Toys: WakTek is a manufacturer of electronic toys, with a specialty in remote controlled miniature vehicles. WakTek is considering the introduction of a new product, a remote-controlled hovercraft called WakAtak. Preliminary designs have already been produced at a cost of $2 million. To introduce a marketable product requires the building of a dedicated production line at a cost of $12 million. In addition, before the product can be launched a prototype must be built and tested for safety. The prototype can be crafted in the absence of a production line, at a cost of $0.5 million, but if the prototype is created after the production line is built then its cost is negligible (you can treat it as zero). There is uncertainty over what safety rating WakAtak will get. This could have a significant impact on demand, as a lower safety rating will increase the minimum age required of users. Safety testing costs $1 million. The outcome of the safety test is estimated to have a 65% chance of resulting in a minimum user age of 8 years, a 30% chance of a minimum age of 15 years, and a 5% chance that the product will be declared unsafe-in which case it could not be sold at all. (The cost of improving the safety rating of a finished design is deemed prohibitive.) After successful safety testing the product could be launched at a cost of $1.5 million. There is also uncertainty over demand, which will have a crucial impact on the eventual profits. Currently the best estimate is that the finished product, if available to the 8- to 14-year demographic, has a 50-50 chance of resulting in profits of either $10 million or $5 million from that demographic. Similarly there is a 50-50 chance of either $14 million or $6 million in profits from the 15-year-or-above demographic. These demand outcomes are independent across the demographics. The profits do not take into account the costs previously defined; they are measured in expected present-value terms, so they are directly comparable with the costs.

a. What is the optimal plan of action for WakTek? What is the current expected economic value of the WakAtak project?

b. Suddenly it turns out that the original estimate of the cost of safety testing was incorrect. Analyze the sensitivity of WakTek's optimal plan of action to the cost of safety testing.

c. Suppose WakTek also has the possibility of conducting a market survey, which would tell it exactly which demand scenario is true. This market research costs $1.5 million if done simultaneously for both demographics and $1 million if done for only one demographic. How, if at all, is your answer to part (a) affected?

d. Suppose that demand is not independent across demographics after all, but instead is perfectly correlated (i.e., if demand is high in one demographic then it is for sure high in the other one as well). How, if at all, would that change your answer to part (c)?