Quantitative Analysis

Lisa, a perceptive student in the MBA program, noted the popularity of the HP$-12$c calculators

used by students in her finance classes. She also saw that certain business school professors

doggedly carried these calculators around for decades like some religious talisman. She saw an

opportunity and decided to start a company selling accessories that support the HP$-12$c lifestyle

and make the lives of HP$-12$c lovers more enjoyable and fulfilling.

Lisa is considering several products to include in her initial line:

Carrying case: Made from genuine leather and spandex. Comes in a variety of colors. Clips

to belt or purse to keep the HP$-12$c always close at hand.

The carrying case would be sold to the end consumer for $$49\mathrm{.}99.$ Lisa will not sell directly to the

consumer but will use a wholesaler who will sell to a retailer $($e$.$g$.,$ university bookstores$).$ The

retailer's margin is $45\%,$ and the wholesaler's margin is $15\%.$ The fixed cost of manufacturing

the cases is $$280,000$ and the variable costs are $$7\mathrm{.}25$ per case. Lisa is considering an advertising

budget of $$300,000.$ Miscellaneous variable costs $($e$.$g$.,$ shipping and handling$)$ paid by Lisa's

company come to $$0\mathrm{.}10$ per case. Lisa has decided to use salespeople to encourage adoption by

wholesalers, and the salespeople will be paid entirely by a $10\%$ commission on the

manufacturer's $($i$.$e$.,$ Lisa's$)$ selling price. The product manager's salary is $$75,000.$

What is the price the manufacturer $($Lisa$\text{'}$s company$)$ charges the wholesaler?

What is the manufacturer's $($Lisa$\text{'}$s$)$ unit margin $($contribution$/$profit per unit excluding

fixed costs$)$ for the cases $($in $$)?$

How many units must be sold to turn a profit?

After conducting an extensive market$-$sizing study, Lisa's best guess is that shewill likely sell

$82,000$ cases in her first year. This projection is based on the above mentioned price, advertising,

and sales support. Lisa is considering several possible marketing plan changes to increase her

sales over the $82,000$ baseline.

How much profit will Lisa's company earn if she sells $82,000$ cases?

Strategy $1$: Increasing advertising expenditures

If Lisa doubles her advertising budget, Calculate the total sales volume $($in units$)$ needed

to maintain the current estimated profit $($#$4).$

Strategy $2$: Lowering the price.

Calculate the total sales volume $($in units$)$ needed to maintain the current estimated

profit $($#$4)$ if Lisa lowers the price to the wholesalers to $$12\mathrm{.}00.$

Strategy $3$: Increasing the sales commission.

Calculate the total sales volume $($in units$)$ needed to maintain the current estimated

profit $($#$4)$ if Lisa increases the sales force's commission to $15\%.$