13.16 Growth Options
You are considering an investment in a Christmas tree farm overtwo years. The fam already has trees planted a year ago, and thesetrees grow each year by the following factors.
Year1 : growth 1.6, year2 : growth 1.5
The price of the trees follows a binomial lattice with u = 1.25and d=0.80. As the trees grow older, the value of the investment ingeneral will increase. However, if the trees get too big, they areles attractive, so a three-year rotation appears to be a typicallife-cycle for this type of Christmas tree. The interestrate(risk-free) is constant at continuous 6%. It costs $400,000each year ----payable at the beginning of the year----to lease theforest land. The initial value of the one-year old trees is$1million (assuming they were harvested immediately) you can cutthe trees at the beginning of the Christmas season (say, December1st) of any year and then not pay rent after that. Withrent of $400,000 per year, find the best cutting policy(when tocut) and the value of the investment opportunity with the bestcutting policy.
13.16 Growth Options
You are considering an investment in a Christmas tree farm overtwo years. The fam already has trees planted a year ago, and thesetrees grow each year by the following factors.
Year1 : growth 1.6, year2 : growth 1.5
The price of the trees follows a binomial lattice with u = 1.25and d=0.80. As the trees grow older, the value of the investment ingeneral will increase. However, if the trees get too big, they areles attractive, so a three-year rotation appears to be a typicallife-cycle for this type of Christmas tree. The interestrate(risk-free) is constant at continuous 6%. It costs $400,000each year ----payable at the beginning of the year----to lease theforest land. The initial value of the one-year old trees is$1million (assuming they were harvested immediately) you can cutthe trees at the beginning of the Christmas season (say, December1st) of any year and then not pay rent after that. Withrent of $400,000 per year, find the best cutting policy(when tocut) and the value of the investment opportunity with the bestcutting policy.
