Excel Online Structured Activity: Investment Timing Option: Option Analysis Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an initial investment of $20 million. Kim expects that the hotel will produce positive cash flows of $3 million a year at the end of each of the next 20 years. The project's cost of capital is 13%. While Kim expects the cash flows to be $3 million a year, it recognizes that the cash flows could, in fact, be much higher or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a 50% chance that the tax will be imposed, in which case the yearly cash flows will be only $2.2 million. At the same time, there is a 50% chance that the tax will not be imposed, in which case the yearly cash flows will be $3.8 million. Kim is deciding whether to proceed with the hotel today or to wait 1 year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $20 million. Assume that all cash flows are discounted at 13%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below X Open spreadsheet Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 8.34% and the risk-free rate is 6%. Enter your answer in millions. For example, an answer of $1.22 million should be entered as 1.22, not 1,220,000. Do not round intermediate calculations. Round your answer to two decimal places. million $ B 2 No Timing Option: Initial investment at t 0 (in millions) $20.00 5 $3.00 Annual expected cash flow (in millions) Number of years cash flow expected 6 20 7 13% Project cost of capital 8 Timing Option: Initial investment at t 1 (in millions) 9 10 $20.00 Number of years cash flow expected 11 20 12 Probability that tax will be imposed 50% 13 $2.20 Annual CF if tax will be imposed, Years 2 to 21 Probability that tax will not be imposed 14 50% 15 $3.80 Annual CF if tax will not be imposed, Years 2 to 21 16 Projected cost of capital 13% 17 18 $15.45 PV of CFs (in millions) at t = 1, if tax will be imposed 19 $26.69 PV of CFs (in millions) at t = 1, if tax will not be imposed 20 $21.07 PV of Expected CFs (in millions) at t 1, with timing option 21 Value of Option Using Black-Scholes Model: Number of years until expiration expires Variance of projec's expected rate of return, o Risk-free rate of return, rRF 22 23 1 24 8.34% 25 6.00% 26 $20.00 Strike price (in millions) of underlying investment att 0, X 27 Formulas 28 Price (in millions) of underlying investment, P d1 N(d1) d2 #N/A 29 #N/A 30 #N/A 31 #N/A 32 N(d2) Value of option (in millions) #N/A 33 #N/A
