Keeping Time

Founded nearly $50$ years ago by Alfned Letier$-$Smith, Beautinul Clocks specializes in developing and marketing a diverse line of ligge omannental clocks for the finest bomes. Tasies have changed over the years, but the company has prospered by continually updating its product line to satisfy its affluent clientele. The LesterSmith family continues to own a majority share of the company and the grandchildren of Alfred Lester$-$Smith now bold several of the top managerial positions. One of these grandchildren is Meredith Lester$-$Smith, the new CEO of the company.

Meredith feels a great responsibility to maintain the family herituge with the company. She realizes that the company needs to continue to develop and market exciting new products. Since the $50$th anniversary of the founding of the company is rapidly approaching, she has decided to select a particularly special new product to launch with great fanfure on this annivernary. But what should it be$?$ As she pooders this crocial decision, Merodith's thoughts go back to the magnificeat grandfather clock that her grandparents had in their home many years ago. She had admired the myjesty of that clock as a child. How about launching a modem version of this clock?

This is a difficult decision. Meredith realizes that grandfather clocks now are largely out of style. However, if she is so nostalgic about the memory of the grandfather clock in her grandparents' home, woulda't thero be a considerable number of other relatively wealthy couples with similar memories who would welcome the prestige of adding the grandeur of a beautifilly designed limited$-$edition grandfather clock in their bome? Maybe. This also would highlight the heritage and continuity of te company. It all depends on whether there would be enough sales potential to make this a profitable product.

Meredith had an excellent management science course as part of her MBA prognm in college, so she realizes that break$-$even malysis is needed to help make this decision. With this in mind, ine instructs several staff members to investigate this prospective product further, including developing estimates of the relared costs and revenues as well as forecasting the potential sales.

One month later, the preliminary estimates of the relevant finuncial figures come back. The cost of designing the grandfather clock and then setting up the production facilities to produce this product would be approximately $$250,000.$ There would be only one production run for this limited$-$edition grandfather clock. The additional cost for each clock produced would be roughly $$2,000.$ The marketing department estimates that their price for selling the clocks can be successfully set at thout $$4,$$$00$ apiece, but a firm forecast of bow many clocks can be sold at this price has not yet been obtained. However, it is believed that the sales likely would reach into three digits.

Meredith wants all these numbers pinned down considerably further. However, she foels that some analyis can be done now to draw preliminary conclusions.

a$.$ Assuming that all clocks produced are soid, develop a spreadsheet model for estimating the profit or loss from prodacing any particular number of clocks.

b$.$ Use this spreadsheet to find the break$-$even point by trial and exror.

c$.$ Develop the corresponding mathematical expression for the estimated profit in terms of the number of clocks produced.

d$.$ Use a graphical procedure to find the break$-$even point.

e$.$ Use the algebraic procedure to find the break$-$even point.

A fairly relinble forceast now has been obtained indieating that the company would be able to sell $300$ of the limited$-$edition grfiffather clocks, which appcars to be enough to justify introdu this new product. However, Meredith is concerned that this tonclusion might change if more accurate extimates were wailable for the various costs and revenues. Therefore, she wants what$-$if analysis done on these estimates. Perform whatIf analysis by independently investigating each of the following questions.

f$.$ How large can the cost of designing this product and setting up the production facilities be before the grandfather clocks cease to be profitable?

$8.$ How large can the production cost for each additional elock be before the grandfather clocks cease to be profitable?

h$.$ If both of the costs ideatified in parts $f$ and $g$ were $50\%$ larger than their initial estimates, would producing and selling the grandfather clocks still be profitable?

How small can the price for selling each clock be before the grandfather clocks cease to be profitable?

Now suppose that $300$ grandfather clocks are produced but only $200$ are sold.

Would it still be profitable to produce and sell the grandfather clocks under this circumstance?

Additional Case

An additional case for this chapter is also available at the University of Western