You work for a firm that owns land for timber. You are tasked with finding the optimal age to cut the maple trees on the property to sell to Louisville Slugger to manufacture baseball bats. The earliest a tree can provide any commercial wood is when it is 10 inches in diameter, which is usually around 20 years old (footnote: this is a simplification of the actual process). Assume that when the tree is cut, you can get 20 cents per board foot in cash flow after expenses and taxes. Your discount rate is 7%. To simplify the analysis, ignore things like changes in quality of the timber with age, fluctuations in price, and the amount of land required per tree. You will own the land in perpetuity, and you can replant in the same area for $15 per tree.

At what age should the tree be cut? Thoroughly explain your reasoning. Use the information in the following table:

Age (years)	Diameter at Breast Height (DBH)	Number of 16 ft logs per tree	Board Feet per tree
20	10.0	0.5	4.36
21	10.2	0.55	4.99
22	10.4	0.6	5.66
23	10.6	0.65	6.37
24	10.8	0.7	7.12
25	11	0.75	7.92
50 (max height)	+ 0.2 a year forever 16	+ 0.05 per year until 50 years 2	=3.14*(DBH/24)^2*number of logs*16 44.66
51	16.2	2 (stops getting taller)	46.93

You may use excel to assist you in this problem. Copy-and-paste your excel table so that I can see it, and write out the equations (by hand) that you use to solve it. Do as much hand-written as you can.

Remember to clearly explain your reasoning at each step. This is a big part of this problem.

You may use 2 pages to solve this problem, but please do not turn in more unless it is absolutely necessary.