1. A timber company is considering planting trees on a plot of land. The investment would have the following characteristics: = Cost of planting = $1300 Volume of wood in year 0 = 1000 cubic feet Cost of harvesting one cubic foot of wood = $1 Price per cubic foot of wood = $2 Dicount rate = 5% No opportunity to replant the forest a. The CEO of the company is concerned that he will only be CEO for the next 4 years and doesn't care about profits after that (alternatively, you can think of him as having a discount rate of 5% per year for the next 4 years and then an infinite discount rate after that). If wood grows at a rate of 2% per year in the first 10 years, how much wood will there be in year 1? How much wood will there be in year 4? Will the CEO decide the plant the forest? If so, when will he harvest the wood? b. However, if the company plants and then waits until year 11, the wood will grow at a rate of 15% per year for 10 years (so 10 years of growth at 2% per year followed by 10 years of growth at 15% per year). How much wood will there be in year 10? How much wood will there be in year 20? Should the shareholders of the company want to plant the forest (assume that the shareholders have a 5% discount rate in all periods)? What year would the shareholders want to harvest the wood? Assume that the amount of wood in the forest will increase at a rate of 1% per year after year 20. C. The local community gets an annual benefit of $500/year for every year that there is at least 1200 cubic feet of wood in the forest. What is the present discounted value of the benefit to the community if the CEO gets to decide whether to plant the forest? What is the present discounted value of the benefit to the community if the shareholders get to decide? Assume that the land will not be planted by another company if this company chooses not to plant and that the community has a discount rate of 5%