Problem #$1$

You have just been promoted to product manager for the Harry Hat Company's brand of hats called The Megan. The hat is currently selling at a retail price of $$30\mathrm{.}00.$ The hats are sold at boutiques in major metropolitan areas. Retail margins on the product are $40\%,$ while wholesalers take a $20\%$ margin.

Harry Hat and its direct competitors sell a total of $300$ million hats annually; The Megan has $30\%$ share of this market. Variable manufacturing costs for The Megan are $$2\mathrm{.}25$ per unit. Fixed manufacturing costs are $$950,000.$ The advertising budget for The Megan is $$10,000,000.$ The Megan sales reps are paid a $9\mathrm{.}5\%$ commission on dollar sales. Shipping costs, breakage, insurance, and so forth are $$4\mathrm{.}35$ per unit.

What is the manufacturer's unit selling price for The Megan?

How many units does The Megan sell annually?

What is the per unit variable cost for The Megan?

What is the unit contribution? What is the contribution margin?

What is The Megan' break$-$even in units? In dollars?

What market share does The Megan need to break even?

What is The Megan' profit at their current level of sales?

Industry demand is expected to increase to $500$ million units next year. You are still the Marketing manager for The Megan and are considering raising your advertising budget by an additional $$15$ million.

$8.$ If the advertising budget is raised, how many units will The Megan have to sell to break even?

$9.$ How many units will The Megan have to sell in order for it to achieve the same dollar profit that it did last year?

$10.$ What will The Megan market share have to be next year for its dollar profit to be the same as this year?