Question

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 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%.

Kim expects the cash flows to be $3 million a year, but it recognizes that the cash flows could actually 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 a 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%. Use the Black-Scholes model to estimate the value of the option. Assume that the variance of the project's rate of return is 0.0654 and that the risk-free rate is 8%. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to three decimal places.

Use computer software packages, such as Minitab or Excel, to solve this problem.

$   million

Answer 1

Value of the option to delay:

1). The value of the underlying asset is the Present Value (PV) of the future cash flows from the project (ignoring the initial investment) if the project is started today.

Cash flows if tax is not imposed = 3.8 million for 1-20 years:

PV(scenario: Tax not imposed): PMT = 3.8; N = 20; rate = 13%, CPT PV. PV = 26.69 million

Cash flows if tax is imposed = 2.2 million for 1-20 years:

PV(scenario: Tax not imposed): PMT = 2.2; N = 20; rate = 13%, CPT PV. PV = 15.45 million

Expected PV of cash flows from the project = sum of (probability*PV of cash flows) = (50%*26.69) + (50%*15.45) = 21.07 million

2). Strike price is the initial required investment in the project which, in this case, is 20 million

3). Volatility = standard deviation = (Variance)^0.5 = (0.0654)^0.5 = 25.6%

4). Time until expiry for the option is the 1-year period at the end of which the company will have definite information about the proposed tax implementation.

Applying the Black-Scholes model, as follows:

Inputs:
Current stock price (S)	21.07
Strike price (K)	20.00
Time until expiration(in years) (t)	1.000
volatility (s)	25.6%
risk-free rate (r)	8.00%

Formulae:
d1 = {ln(S/K) + (r +s^2/2)t}/(s(t^0.5))
d2 = d1 - (s(t^0.5))
N(d1) - Normal distribution of d1
N(d2) - Normal distribution of d2
C = S*N(d1) - N(d2)*K*(e^(-rt))

Output:
d1	0.6445
d2	0.3888
N(d1)	0.7404
N(d2)	0.6513
Call premium (C)	3.5756

The value of the option to delay is $3.576 million.