$2.$ The Wharton Company retails two products, a standard and a deluxe version of a luggage carrier. The budgeted statement of comprehensive income is as follows:

Budgeted statement of comprehensive income

Standard Carrier Deluxe Carrier Total

Units sold $150,00050,000200,000$

Revenues at $$20$ and $$30$ per unit $$3,000,000$ $$1,500,000$ $$4,500,000$

Variable costs at $$14$ and $$18$ per unit $2,100,000900,0003,000,000$

Contribution margin at $$6$ and $$12$ per unit $$900,000$ $$600,0001,500,000$

Fixed costs $1,200,000$

Operating income $$300,000$

Required

$(1)$ Compute the breakeven point in units, assuming that the planned revenue mix is maintained.

$(2)$ Compute the breakeven point in units $($a$)$ if only standard carriers are sold and $($b$)$ if only deluxe carriers are sold.

$(3)$ Suppose $200,000$ units are sold, but only $20,000$ of them are deluxe. Compute the operating income. Compute the breakeven point if these relationships persist in the next period. Compare your answers with the original plans and the answer in requirement $1.$ What is the major lesson of this problem?

Requirement $1.$

Compute the breakeven point in units, assuming that the planned sales mix is attained.

Begin by determining the sales mix. For every $1$ deluxe unit$($s$)$ sold

$3$ standard units are sold.

Begin by determining the sales mix. To determine the sales mix, divide the standard units by the deluxe units.

SALES MIX $=$ Standard units $/$ deluxe units

SALES MIX$=150,000/50,000$

SALES MIX$=3$

Determine the formula used to calculate the breakeven point when there is more than one product sold. Then, enter the amounts in the formula to calculate the breakeven point.

Total fixed costs $/$ Contribution Margin per bundle $=$ Breakeven point in bundles

Now, determine the contribution margin of the bundle. Standard Carrier Deluxe Carrier

Contribution margin Contribution margin Contribution margin

$($ Sales mix x per unit $)+($ Sales mix x per unit $)=$ of the bundle

$(3$ x $$6)+(1$ x $$12)=30$

Next, use the formula below to calculate the breakeven point in bundles.

Total Contribution margin Breakeven point

fixed costs $/$ per bundle $=$ in bundles

$$1,200,000/30=40,000$ bundles

Now, knowing the breakeven point in bundles, calculate the breakeven point for the standard and deluxe units using the sales mix found in each bundle.

Ratio to breakeven point in bundles x Breakeven point in bundles $=$ Breakeven point in carriers

Standard $3$ x $40,000=120,000$

Deluxe $1$ x $40,000=40,000$

Requirement $2.$ Compute the breakeven point in units $($a$)$ if only standard carriers are sold and $($b$)$ if only deluxe carriers are sold. We do not need to take sales mix into account in these scenarios. Simply use the

breakeven point in units formula to calculate the amounts.

$($a$)$ If only standard carriers are sold, the breakeven point is $200,000$ units. $(1,200,000/6=200,000)$

$($b$)$ If only deluxe carriers are sold, the breakeven point is $100,000$ units. $(1,200,000/12=100,000)$

Requirement $3.$ Compute the operating income if $200,000$ units are sold but only $20,000$ of them are deluxe.

Standard Carrier Deluxe Carrier Total

Units sold $20,000200,000$

Revenues at $$20$ and $$30$ per unit

Variable costs at $$14$ and $$18$ per unit

Contribution margin

Fixed costs

Operating income