Question

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Peach, Inc. roasts and sells premium coffee in one pound ba At their current facilities they have one roaster that is able to produce 5,000 pounds of coffee per month. They purchased this machine they twelve years ago for $300,000 total and estimated a twenty year useful life. In the coming year, they plan to produce 55,000 pounds of roasted coffee and sell it for $15/pound. They pay a master roaster $78,000/year in salary,$35,000 in insurance per year, and facility rent of $45,000 per year. The tax rate is 30%. They also have the following costs related to production:

A. Utilities cost -Upon running a linear regression with utilities as the dependen (y) variable and sales in units as the independent (x) variable, they found an adjusted R2=0.55 The equation of the line was, total cost=1.5x 2,000.

B. wages to packaging laborers -Peach pays their laborers $12/hour and they can package 4 bags/hour

c. Each pound of coffee requires 1.25 pounds of unroasted coffee beans to begin the process. After the roasting process is complete, the beans lose some moisture and only weigh pound. Peach currently buys coffee beans from a local farmer for 3.50/ pound.

D. The cost of packaging is $0.35/ pound ofcoffee. Please assume that one bag of coffee includes one pound ofroasted coffee beans.

Questions

1. What is the contribution margin per finished pound ofroasted coffee?

2. If Peach meets his estimated production goals, what will be his total annual profit after tax?

3. What is the break-even point (in bags of coffee)?

4. Give the above facts, at which point of production will Peach’s total cost per pound (including variable and fixed) be minimized?

5. What will be his cost/pound at this point?

Please list out the works.

Answer 1

1. a) Utility Cost = $1.5/unit

b) Labour Cost / Wages:

Production is 4bags per 1hr and Pay is $12 per hr

ie- 4 bags costs = $12

hense Per bag costs = 12 / 4 = $3/unit

c) Purchase:

1 pound = $3.50

1.25 pound = $3.50 x 1.25 = $4.38/unit

d) Packging cost =$0.35

Total Variable cost = 1.5 + 3 + 4.38 + 0.35 = $9.23

Hence the contribution margin is =Sales - Variable Cost

Contribution Margin = 15 - 9.23 = $5.78

2. Annual Sales    (55000 x 15) = $825000

Less: Variable cost (55000 x 9.23) = $507650

Contribution Margin = $317350

Less: Fixed cost:

(Salary + Insurance + Facility Rent)

(78000 + 35000 + 45000) = $158000

Gross Profit = $159350

Less: Depreciation on Machinery = $15000

(300000 / 20)

Net Income before Tax = $144350

Less: Taxes (144350 x 30%) = $43305

Annual Net Income = $101045

3.

Workings:

4. The point of intersection where Marginal Cost = Average Total Cost, that cost of production will be at its minimum. Ie- Minimum Average Total Cost