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4. Estimating the inputs using the Black- Scholes option pricing model in the option analysis of the investment timing option Option analysis involves gathering significant amounts of information, synthesizing the data, and using the data in models applied in option analysis. Consider the case of Smith and Thomas Co.: Smith and Thomas Co. is considering a project for a new cloud-based online storage system for companies and individuals to back up their data. The cost of the project is $45 million, but the future cash flows depend on how this new cloud- based online storage will compete with existing companies that offer online data backup. The company believes that this project has a strong selling feature but is uncertain that it would earn cash flows as projected. The team proposing this project has come up with the following data: AnnualCasll Demand Probability Flow High 045 $40 million Average 035 $25 million Low 0.20 $10 million Project's cost of capital 13% Life of project Three years 52-week Treasury note 5% The project team also noted that the company has an option to wait for one year in order to see its competitors' positions and observe how the market responds. This will help in getting more information about market demand and in figuring out which set of cash flows will occur. Analysts used different approaches to evaluate the project, but the management team insists that the BIackScholes option pricing model (0PM) will help them make a more informed decision. The model requires five inputs: (1) the risk-free rate; (2) the time until the option expires; (3) the strike price; (4) the current price of the stock, which in this case would be a proxy for the value of the underlying asset; and (5) the variance of the project's expected return. You need to calculate both the value of the underlying asset in the project and its rate of return. For Smith and Thomas Co., the underlying asset is the project itself. The current value of the project will be theError! Filename not specified. value of its expected cash flows. Based on the data given, calculate the value of the project, its return, and the standard deviation of the returns (using the direct method) if the company decides to wait for a year. (Cash flow values in the table are in millions. Round your answers to two decimal places). Return = PV Cash Flows, - K K PriceYear0 Probabili r PV Cash PV Cash Year0) / Probabili ty (Pij) x GEOFKE .Z flows flows PriceYear0 ty (Pjj) x PV Cash OfAN. EK ONA . HK (t=1) (t=0) Year0 Return flows, Of A W . Error! Error! Error! Error! Error! Filename Filename Filename Filename Filename UI A . not not not not not specified. specified. specified. specified. specified. Error! Error! Error Error! Error! O UNEA Filename Filename Filename Filename Filename un w . not not not not not specified. specified. specified. specified. specified. O Error! Error! Error! Error! Error! Filename Filename Filename Filename Filename ON . not not not not not specified. specified. specified. specified. specified. Expected Error! return Filename (t=1): not specified. Standard Error! deviation Filename of not returns: specified. Expected Error! Value of Filename PVs not (t=1): specified. Expected Error! Value of Filename PVs not (t=0): specified. Analysts will use these values in the Black-Scholes model, which is represented by the following formula: V = P[N(di)] - Xe-TRFt[N(d2)]P[N(d1)] -Xe-rRFt[N(d2)] Based on the data collected and results from the calculations, estimate the input values to be used in the Black-Scholes OPM: TRFIRF = Risk-Free Error! Filename not specified. Interest Rate it = Time until = Error! Filename not specified. Option Expires XX = Cost to = Error! Filename not specified. Implement the Project PP = Current Value = Error! Filename not specified. of the Project 6202 = Variance of the = Error! Filename not specified. Project's Rate of Return NdiNdi = Cumulative N ({In (Error! Filename not specified. ) + Normal [TRFIRE + (022022)]t} / (ot1/2at1/2)) Distribution Function of didl Nd2Nd2 = Cumulative N (didi - Error! Filename not specified. Normal Distribution Function of dad2