Answer to Question #158600 in Math for saleemaslam

Question

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Question 1:

A firm manufactures a product that sells for $12 per unit. Variable cost per unit is $8 and fixed cost per month is $1200. Capacity is 1000 units per month.

a. How much is the contribution margin? __________

b. How much is the contribution rate? __________

c. How many units must they sell per month in order to break even? __________

d. How many units must they sell in order to have a profit of $2,500 per month? __________

Question 2:

The following data pertain to the operating budget of Harrow Seed and Fertilizers which projects sales of $120,000. The total of its variable costs is estimated at $48,000 while fixed costs are $43,200.

a. How much is the contribution margin? __________

b. How much is the contribution rate? __________

c. What is the firm’s break-even point expressed in dollars of revenue? __________

Question 3:

ABC Corp. lists a product for $440.00 less discounts of 25% and 15%.

a.  What is the net price? __________

b.  What is the total amount of the discount? __________

c.   Suppose a competitor sells the same product for $229.00. What additional rate of discount must ABC Corp. offer to meet the competitor’s price? __________

Question 4:

The SKI SHOPPE purchased Rossignol skis for $492 per pair and priced them to give a 40% rate of markup on selling price. When this model was discontinued, the store marked down its remaining stock by 30%. What was the sale price after the markdown? __________

The End

Answer 1

Solution

Question 1:

a) Contribution Margin:

Following formula can be used to calculate the contribution margin:

Contribution Margin = Total Sales - Total Variable Cost

Contribution Margin = $\$ 12 \times 1000 - \$8\times 1000 = \$ 4000$

b) Contribution rate:

Following formula can be used to calculate the contribution rate:

Contribution rate:  (Total Sales - Total Variable Cost)/Total Sales

Contribution Rate = 4000/12000 = 0.333 or 33.3%

c) Break-Even:

The formula for break-even point is as follows:

Break-Even = Fixed Cost/Contribution margin per unit

Break-Even = 1200/(12-8) = 1200/3 = 400 units

Thus break-even will be at 400 units

d) to calculate the number of units at a particular profit, the following formula should be used:

Number of units = (Fixed Cost + Target Profit)/Contribution margin per unit

Number of units = (1200+2500)/4 = 925 units

925 units should be made to get the profit of $ 2500

Question 2:

a)How much is the contribution margin?

contribution margin = Sales revenue - Variable Cost

= 120000 - 48000

= 72000

b) How much is the contribution rate?

Contribution Margin Ratio = $\frac{Sales\ Revenue - Variable Cost}{Sales\ Revenue}=\frac{120000-48000}{120000}=0.6$

c.) What is the firm’s break-even point expressed in dollars of revenue?

Break even Point = Fixed Cost / Gross Margin

Fixed cost = 43,200

$$\frac{Sales( Revenue) - Total\ Cost}{Sales( Revenue)}=\frac{120000-(43200+48000)}{120000}=\frac{91200}{120000}=0.76$$

Break even Point = Fixed Cost / Gross Margin = 43200 / 0.76 = 56,842.105 = $56843 (Approx)

Question 3:

a)

Net price=$440(100%-25%)(100-15%)=$440(75%)(85%)=$280.5

b)

Total amount of discount =$440 -$280.5= $159.5

c)

Additional rate of discount must ABC Corp. offer to meet the competitor’s price= $(1-229/280.5)100\%=(1-0.8164)\times100\%=18.36$

Question 4:

The formula for calculating marked price when price is marked up is given as

Marked price = cost price × ( 100%+ mark up%)

Given,

Cost price per pair = $492

Markup =40%

Putting values in formula, we get

Marked price = 492×(100%+40%) = (492×140)÷100 = $688.80

When this model was discontinued , remaining stock is marked down by 30%

So, sale price after the markdown = marked price × (100%-markdown%)

We know, marked price = $688.80

Markdown = 30%

Putting values in formula, we get

Sale price after markdown = 688.80×(100%-30%) = (688.80×70)÷100 = $482.16