Forever Young Laboratories Inc. $($FYL$)$ was started a few years ago by a group of engineers to design and develop power mobility device $($PMDs$)$ for the regional countries. FYL has invented and patented two models of PMDs: Joy and Happy. As the technology involved in the manufacturing process is both complex and expensive, FYL has been beset by high fixed costs. Bowen, the company$$s founder, is particularly concerned and has arranged a conference call over Zoom to discuss about profitability. He illustrated that average unit cost will fall with increase in production volume. He reasons that this was due to the company$$s fixed cost base. He extracted FYL data to produce the following table:

Projected Production Volume of $10,000$ units:

Average Cost Per Joy PMD$*($$$)-435$

Average Cost Per Happy PMD$*($$$)-355$

Projected Production Volume of $50,000$ units:

Average Cost Per Joy PMD$*($$$)-325$

Average Cost Per Happy PMD$*($$$)-315$

$*$Defined as the total of fixed and variable manufacturing costs, divided by the production volume.

FYL currently has a production facility with a capacity of producing $60,000$ PMDs per year. Bowen explains that if production reaches full capacity, FYL$$s profits will soar as all sales proceeds would not have to recover fixed costs $($like rent, depreciation, fixed admin and selling expenses$)$ and will contribute entirely to profits. As such, he believes presenting and analysing all product $($manufacturing$)$ costs as average unit cost can help management better control costs

and achieve its profits targets. It is his belief that fixed costs is bad for business.

Your team is the management accounting group, and shortly after the conference call, your Controller called a meeting to address the situation. She wants to know how profitability changes with production. The current production and sales volume is $30,000$ units of Joy PMD and $20,000$ units of Happy PMD respectively. Joy sells at an average selling price of $$600$ per unit and Happy, $$700$ per unit.

Required:

$($a$)$ Apply cost$-$volume$-$profit analysis to calculate the break$-$even point in units for each PMD sold by FYL$.$ Other non$-$manufacturing fixed costs amounted to $$2,000,000$ per year.

$($b$)$ Explain if Bowen is correct about product costs. In particular, discuss if product costs can be all presented as unit variable costs for decision making, and whether fixed costs is bad for business as claimed by Bowen.