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. Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 5.62% and the risk-free rate is 7%. 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. $ ______millions Investment Timing Option: Option Analysis No Timing Option: Initial investment at t = 0 (in millions) $20.00 Annual expected cash flow (in millions) $3.00 Number of years cash flow expected 20 Project cost of capital 13% Timing Option: Initial investment at t = 1 (in millions) $20.00 Number of years cash flow expected 20 Probability that tax will be imposed 50% Annual CF if tax will be imposed, Years 2 to 21 $2.20 Probability that tax will not be imposed 50% Annual CF if tax will not be imposed, Years 2 to 21 $3.80 Projected cost of capital 13% PV of CFs (in millions) at t = 1, if tax will be imposed $15.45 PV of CFs (in millions) at t = 1, if tax will not be imposed $26.69 PV of Expected CFs (in millions) at t = 1, with timing option $21.07 Value of Option Using Black-Scholes Model: Number of years until expiration expires 1 Variance of project's expected rate of return, σ2 5.62% Risk-free rate of return, rRF 7.00% Strike price (in millions) of underlying investment at t = 0, X $20.00 Formulas Price (in millions) of underlying investment, P = #N/A d1 = #N/A N(d1) = #N/A d2 = #N/A N(d2) = #N/A Value of option (in millions) = #N/A

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. Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 5.62% and the risk-free rate is 7%. 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. $ ______millions Investment Timing Option: Option Analysis No Timing Option: Initial investment at t = 0 (in millions) $20.00 Annual expected cash flow (in millions) $3.00 Number of years cash flow expected 20 Project cost of capital 13% Timing Option: Initial investment at t = 1 (in millions) $20.00 Number of years cash flow expected 20 Probability that tax will be imposed 50% Annual CF if tax will be imposed, Years 2 to 21 $2.20 Probability that tax will not be imposed 50% Annual CF if tax will not be imposed, Years 2 to 21 $3.80 Projected cost of capital 13% PV of CFs (in millions) at t = 1, if tax will be imposed $15.45 PV of CFs (in millions) at t = 1, if tax will not be imposed $26.69 PV of Expected CFs (in millions) at t = 1, with timing option $21.07 Value of Option Using Black-Scholes Model: Number of years until expiration expires 1 Variance of project's expected rate of return, σ2 5.62% Risk-free rate of return, rRF 7.00% Strike price (in millions) of underlying investment at t = 0, X $20.00 Formulas Price (in millions) of underlying investment, P = #N/A d1 = #N/A N(d1) = #N/A d2 = #N/A N(d2) = #N/A Value of option (in millions) = #N/A

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Question

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.

Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 5.62% and the risk-free rate is 7%. 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.

$ ______millions

Investment Timing Option: Option Analysis

No Timing Option:
Initial investment at t = 0 (in millions)	$20.00
Annual expected cash flow (in millions)	$3.00
Number of years cash flow expected	20
Project cost of capital	13%

Timing Option:
Initial investment at t = 1 (in millions)	$20.00
Number of years cash flow expected	20
Probability that tax will be imposed	50%
Annual CF if tax will be imposed, Years 2 to 21	$2.20
Probability that tax will not be imposed	50%
Annual CF if tax will not be imposed, Years 2 to 21	$3.80
Projected cost of capital	13%

PV of CFs (in millions) at t = 1, if tax will be imposed	$15.45
PV of CFs (in millions) at t = 1, if tax will not be imposed	$26.69
PV of Expected CFs (in millions) at t = 1, with timing option	$21.07

Value of Option Using Black-Scholes Model:
Number of years until expiration expires	1
Variance of project's expected rate of return, σ²	5.62%
Risk-free rate of return, r_RF	7.00%
Strike price (in millions) of underlying investment at t = 0, X	$20.00
		Formulas
Price (in millions) of underlying investment, P =		#N/A
d₁ =		#N/A
N(d₁) =		#N/A
d₂ =		#N/A
N(d2) =		#N/A
Value of option (in millions) =		#N/A

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