Assignment task:
Chime-A-Verse (CAV) is a Taiwanese manufacturer of custom alarm clocks that recite verses as wake-up call. CAV is the sole supplier for Vazood-E-Muhammad (VEM), a Saudi retailer who sells alarm clocks reciting verses from Holy Quran to visitors in Mecca during the month of Ramadan. VEM must order these upscale designer clocks from CAV several months in advance. At the time of ordering the demand is uncertain and is estimated to be Normally distributed with a mean and standard deviation of 1000 and 300, respectively. VEM buys each clock at a wholesale price of 50 Riyals and sells it at a retail price of 100 Riyals. Excess clocks are sold at a discount price of 20 Riyals each after Id-ul-Fitr, the end of the Ramadan season. CAV spends NT$235(30 Riyals) to manufacturer and ship a clock to Mecca.
Real Options Supply Contract: Instead of wholesale contract, suppose CAV (the manufacturer) offers the following deal to VEM (the retailer): Ahead of Ramadan, VEM buys Q call options at unit cost C. Each call option gives VEM the right (but not the obligation) to buy one alarm clock from CAV at a unit exercise price of X after VEM observes the demand. In effect, VEM makes CAV produce Q alarm clocks ahead of Ramadan, by paying a price C for each unit. After the demand is known, VEM pays an additional price X to buy each clock, but the quantity is limited up to Q. Note that there is no fixed "wholesale price" for the real option contract.
a) If CAV offers an option price C = 8 Riyals and an exercise price, X = 40 Riyals, how many call options should VEM buy in anticipation of Ramadan?
b) Does this real option contract achieve channel coordination? If not, can you propose another set of parameters (C and X) that will achieve channel coordination? Is your answer unique (i.e., will your classmates arrive at the same result)? If not, how will you decide which set of parameters to offer in your contract?