Chapter 4, Problem 56P

M. Anthony, LLP, produces music in a studio in London. The cost of producing one typical song follows:

The fixed costs allocated to each song are based on the assumption that the studio produces 60 songs per month.

Required

Treat each question independently. Unless stated otherwise, M. Anthony charges $80,000 per song produced.

1.       a.            How many songs must the firm produce per month to break even?
2.       b.            Market research estimates that a price increase to $90,000 per song would decrease monthly volume to 52 songs. The accounting department estimates that fixed costs would remain unchanged in total, and variable costs per song would remain unchanged if the volume were to drop to 52 songs per month. How would a price increase affect profits?
3.        c.            Assume that M. Anthony’s studio is operating at its normal volume of 60 songs per month. It has received a special request from a university to produce 30 songs that will make up a two-CD set. M. Anthony must produce the music next month or the university will take its business elsewhere. M. Anthony would have to give up normal production of 10 songs because it has the capacity to produce only 80 songs per month. Because of the need to produce songs on a timely basis, M. Anthony could not make up the production of those songs in another month. Because the university would provide its own musicians, the total variable cost (labor plus overhead) would be cut to $15,000 per song on the special order for the university. The university wants a discounted price; it is prepared to pay only $40,000 per song and believes a fee reduction is in order. Total fixed costs will be the same whether or not M. Anthony accepts the special order. Should M. Anthony accept the special order?
4.       d.            Refer to the situation presented in requirement (c) above. Instead of offering to pay $40,000 per song, suppose the university comes to M. Anthony with the following proposition. The university official says, “We want you to produce these 30 songs for us. We do not want you to be worse off financially because you have produced these songs. On the other hand, we want the lowest price we can get.” What is the lowest price that M. Anthony could charge and be no worse off for taking this order?

To determine

Calculate the number of songs that are needed to be produced for the break-even.

Answer to Problem 56P

The break-even point is 46 songs.

Explanation of Solution

Break-even point:

The breakeven point or BEP is that level of output at which the total revenue is equal to the total cost. The BEP means there are no operating income and no operating losses. The management keeps an eye on the breakeven point in order to avoid the operating losses.

Calculate the break-even point:

$\begin{array}{c}\text{Break-even point = }\frac{\text{Fixed costs}}{\text{Contribution margin per unit}}\\ =\frac{\$2,760,000(1)}{\$60,000\text{ (3)}}\\ =\text{ 46 songs }\end{array}$

Thus, the break-even point is 46 songs.

Working note 1:

Calculate the fixed costs:

$\begin{array}{c}\text{Fixed costs = Fixed cost per unit }\times \text{ Unit produced}\\ \text{= \$46,000 (2) }\times \text{ 60}\\ \text{= \$2,760,000}\end{array}$

Working note 2:

Calculate the fixed cost per unit:

$\begin{array}{c}\text{Fixed cost per unit = Fixed overhead + Marketing and administrative costs}\\ =\text{ \$21,000 + \$25,000}\\ \text{= \$46,000}\end{array}$

Working note 3:

Calculate the contribution margin per unit:

$\begin{array}{c}\text{Contribution margin per unit = Selling price (unit) - Variable cost (unit)}\\ \text{= \$80,000 - \$20,000}\\ \text{= \$60,000}\end{array}$

Working note 4:

Calculate the variable cost (unit):

$\begin{array}{c}\text{Variable cost (unit)}\text{}\text{ = }\left(\begin{array}{c}\text{Labor, including musicians and technicians }\\ \text{+ Variable overhead, including clerical support}\end{array}\right)\\ \text{= \$17,000 +}\text{}\text{\$3,000}\\ \text{= \$20,000}\end{array}$

To determine

Calculate the change in price affect the profit of the company.

Answer to Problem 56P

The change in profit is $40,000 in the case of the price increase.

Explanation of Solution

Operating profit:

The operating profit is the excess of total revenues over total expenses after adjusting for depreciation and taxes.

Calculate the change in the profit after the increase in price:

Particulars	Amount (60 songs)	Amount (52 songs)	Change
Revenue $\left(\text{Songs }\times \text{ Price per songs}\right)$	$4,800,000	$4,680,000	$120,000 lower
Less: variable costs $\left(\text{Songs }\times \text{ Variable cost per songs}\right)$	$1,200,000	$1,040,000	$160,000 lower
Contribution margin	$3,600,000	$3,640,000	$440,000 higher
Fixed costs	$2,760,000	$2,760,000	No change
Profit	$840,000	$880,000	$40,000 higher

Table: (1)

Thus, the change in profit is $40,000 in the case of the price increase.

To determine

Suggest whether Mr. M should accept the special offer or not.

Answer to Problem 56P

The change in profit is $150,000 in case of special order.

Explanation of Solution

Special order:

When the company gets a bigger order, then the usual order and the price of the unit is relatively lower than the price of normal units. Then this order is known as special order.

Calculate the change in profit:

Particulars	Amount (Status quo sales)	Amount (alternate)	Change
Revenue $\left(\text{Songs }\times \text{ Price per songs}\right)$	$4,800,000	$5,200,000	$400,000 lower
Less: variable costs $\left(\text{Songs }\times \text{ Variable cost per songs}\right)$	$1,200,000	$1,450,000	$250,000 lower
Contribution margin	$3,600,000	$3,750,000	$150,000 higher
Fixed costs	$2,760,000	$2,760,000	no change
Profit	$840,000	$990,000	$150,000 higher

Table: (2)

Thus, the change in profit is $150,000 in case of special order.

To determine

Calculate the change in case of special order.

Answer to Problem 56P

The change in price is $35,000.

Explanation of Solution

Special order:

When the company gets a bigger order, then the usual order and the price of the unit is relatively lower than the price of normal units. Then this order is known as special order.

Calculate the change in price:

$\begin{array}{c}\text{Price charged = Variable costs +}\text{}\text{ Contribution margin (forgone)}\\ \text{= \$15,000 + \$20,000 (5)}\\ =\text{ \$35,000}\end{array}$

Thus, the change in price is $35,000.

Working note 5:

Calculate the contribution margin per unit:

$\begin{array}{c}\text{Contribution margin = }\frac{\text{Contribution margin}}{\text{Number of songs}}\\ =\frac{\$600,000\text{ (6)}}{30}\\ =\text{ \$20,000}\end{array}$

Working note 6:

Calculate the contribution margin foregone:

Mr. M  has to foregone the contribution margin of 10 songs in order to produce the school’s songs.  Contribution margin  is calculated as follows:

$\begin{array}{c}\text{Contribution margin = Number of songs }\times \text{ Contribution margin}\\ \text{= \$10 }\times \text{ \$60,000}\\ \text{=\$600,000}\end{array}$