Tuck School of Business at Dartmouth

Modeling for Insight

Unsolved Problems

Ill-structured problems are everywhere once you learn to recognize them. One of our favorite sources is the news programs on National Public Radio. Almost any day you listen in you will hear at least one good problem described. Most of these arise from policy debates in Washington. For example:

Here are some small problems that can provide further practice in modeling.

  1. Anticipating Demand for Passports
    Congress is considering a new law that would require U.S. citizens to carry a passport when traveling to Canada and the Caribbean. Build a model to forecast the number of applicants for new passports in the first 18 months following passage of the bill.

  2. Making a Market in Movie Royalties
    Movie stars typically negotiate contracts with production companies that provide them with royalties (perhaps at different rates) on all products related to a movie. This includes movie showings, DVD sales, action figures, games, and so on. Some movies and related products have a very short life while others generate significant revenues for decades. Before a movie is released the uncertainty as to the level of sales it will enjoy spans several orders of magnitude.

    Tom Cruise is a little strapped for cash as he finishes up the movie Top Gun. Build a model to determine how much you would be willing to offer him in a lump sum in exchange for all future royalties on that movie. Of course, to make a deal he must accept your offer.

  3. Is the Market for Used Games Profitable?
    GameStop is a video game retailer that specializes in store sales but has a small online business as well. They are considering entering the used game market. Under this plan, used games can be returned to the store for store credit of around $7 per game. The store would then ship the game to a refurbishment center where the game would be upgraded and packaged for resale. The price for refurbished games would be about $14. Initial estimates are that the margins on this business will be about 50%. Build a model to explore the attractiveness of this new line of business to GameStop.

  4. When to Pay Points on a Mortgage
    Residential mortgages are offered in a bewildering variety of loan structures. Fifteen and 30-year maturities are available. Interest rates can be fixed, adjustable, or a combination of the two (for example, a 15-year adjustable with a fixed rate for the first two years). The amortization of the loan principal can follow the conventional level pattern or utilize a balloon payment, in which the borrower pays a large proportion of the principal at the end of the loan. Some loans only require interest payments for as long as 5 or 10 years.

    One of the most difficult aspects of choosing a loan is deciding whether to pay points. Points are simply additional costs paid by the borrower at the beginning of the loan. They are calculated as a percentage of the principal. The effect of paying points is to reduce the interest payments and thereby reduce the nominal interest rate on the loan.

    Build a model that can be used to help a borrower decide whether or not to pay points. Your model should take into account the option to refinance the loan at a later date if interest rates decline.

Here are some case-length problems that can be used in modeling courses.

  1. Humber Tunnel Authority (PDF)
  2. Monetta Financial Services (PDF)
  3. Kerkorian versus Chrysler (PDF)
  4. Strategic Customer Targeting Using Legal Collections (PDF)
    Data Dictionary for Legal Collections Case (PDF)
    Legal Collections Data (XLS)