Variable costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 51 Contribution chart (7) c. Draw the revenue line, which will be a straight line from the point of origin sloping upwards at an angle determined by the selling price. 52
Contribution chart (8) Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 Sales 900 600 Total costs Fixed costs 300 Variable costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 53 Contribution chart (9) d. The break-even even point (in units and in $ sales) can be determined as the inter-section of the total cost line and the revenue line. The profit generated from sales above the break- even point and the loss suffered from sales below the break-even even point can easily be determined in the chart. Contribution for different level of activity can also be determined in the chart. 54
Contribution chart (10) Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Total costs Break-even point Sales Profit Profit Fixed costs Contribution 300 Loss Variable costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 55 Contribution chart (11) e. The margin of safety (in units and in $ sales) can be determined as the difference between the budgeted sales (in units and in $) and the break- even (in units and in $). 56
Contribution chart (12) Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Margin of safety Total costs Break-even point Sales Profit Profit Fixed costs Contribution 300 Loss Variable costs Margin of safety 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 57 Profit-volume chart (1) Profit-volume chart The profit-volume chart is a variation of the break-even even chart, which can show the effect on profit for different level of sales. The profit-volume chart concentrates on profit and shows only a profit line. The horizontal axis shows the levels of activity expressed as sales units and the vertical axis shows the profit or loss values in dollars. 58
Profit-volume chart (2) Profit volume chart A profit volume chart can be drawn in the following steps: a. Draw the horizontal and vertical axes. The horizontal axis shows the levels of activity expressed as sales units and the vertical axis shows the profit or loss values in dollars. 59 Profit-volume chart (3) Profit-volume chart Profit / Loss ($ 000) 400 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 600 60
Profit-volume chart (4) b. Draw the profit/loss line, which will be a straight line from vertical axis slopping upward at an angle depending on the level of profit (sales less total costs) starting at a loss equal to the fixed costs (since there would be no revenue at zero sales). 61 Profit-volume chart (5) Profit-volume chart Profit / Loss ($ 000) 400 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 600 62
Profit-volume chart (6) c. The break-even even point (in units and in $ sales) can be determined as the inter-section of the total profit/loss line and the horizontal axis. The profit generated from sales above the break- even point and the loss suffered from sales below the break-even even point can easily be determined in the chart. 63 Profit-volume chart (7) Profit-volume chart Profit / Loss ($ 000) 400 Profit Profit 0 Loss 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) Fixed costs Contribution 600 64
Profit-volume chart (8) d. The margin of safety (in units and in $ profit) can be determined as the difference between the budgeted profit (in units and in $) and the break- even point (in units and in $). 65 Profit-volume chart (9) Profit-volume chart Profit / Loss ($ 000) 400 Margin of safety Break-even point Profit Profit 0 Loss 1,000 2,000 3,000 4,000 Margin of safety 5,000 Activity (Sales units) Fixed costs Contribution 600 66
Example 3 (1) Example 3 Chai Wan Limited also produces and sells wireless computer keyboards. The company intends to produce and sell 5,000 units per year. The unit sales price is $300 and the unit variable cost is $100. Fixed costs are $600,000 a year. 67 Example 3 (2) Required: Determine the break-even even point and the margin of safety for wireless computer keyboards by constructing: a. break-even even chart, b. contribution chart, and c. profit-volume chart. 68
Example 3 (3) Solution: a. Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 300 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 69 Example 3 (4) Solution: a. Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Fixed costs 300 Fixed costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 70
Example 3 (5) Solution: a. Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Total costs Fixed costs Variable costs 300 Fixed costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 71 Example 3 (6) Solution: a. Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 Sales 900 600 Total costs Fixed costs Variable costs 300 Fixed costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 72
Example 3 (7) Solution: a. Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 Sales Profit Profit 900 600 Total costs Fixed costs Variable costs 300 Loss Fixed costs 73 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) Example 3 (8) Solution: a. Break-even even chart Sales revenue/costs ($ 000) 1,500 1,200 Margin of safety Break-even point Sales Profit Profit 900 600 Total costs Fixed costs Variable costs 300 Loss Margin of safety Fixed costs 74 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units)
Example 3 (9) From the break-even even chart, we can easily get the following information: Break-even even point: 3,000 units, or $900,000 If sales are above $900,000 or 3,000 units, the company will make a profit. If sales are below $900,000 or 3,000 units, the company will suffer a loss. 75 Example 3 (10) Margin of safety: (5,000-3,000) units = 2,000 units, or $(1,200,000 900,000) = $600,000 If sales drop by not more than $600,000 or 2,000 units, the company will make a profit. If sales drop by more than $600,000 or 2,000 units, the company will suffer a loss. 76
Example 3 (11) b. Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 300 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 77 Example 3 (12) b. Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 300 Variable costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 78
Example 3 (13) b. Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Total costs Fixed costs 300 Variable costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 79 Example 3 (14) b. Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Total costs Sales Profit Profit Fixed costs Contribution 300 Loss Variable costs 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 80
Example 3 (15) b. Contribution chart Sales revenue/costs ($ 000) 1,500 1,200 900 600 Margin of safety Total costs Break-even point Sales Profit Profit Fixed costs Contribution 300 Loss Variable costs Margin of safety 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 81 Example 3 (16) The information you can get from the contribution chart is similar to that from the break-even even chart. 82
Example 3 (17) c. Profit-volume chart Profit / Loss ($ 000) 400 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 600 83 Example 3 (18) c. Profit-volume chart Profit / Loss ($ 000) 400 0 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) 600 84
Example 3 (19) c. Profit-volume chart Profit / Loss ($ 000) 400 Profit Profit 0 Loss 1,000 2,000 3,000 4,000 5,000 Activity (Sales units) Fixed costs Contribution 600 85 Example 3 (20) c. Profit-volume chart Profit / Loss ($ 000) 400 Margin of safety Break-even point Profit Profit 0 Loss 1,000 2,000 3,000 4,000 Margin of safety 5,000 Activity (Sales units) Fixed costs Contribution 600 86
Example 3 (21) From the profit-volume chart, we can easily get the following information: At sales of 3,000 units: The company will break-even even with no profit and no loss. At sales of 0 units: The company will suffer a loss of $600,000. At target sales of 5,000 units: The company will make a profit of $400,000. The margin of safety is: 2,000 (5,000 3,000) units, or $400,000 ($200 x 2,000 units) contribution/profit 87 Effects of changes in costs, selling price and units sold on the break-even even point and target profit CVP is a very useful management tool in that by varying the variable cost, fixed cost, selling price and units sold, simple and quick estimates of break-even even points and profitability can be made. 88
Example 4 (1) Example 4 One of the divisions of Chai Wan Limited produces and sells laser pointers. The following information is extracted from its current year s budget: Production and sales units 60,000 units Selling price per unit $40 Variable cost per unit $30 Fixed costs per annum $400,000 89 Example 4 (2) Required: To calculate the following for Chai Wan Limited: a. the break-even even point (in units and $ sales), b. the budgeted profit for current year, c. the revised breakeven point (in units) and revised budgeted profit, under each the following independent changes: i. the variable cost increases by $2. ii. the fixed costs decrease by 10% and sales volume increases by 5%, selling price and variable cost remain unchanged. iii. the fixed costs and variable cost increase by 10%, selling price decreases by 5% while sales volume increases by 20%. 90
Example 4 (3) Solution: a. Contribution per unit = Selling price variable cost 91 Example 4 (4) Solution: a. Contribution per unit = Selling price variable cost = $40 - $30 = $10 92
Example 4 (5) Solution: a. Break-even even point (in units) = Fixed costs Contribution per unit 93 Example 4 (6) Solution: a. Break-even even point (in units) = Fixed costs Contribution per unit = $400,000 $10 = 40,000 units 94
Example 4 (7) Solution: a. Break-even even point (in sales) = BE units x unit selling price 95 Example 4 (8) Solution: a. Break-even even point (in sales) = BE units x unit selling price = 40,000 x $40 = $1,600,000 96
Example 4 (9) b. Total contribution $ b. Less: Fixed costs Profit 97 Example 4 (10) b. Total contribution ($10 x 60,000) $600,000 Less: Fixed costs 400,000 Profit $200,000 98
Example 4 (11) c.i. Revised contribution per unit = Selling price variable cost 99 Example 4 (12) c.i. Revised contribution per unit = Selling price variable cost = $40 - $32 = $8 100
Example 4 (13) c.i. Break-even even point (in units) = Fixed costs unit contribution 101 Example 4 (14) c.i. Break-even even point (in units) = Fixed costs unit contribution = $400,000 $8 = 50,000 units 102
Example 4 (15) c.i. Total contribution $ Less: Fixed costs Profit 103 Example 4 (16) c.i. Total contribution ($8 x 60,000) $480,000 Less: Fixed costs 400,000 Profit $80,000 104
Example 4 (17) ii. Contribution per unit remains at $10 Break-even even point (in units) = Revised fixed costs unit contribution 105 Example 4 (18) ii. Contribution per unit remains at $10 Break-even even point (in units) = Revised fixed costs unit contribution = $400,000 x 90% $10 = 36,000 units 106
Example 4 (19) ii. Total contribution $ Less: Fixed costs Profit 107 Example 4 (20) ii. Total contribution ($10 x 60,000 x 105%) $630,000 Less: Fixed costs ($400,000 x 90%) 360,000 Profit $270,000 108
Example 4 (21) iii. Revised contribution per unit = Revised selling price per unit revised variable cost per unit 109 Example 4 (22) iii. Revised contribution per unit = Revised selling price per unit revised variable cost per unit = $(40 x 95% 30 x 110%) = $5 110
Example 4 (23) iii. Revised break-even even point (in units) = Revised fixed costs revised contribution per unit 111 Example 4 (24) iii. Revised break-even even point (in units) = Revised fixed costs revised contribution per unit = $400,000 x 110% $5 = 88,000 units 112
Example 4 (25) iii. Total contribution $ Less: Fixed costs Profit/(Loss) 113 Example 4 (26) iii. Total contribution ($5 x 60,000 x 120%) $360,000 Less: Fixed costs ($400,000 x 110%) 440,000 Loss ($80,000) 114
Limitations of CVP analysis (1) CVP can provide very useful insights to the relationship between fixed costs, variable costs and the volume of sales. However, there are major limitations which affect its usefulness. These limitations are shown in the following. 115 Limitations of CVP analysis (2) a. Non-linear relationships of unit variable cost and selling price Unit variable cost and selling price are assumed to be the same at all levels of output or sales under the CVP. However, it may not be true in reality because of bulk purchase discounts from suppliers of raw materials or trade discounts offered to customers to attract more sales. 116
Limitations of CVP analysis (3) b. Step cost function b. Fixed costs remain fixed within a relevant range and beyond that relevant range, it might become a step cost. 117 Limitations of CVP analysis (4) c. Companies selling multi-products c. CVP analysis is quite helpful for companies selling single product where the measure of activity is simply the unit of output. For companies selling multi-products, it is not easy to split the fixed costs among the products. CVP cannot work properly unless there is a standard mix for the products of the company. 118
Limitations of CVP analysis (5) d. Inappropriateness for long-term planning purpose CVP analysis has many applications in profit planning and short-term term decision making, where fixed costs do not change as a consequence of the decision taken. It is, however, not appropriate for long-term planning because all costs, in the long-run, are variable costs. 119 Further readings (1) Horngren et al, (2006), Cost Accounting, A Managerial Emphasis,, Pearson, 12th Edition, Chapter 3. Drury, C. (2004), Management and Cost Accounting,, London, Thomson, 6th Edition, Chapter 8. Garrison et al, (2006), Managerial Accounting, McGraw-Hill, 11th Edition, Chapter 6. Li, T. M. and Ng, P. H. (2007), HKAL Principles of Accounts (Volume 2),, Pilot Publishing Company Ltd, 2nd Edition, Chapter 24. 120
Further readings (2) 王 怡 心 ( 二 00 二 年 ), 管 理 會 計, 台 北 : 三 民 書 局, 修 訂 二 版, 第 七 章 121 End of the Unit End-of of-unit Assessment This is the end of Unit 8. Please go to the Unit Assessment before attempting the next unit. 122