Advice on how to answer these questions would be a big help. Thank you. Smiths\'

Question

Advice on how to answer these questions would be a big help. Thank you.

Smiths' Tree Farm, Inc., is doing well after its incorporation. Jake Smith, 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.

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? Please show work.

2. If Jake discounts the future price of the trees at 10% per year, what is the present value of their future prices? Please show work.

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. Please show work.

4. When should Jake sell the trees? Please show work.

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 $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 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%. Please show work.

Explanation / Answer

Please find below the detailed answer:

1. All his trees are 6 feet tall currently. Number of years before they become 8 feet tall = 3 years. During this time, the price of the 8 feet trees grows by 3% per year.

Current price of 8 feet trees = $34

So price of 8 feet trees in 3 years = 34 * (1+3%)^3 = 37.15

Similarly, number of years before they become 10 feet tall = 6 years. During this time, the price of the 10 feet trees grows by 3% per year.

Current price of 8 feet trees = $40

So price of 8 feet trees in 3 years = 40 * (1+3%)^6 = 47.76

Answer: Price of 8 feet trees = $37.15 and price of 10 feet trees = $47.76

2. Jake uses a disount rate of 10% per year.

So present value of 8 feet trees = 37.15 / (1+10%)^3 = 27.91

And present value of 10 feet trees = 47.76 / (1+10%)^6 = 26.96

Answer: Present value of 8 feet trees = $ 27.91 and present value of 10 feet trees = $26.96

3. Price of tree at age of 3 years = 24

Price of tree at age of 6 years = 37.15 (as this is the same as that of 8 feet trees as calculated earlier)

Let growth rate of trees between 3rd and 6th years be r%

So 24 * (1+r)(6-3) = 37.15

Or 24 * (1+r)3 = 37.15

Solving, we get r = 15.68%

Similarly, we can calculate for the growth rate between the 6th to 9th years also.

Price of tree at age of 6 years = 37.15

Price of tree at age of 9 years = 47.76 (as this is the same as that of 10 feet trees as calculated earlier)

Let growth rate of trees between 6th and 9th years be r%

So 37.15 * (1+r)(9-6)= 47.76

Or 37.15 * (1+r)3 = 47.76

Solving, we get r = 8.73%

Answer: Rate of growth between 3rd and 6th years = 15.68% and rate of growth between 6th and 9th years = 8.73%

4. Jake uses a discount rate of 10%. So he should sell before the rate of growth drops below 10%. As we can see, the rate of growth between 3rd and 6th years = 15.68% (>10%) and rate of growth between 6th and 9th years = 8.73% (<10%). So Jake should sell when his trees are 8 feet, i.e. in another 3 years time.

5. I am assuming there is a typo in the question and that the offer price is 280,000 (and NOT 28,000) as a price of 28,000 for 10,000 trees means an effective price of $2.8 per tree which cannot be possible as it is too low.

So an offer of $280,000 for 10,000 trees means an effective offer price of $28 per tree.

As we calculated in part 2, the present value of the trees 3 years from now = 27.91. As this is lower than what the landscape contractor is offering now (which is $28), Jake should accept the offer.

Hope this helped ! Let me know in case of any queries.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.