Richards' Tree Farm, Inc. Richards' Tree Farm, Inc., is doing well after its incorporation. Jake Richards, president, chief of operations, and majority shareholder, currently has a planting of 10,000 three-year-old Japanese dogwood trees in a recently introduced pink-flowered variety. This type of tree can be sold at a higher price than the more common white-flowered variety. The trees are now 6 feet tall on average and can be sold for $24 each. At present, 8-foot trees are priced at $34 and 10-foot trees at $40. Landscape contractors avoid trees larger than 10 feet tall because they are difficult to transplant successfully. With average weather, the 6-foot trees will be 8 feet tall in another three years and 10 feet tall in six years. Jake has to make financial decisions almost everyday. Today's decision involves present value and future value computations, which Jake learned as a student at Oregon State University. He wants to know if he should sell the trees immediately at 6 feet tall, three years from now at 8 feet tall, or six years from now at 10 feet tall. In your initial response to the topic you have to answer all 5 questions. 1. Because if inflation, Jake expects the price at which he can sell the trees to increase by 3% per year. What price does he expect to receive if he keeps the trees until they reach 8 feet or 10 feet tall? You should show your work! Please explain your answer. 2. If Jake discounts the future price of the trees at 10% per year, what is the present value of their future prices? You should show your work! Please explain your answer. 3. Using the time value of money equation, compute the growth rate of the trees between the third year and the sixth year and between the sixth year and the ninth year. You should show your work! Please explain your answer. 4. When should Jake sell the trees? Please explain your answer. 5. A major landscape contractor who has bid successfully on a large-scale Boston beautification and urban greening project has offered to buy all 10,000 flowering dogwood trees at a price of $280,000, payable immediately. However, the contractor does not need the trees for three years. If Jake accepts, he will be obliged to deliver 10,000 trees three years from today. If anything should happen to his own crop, he would need to buy trees on the open market at the prevailing price, which might be higher or lower than the price estimated in Question 1. Should Jake accept the offer if his required rate of return is 10%? Hint: What is the present value of the price he expects to receive for the trees three years in the future? Discount the price at 10%. You should show your work! Please explain your answer. MINI-CASE Richardses' Tree Farm, Inc.: The Continuing Saga Richardses' Tree Farm, Inc. is doing well after its incorporation. Jake Richards, president, chief of operations, and majority shareholder, currently has a planting of 10,000 three-year-old Japanese dogwood trees in a recently introduced pink-flowered variety. Richards can sell this type of tree at a higher price than the more common white-flowered variety. The trees are now 6 feet tall on average and can command $24 each. At present, Richards has priced 8-foot trees at $34 and 10-foot trees at $40. Landscape contractors avoid trees larger than 10 feet tall because they are dif- ficult to transplant successfully. With average weather, the 6-foot trees will be 8 feet tall in three years and 10 feet tall in six years. Jake has to make financial decisions almost every day. Today's decision involves present value and future value computations, which Jake learned as a student at Oregon State University. He wants to know if he should sell the trees immediately at 6 feet tall, three years from now at 8 feet tall, or six years from now at 10 feet tall. Size Age Current Market Value 6' 3 years $24.00 8' 6 years $34.00 10' 9 years $40.00 Questions This mini-case is available in MyFinanceLab. 1. Because of inflation, Jake expects the price at which he can sell the trees to increase by 3% per year. What price does he expect to receive if he keeps the trees until they reach 8 feet or 10 feet tall? 2. If Jake discounts the future price of the trees at 10% per year, what is the present value of their future prices? 3. Using the time value of money equation, com- pute the growth rate of the trees between the third year and the sixth year and between the sixth year and the ninth year. 4. When should Jake sell the trees? 5. Challenge question. A major landscape contractor who has bid successfully on a large-scale Boston beautification and urban greening project has offered to buy all 10,000 flowering dogwood trees at a price of $28,000, payable immediately. However, the contractor does not need the trees for three years. If Jake accepts, he will be obliged to deliver 10,000 trees three years from today. If anything should happen to his own crop, he would need to buy trees on the open market at the prevail- ing price, which might be higher or lower than the price estimated in Question 1. Should Jake accept the offer if his required rate of return is 10%? Hint: What is the present value of the price he expects to receive for the trees three years in the future? Discount the price at 10%. 4 Binomial trees Problem 4.1 (2 points) Consider the multi-period binomial model with two periods: t {0, 1, 2}. Consider values u = 1.2 and d = 0.9. The periodic continuously compounded risk-free rate is r = 0.04, and the periodic contin- uously compounded dividend rate of the risky asset is 8=0.02. Assume that the initial risky asset price is So = 100. What is the unique time-0 price of an at-the-money European call op- tion which does not generate arbitrage opportunities? What is, for each respective tree node, the replicating portfolio compo- sition for this call option?