Question

Conceptual Analysis of Real Options The destruction that Hurricane
Katrina brought to the Gulf Coast in 2005 devastated the city of New Orleans as
well as the Mississippi Gulf Coast. The burgeoning casino gambling industry along
the Mississippi coast was nearly destroyed. CGC Corporation owns one of the
oldest casinos in the Biloxi, Mississipi, area, and it was not destroyed by Katrina’s
tidal surge because it is located several blocks off the beach. Because of the neartotal
destruction of many of the gambling properties located along the beach, CGC
is considering the opportunity to make a major renovation in its casino. The
renovation would transform the casino from a second-tier operation into one of the
top attractions along the Mississippi Gulf Coast. The question that the firm faces
involves placing a value on the opportunity to renovate the property.
CGC’s analysts estimate that it would cost $50 million to do the renovation.
However, based on the uncertainties associated with the redevelopment of the
region, the firm’s financial analyst estimated that the casino, under the current
conditions, would be valued at only $45 million. Alternatively, CGC could continue
to operate the casino, in which case it expects to realize an annual rate of return of
10% on the value of the investment. Moreover, the estimated return of 10% is
highly uncertain. In fact, the volatility (standard deviation) in this rate of return is
probably on the order of 20%, while the risk-free rate of interest is only 5%.
a. What is the NPV of renovation of the property if the renovation is
undertaken immediately?
b. What is the value of having the option to renovate in the future? (Hint: You
can assume that the option never expires.)

The right to develop the casino can be thought of as a American Call Option with infinite life. Immediate exercise of this option results in a negative NPV (-50 m + 45 m = -5 million). However, the real estate development option has a value of $3.317 million because of the inherent uncertainty in the prospects of the casino industry in that region. This uncertainty suggest that it may be worth waiting.

b
Call Option Value		Casino Development Option Value
V*		Critical Value
Call (Infinite life option)
NPV*		Critical NPV value

Answer 1

(a)

CGC’s analysts estimate that it would cost $50 million to do the renovation.

Based on the uncertainties associated with the redevelopment of the region, the firm’s financial analyst estimated that the casino, under the current conditions, would be valued at only $45 million.

So the NPV of renovation of the property if the renovation is undertaken immediately is -$ 5 million (outflow) [- $50 million (outflow) + $45 million (inflow) ].

(b)

CGC could continue to operate the casino, in which case it expects to realize an annual rate of return of 10% on the value of the investment. The volatility (standard deviation) in this rate of return is probably on the order of 20%, while the risk-free rate of interest is only 5%.

Based on the uncertainties associated with the redevelopment of the region, the firm’s financial analyst estimated that the casino, under the current conditions, would be valued at only $45 million.

	Particulars	Amount
a	Annual rate of return on the value of the investment	0.1
b	Volatility (standard deviation) in this rate of return	0.02
	(0.2*0.1)
c	Minimum annual rate of return on the value of the investment (a-b)	0.08
d	Risk-free rate of interest	0.05
e	Incremental minimum annual rate of return on the value of the investment (c-d)	0.03
f	Value of the investment	45000000
	The value of having the option to renovate in the future (e*f)	1350000

The value of having the option to renovate in the future is $ 1,350,000