# Calculate NPV and Apply Black-Scholes Model

Need help calculating the NPV and applying Black-Scholes model to estimate value of option. Please explain how to complete each step and calculate the answers.

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%.

a. What is the project's net present value?
b. 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%. Using decision tree analysis, should Kim proceed with the project today or should it wait a year before deciding?
c. Use the Black-Scholes model to estimate the value of the option. (Hint: Assume the variance of the project's rate of return is 6.87% and the risk-free rate is 8%).

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Manal Elkhoshkhany, MBA

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Active since 2005

BA, Ain Shams University, Cairo Egypt
MBA, California State University, Sacramento

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