Question

In: Statistics and Probability

Cavalier's Journals has forecast next year's demand to be 41,000. The journals are considered to incur...

Cavalier's Journals has forecast next year's demand to be 41,000. The journals are considered to incur annual fixed costs of $26,000 and per-unit variable costs of 35 cents.

a.	If journals can be sold for $1 each, what is the break-even quantity?. (Round your answer to the next whole number.)

Q_BEP

units

b.	If we assume that the forecast is correct, what should be the per-unit price of journals, if the company seeks to earn an annual profit of $16,000? Hint: solve for revenue (R). (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Price

$

Expert Solution

a. forecast next year's demand = 41,000 units

fixed costs = $26,000

per-unit variable cost = 35 cents = $0.35

journals can be sold for $1 each;

Sale price per Journal (unit)=$1

Let 'N' be number of Journals sold.

Total Revenue obtained for 'N' Journals = Sale price per Journal (unit) x Number of journals sold = 1 x N = N

Break even happen when total cost for 'N' Journals = Total Revenue obtained for 'N' Journals.

Total cost for 'N' Journals = Fixed cost + Number of units x per-unit variable cost

= $26,000 + 0.35N

For Break-even ;

$26,000 + 0.35N = N

N-0.35N = 26000

0.65N = 26000

N = 26000/0.65 = 40000

Therefore 40000 journals to be sold for break-even

Break-even Quantity = 40000 Journals

QBEP : 40000 Journals

b.

Forecast =41000

Let 'X' be the per-unit price of journal.

Profit = Revenue - Cost

Total cost for '41000' Journals = Fixed cost + 41000 x per-unit variable cost = 26000+41000 x 0.35 = 26000+14350=40350

Revenue = per-unit price of journal x 41000 = 41000X

Profit = Revenue - Cost = 41000X - 40350

company seeks to earn an annual profit of $16,000

i.e

16000 = 41000X - 40350

41000X = 16000+40350 = 56350

X = 56350/41000 = 1.374390 rounded to 1.37

The unit-price of journal to be $1.37 to earn an annual profit of 16000

Price : 1.37

orchestra answered 2 years ago

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