We are evaluating a project that costs $690,000, has a five-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project.

We are evaluating a project that costs $690,000, has a five-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project.

   

a-1	Calculate the accounting break-even point.

Break-even point

units

   

a-2	What is the degree of operating leverage at the accountin g break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))

   

DOL

   

b-1	Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16))

Cash flow	$
NPV	$

b-2	What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

ΔNPV/ΔQ

$

  

c.	What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign.)

  

ΔOCF/ΔVC

$

Explanation: a.

To calculate the accounting breakeven OCF, we first need to find the depreciation for each year. The depreciation is:

Depreciation = $690,000/5

Depreciation = $138,000 per year

   

And the accounting breakeven is:

QA = ($790,000 + 138,000)/($75 – 50)

QA = 37,120 units

   

To calculate the accounting breakeven, we must realize at this point (and only this point), the OCF is equal to depreciation. So, the DOL at the accounting breakeven is:

DOL = 1 + FC/OCF = 1 + FC/D

DOL = 1 + [$790,000)/$138,000)]

DOL = 6.725

b. 

We will use the tax shield approach to calculate the OCF. The OCF is:

  

OCFbase = [(P – v)Q – FC](1 – T) + TD

OCFbase = [($75 – 50)(71,000) – $790,000](0.65) + 0.35($138,000)

OCFbase = $688,550

Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:

NPVbase = –$690,000 + $688,550(PVIFA15%,5)

NPVbase = $1,618,126.39

  

To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 76,000 units. The NPV at this sales level is:

OCFnew = [($75 – 50)(76,000) – $790,000](0.65) + 0.35($138,000)

OCFnew = $769,800

  

And the NPV is:

NPVnew = –$690,000 + $769,800(PVIFA15%,5)

NPVnew = $1,890,488.99

  

So, the change in NPV for every unit change in sales is:

ΔNPV/ΔS = ($1,618,126.39 – 1,890,488.99)/(71,000 – 76,000)

ΔNPV/ΔS = +$54.473

  

If sales were to drop by 500 units, then NPV would drop by:

NPV drop = $54.473(500) = $27,236.26

You may wonder why we chose 76,000 units. Because it doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.

c.

To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of $51. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $51 is:

OCFnew = [($75 – 51)(71,000) – 790,000](0.65) + 0.35($138,000)

OCFnew = $642,400

So, the change in OCF for a $1 change in variable costs is:

ΔOCF/ΔVC = ($688,550 – 642,400)/($50 – 51)

ΔOCF/ΔVC = –$46,150

If variable costs decrease by $1 then, OCF would increase by $46,150

Night Shades Inc. (NSI) manufactures biotech sunglasses. The variable materials cost is $18.50 per unit, and the variable labor cost is $7.00 per unit.

Night Shades Inc. (NSI) manufactures biotech sunglasses. The variable materials cost is $18.50 per unit, and the variable labor cost is $7.00 per unit.

a.	What is the variable cost per unit? (Round your answer to 2 decimal places. (e.g., 32.16))

Variable cost

$

  

b.	Suppose NSI incurs fixed costs of $800,000 during a year in which total production is 350,000 units. What are the total costs for the year?

  

Total cost

$

  

c.	If the selling price is $48.00 per unit, what is the cash break-even point? If depreciation is $600,000 per year, what is the accounting break-even point? (Round your answers to 2 decimal places. (e.g., 32.16))

Cash break-even point	units
Break-even point	units

Explanation:

a.

The total variable cost per unit is the sum of the two variable costs, so:

Total variable costs per unit = $18.50 + 7.00

Total variable costs per unit = $25.50

b.

The total costs include all variable costs and fixed costs. We need to make sure we are including all variable costs for the number of units produced, so:

Total costs = Variable costs + Fixed costs

Total costs = $25.50(350,000) + $800,000

Total costs = $9,725,000

c.

The cash break even, that is the point where cash flow is zero, is:

QC = $800,000 / ($48.00 – 25.50)

QC = 35,555.56 units

And the accounting breakeven is:

QA = ($800,000 + 600,000) / ($48.00 – 25.50)

QA = 62,222.22 units

Deavila Inc. produces and sells two products. Data concerning those products for the most recent month appear below: Product Q91I Product J53Z Sales $ 15,800 $ 11,800 Variable expenses $ 5,800 $ 5,060 ________________________________________ Fixed expenses for the entire company were $13,930. Required: a. Determine the overall contribution margin ratio for the company. (Round your answer to 2 decimal places.) Contribution margin ratio b. Determine the overall break-even point in total sales dollars for the company. (Round your intermediate calculation to 2 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.) Break-even point $ c. If the sales mix shifts toward Product Q91I with no change in total sales, what will happen to the break-even point for the company? It will result in a decrease in the company's overall break-even point. Explanation: a. Product Q91I Product J53Z Total Sales $ 15,800 $ 11,800 $ 27,600 Variable expenses 5,800 5,060 10,860 ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ ________________________________________ Contribution margin $ 10,000 $ 6,740 16,740 ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ Fixed expenses 13,930 ________________________________________ ________________________________________ Net operating income $ 2,810 ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________ Overall CM ratio = Total contribution margin/Total sales = $16,740/$27,600 = 0.61 b. Break-even point in total sales dollars = Fixed expenses/Overall CM ratio = $13,930/0.61 = $22,836 c. Product Q91I Product J53Z Sales (a) $ 15,800 $ 11,800 Contribution margin (b) $ 10,000 $ 6,740 CM ratio (b)÷(a) 0.633 0.571 ________________________________________ Since Product Q91I's CM ratio is greater than Product J53Z's, a shift in the sales mix toward Product Q91I will result in a decrease in the company's overall break-even point.

Deavila Inc. produces and sells two products. Data concerning those products for the most recent month appear below:

 

	Product Q91I				Product J53Z
Sales		$	15,800			$	11,800
Variable expenses		$	5,800			$	5,060

 

Fixed expenses for the entire company were $13,930.

 

Required:
a.	Determine the overall contribution margin ratio for the company. (Round your answer to 2 decimal places.)

 

Contribution margin ratio

b.	Determine the overall break-even point in total sales dollars for the company. (Round your intermediate calculation to 2 decimal places and final answer to the nearest dollar amount. Omit the "$" sign in your response.)

Break-even point

$

c.	If the sales mix shifts toward Product Q91I with no change in total sales, what will happen to the break-even point for the company?

It will result in a decrease in the company's overall break-even point.


Explanation:

a.

	Product Q91I		Product J53Z		Total
Sales	$	15,800	$	11,800	$	27,600
Variable expenses		5,800		5,060		10,860
Contribution margin	$	10,000	$	6,740		16,740
Fixed expenses						13,930
Net operating income					$	2,810

 

Overall CM ratio = Total contribution margin/Total sales = $16,740/$27,600 = 0.61

b.

Break-even point in total sales dollars = Fixed expenses/Overall CM ratio = $13,930/0.61 = $22,836

c.

	Product Q91I				Product J53Z
Sales (a)		$	15,800			$	11,800
Contribution margin (b)		$	10,000			$	6,740
CM ratio (b)÷(a)			0.633				0.571

Since Product Q91I's CM ratio is greater than Product J53Z's, a shift in the sales mix toward Product Q91I will result in a decrease in the company's overall break-even point.

Tyrene Products manufactures recreational equipment. One of the company’s products, a

Problem 5-29 Various CVP Questions: Break-Even Point; Cost Structure; Target Sales [LO1, LO3, LO4, LO5, LO6, LO8]

Tyrene Products manufactures recreational equipment. One of the company’s products, a skateboard, sells for $37.50. The skateboards are manufactured in an antiquated plant that relies heavily on direct labor workers. Thus, variable costs are high, totaling $22.50 per skateboard of which 60% is direct labor cost.

Over the past year the company sold 40,000 skateboards, with the following operating results:

Sales (40,000 skateboards)	$	1,500,000
Variable expenses		900,000
Contribution margin		600,000
Fixed expenses		480,000
Net operating income	$	120,000

Management is anxious to maintain and perhaps even improve its present level of income from the skateboards.

Required:

1a.	Compute the CM ratio and the break-even point in skateboards. (Omit the "%" sign in your response.)

Contribution margin	40	%
Unit sales to break even	32,000	skateboards

1b.	Compute the degree of operating leverage at last year's level of sales.

Degree of operating leverage

5

2.

Due to an increase in labor rates, the company estimates that variable costs will increase by $3 per skateboard next year. If this change takes place and the selling price per skateboard remains constant at $37.50, what will be the new CM ratio and the new break-even point in skateboards? (Omit the "%" sign in your response.)

Contribution margin	32	%
Unit sales to break even	40,000	skateboards

3.	Refer to the data in (2) above. If the expected change in variable costs takes place, how many skateboards will have to be sold next year to earn the same net operating income, $120,000, as last year?

Number of skateboards

50,000

4.

Refer again to the data in (2) above. The president has decided that the company may have to raise the selling price of its skateboards. If Tyrene Products wants to maintain the same CM ratio as last year, what selling price per skateboard must it charge next year to cover the increased labor costs? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Selling price

$ 42.50

5.

Refer to the original data. The company is considering the construction of a new, automated plant. The new plant would slash variable costs by 40%, but it would cause fixed costs to increase by 90%. If the new plant is built, what would be the company’s new CM ratio and new break-even point in skateboards? (Omit the "%" sign in your response.)

Contribution margin	64	%
Unit sales to break even	38,000	skateboards

6.	Refer to the data in (5) above.

a.	If the new plant is built, how many skateboards will have to be sold next year to earn the same net operating income, $120,000, as last year?

Number of skateboards

n/r

b-1.

Assume that the new plant is constructed and that next year the company manufactures and sells 40,000 skateboards (the same number as sold last year). Prepare a contribution format income statement. (Input all amounts as positive values except losses which should be indicated by minus sign. Omit the "$" sign in your response.)

Contribution Income Statement.
Sales	$ 1,500,000
Variable expenses	540,000
Contribution margin	960,000
Fixed expenses	912,000
Net operating income (loss)	$ 48,000

b-2.	Compute the degree of operating leverage

Degree of operating leverage

20