P2. Pinarello Pinarello is building the capacity to produce its newest model carbon fiber bicycle frame. The frame is designed to be lightweight, rigid laterally (to facilitate efficient transfer of power), compliant vertically (to allow for dampening of road vibration), and compatible with the latest component technologies. Because component technologies evolve quite rapidly, the frame will be produced and sold for only one season. Because it takes 6-8 months to develop the tooling that is required to produce the frame, Pinarello needs to decide how much capacity to build long before they begin receiving orders from retailers-i.e., under a good amount of demand uncertainty. Around the time the tooling will be developed, Pinarello will have received enough orders from retailers to effectively know the full amount of demand for the new frame. At that time, they will produce and sell the minimum of demand volume and production capacity. They will never product a unit that they do not sell, but they may have capacity that goes unused. The timeline is shown below. Pinarello chooses its volume (K) of capacity. 6-8 months Pinarello observes the demand volume (d) K units of production capacity are ready to be used. Pinarello produces and sells a quantity S = Min{d,K} Time Building capacity is expensive. There is a fixed cost of $8,000,000 for designing the molds. This does not depend upon the number of molds and has to be paid if Pinarello builds even a single unit of capacity (it can be avoided if they choose to not build any capacity). In addition, each unit of capacity costs $600. Therefore, the total cost of building K units of capacity is $8,000,000+ $600 x K. After the capacity has been built, it costs an additional $300 for materials and labor to produce a frame. Pinarello sells each frame for $3,000. Production capacity has no value at the end of the selling season. At the time that Pinarello must choose how much capacity to build, its probabilistic assessment of the demand is as shown below: Scenario Probability (%) Demand 1 15 5,000 2 20 7,500 3 30 10,000 4 20 12,500 5 15 15,000 (a) If Pinarello purchases 10,000 units of capacity, what will be the expected amount that it will produce and sell? What will the expected amount of contribution margin that it will earn? How much will they have spent on capacity? What will be its expected profit? (b) Assume that demand turned out to be lower than the capacity Pinarello chose to build. By how much would each unit of unneeded capacity reduce Pinarello's profit (compared to not building it)? Now assume that demand turned out to be higher than the capacity Pinarello chose to purchase. By how much would each unit of unsatisfied demand reduce Pinarello's profits (compared to having the capacity to satisfy that demand)? Is K = 10,000 is the optimal capacity? (c) How much capacity would you recommend that Pinarello builds, and what would be their expected profit with that capacity? (d) Pinarello has been approached by a marketing research firm that claims that by using its machine learning technologies to analyze click patterns in social media, the marketing research firm can accurately forecast the demand far enough in advance that Pinarello can "know" the actual demand realization at the time they have to choose their capacity. How much should Pinarello be willing to pay for this? Why? (e) Suppose that the fixed cost for designing the molds were $12,000,000 instead of $8,000,000. How would this affect your answer to part (c)? (Assume Pinarello has not purchased the marketing research firm's service from part (d).) (f) Would the higher fixed cost for designing the molds from part (e) change the amount that Pinarello should be willing to pay for the marketing research firm's services (i.e., for knowing the realization of demand before deciding how much capacity to build)? Why?