Petz, an Irish pet food and accessories retailer, is considering expanding into the UK. The initial expansion would be into a Birmingham, a mid-sized city in the UK. Due to the high set-up costs and small scale of the project it has been estimated that this project has a negative NPV of (1,000,000). However, if the expansion is successful, Petz will expand further in that region of the UK. Based on current forecasts the cost of this further expansion would be 9,000,000 and the present value of future cash flows from the project are expected to be 8,000,000. However this market is highly volatile and this forecast is subject to an annual standard deviation of 40%. A decision to expand into broader UK market would be made 3 years after the initial launch in Birmingham. The current risk-free rate of return is 2%. There are no costs associated with delaying during the 3-year period and Petz cannot expand into the wider UK market without first launching in the Birmingham market. Required: (i) Briefly outline why Discounted Cash Flow Analysis is not appropriate to value this proposed project. (ii) (iii) Explain how the real option available to Petz could be valued using the Black-Scholes model and map the project characteristics onto the Black-Scholes variables. Should Petz expand into the Birmingham market, clearly explain your answer