Question

Gönye&Cetvel Architects is a leading Turkish firm with operations in architectural design, construction, and real estate finance. This company competed with several other rivals in the Gigantic Tuzla Mall Project and won the project competition by presenting the most popular mall design. Thanks to this victory, Gönye&Cetvel Architects now has the right to build the Gigantic Tuzla Mall. For the sake of simplicity, we assume that this mall will be built over the next year. The construction of the mall will cost 190 million USD. Due to economic slowdown and low number of shoppers residing in Tuzla, such a mall is worth roughly 180 million USD today. If the economy recovers, the number of shoppers in Tuzla will increase and the mall would be worth 320 million USD a year from today. If economic slowdown gets worse, the mall would be worth 150 million USD a year from today. Gönye&Cetvel Architects can borrow and lend money at the risk free annual effective rate of 5%. Today, a local competitor named Dayioglu Insaat has offered Gönye&Cetvel Architects 20 million USD for the right to build the Gigantic Tuzla Mall. Should Gönye&Cetvel Architects accept this offer and sell the right to build the mall? Use a two-state model to value this real option.

Answer 1

the right to build office is similar to call option

because company will exercise the option to build if value increases

s=current price of building 180

k=cost to construct building 190

return on land if values increases ={(320-180)/180}

=77.77778%

return on land if value decreases ={(150-180)/180}

=-16.6667%

now value of real call option

if price increases max(320-190,0)=130

if price decreases max (150-190,0)=0

now to find risk neutral probability

we will use followoing equation

RISK FREE RATE = PROB(INCREASE)*(return increase)+PROB(DECREASE)(return decrease)

5%= (x)(77.7778%)+(1-x)(-16.6667%)

5%= (x)(77.7778%)-16.6667%+(x)(16.6667%)

21.6667%= (x)(94.4444%)

x= 0.2294 PROBABILITY OF INCREASE

1-x= 0.7706 PROBABILITY OF DECREASE

SO THE RISK NEUTRAL : VALUE OF CALL OPTION

VALUE OF CALL OPTION= (PROB(INCREASE)*PAYOFF+PROB(DECREASE)*PAYOFF)/(1+RISK FREE RATE) VALUE OF CALL OPTION= ((0.2294*130)+(07706*0))/(1+0.05)

VALUE OF CALL OPTION=28.40

DO NOT ACCEPT THE OFFER AS AMOUNT IS LESS THAN VALUE OF CALL OPTION.