Present Value at Optimal Time to Sell

You own 100 acres of timberland, with young timber worth $20,000 if logged today. This represents 500 cords of wood at $40 per cord. After logging, the land can be sold today for $10,000 ($100 per acre). The opportunity cost of capital is 10%. You have made the following estimates:

(i) The price of a cord of wood will increase by 5% per year
(ii) The price of land will increase by 3% per year
(iii) The yearly growth rate of the cords of wood on your land are: years 1-2: 15%, years 3-4: 10%, years 5-8: 5%, years thereafter: 2%

What is the present value at the optimal time to sell and when does it occur?

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