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5 Figure 1. Finding the maximum NPV for a teak plantation in Hawaii for different stumpage rates and different discount rates. 8,000 6,000 4,000 2,000 0 (2,000) (4,000) Years from establishment Internal rate of return (IRR) calculations As discussed above, the internal rate of return (IRR) is the discount rate at which the NPV equals zero. You may calculate IRR using the spreadsheet by trying different interest rates until the NPV reaches zero. For the three timber prices in the example, the IRRs would be as follows: Internal rates of return at three stumpage prices Stumpage (\$/mbf) IRR (%) 1, , , low discount, low value low discount, med value low discount, high value high discount, low value high discount, med value high discount, high value Remember that these are real rates net of inflation; to compare with other investments, you would have to add anticipated rates of inflation to each. You will notice that NPV reaches a maximum in each scenario and then declines (Figure 1). That is because tree growth rate is assumed to decline gradually over time, and after a time growth does not keep up with interest rates. You may also note that the maximum NPV with 7% comes earlier, at year 30, than the maximum NPV with 4%, which comes later at year 35. This illustrates that higher discount rates will result in shorter rotation periods. The effect of different stumpage prices (same discount rate) Unlike changes in discount rate, changes in stumpage price do not affect the rotation length. If stumpage price increases over time, however, the rotation becomes longer. This is because the rate of increase serves as an offset to the discount rate. The break-even price is the price at which the NPV at a given discount rate goes to zero. You may calculate a break-even price by entering various prices in the spreadsheet until the NPV becomes zero. For the example given, break-even prices are as follows: Break-even prices at two discount rates Discount rate (%) Break-even price/mbf 4 \$552 7 \$1292 Conversion to equivalent annual income Let us say you plan to grow teak for a fixed period of 35 years and you would like to know your equivalent annual earnings for that period. With a discount rate of 4% and a stumpage price of \$1,000/mbf, your NPV is \$2,713 (see Table 1). To convert this to an annual amount, you determine your EAI as follows: EAI = ( )35 ( ) 35 1 This means that you would receive an amount equivalent to annual income of \$145/acre/year for 35 years. You may then compare this amount to another alternative source of annual income. The equivalent annual income may also be calculated using the payment function (PMT) on a computer spreadsheet. Along with the discount rate and number of years in the rotation, you should use the NPV as the loan amount. The payment function calculates a payment that is the same as the equivalent annual income. Land expectation value (LEV) The net present value of the tree farm is \$2,713/acre. The future value at 4% interest rate and 35 years is therefore 2,713 (1.04) 35 = 10,706 = 145 The net present value of this and all other future rotations, 5

7 Appendix 1. Sample costs used in financial calculations for a small teak plantation (10 50 acres) on the Hamakua coast of Hawaii. Establishment Management plan 50 \$/acre Site preparation 200 \$/acre Seedlings 2 \$/seedling No. seedlings 435 seedlings/acre Planting 150 \$/acre Fencing 500 \$/acre Herbicide application 160 \$/acre Second herbicide application 160 \$/acre Fertilizer application 165 \$/acre Operations \$/acre/year Weed control up to year Fertilizer up to year 4 70 Maintenance starting year 5 25 Management costs 0 Land costs 0 Property taxes 0 Appendix 2. Hypothetical yields of a teak plantation on the Hamakua coast of Hawaii. Yields represent total volume of the plantation if clearcut in the given year. Age Yield (mbf/acre) Thinning revenue No. stems cut at year stems/acre Price/stem at year 5 \$0 No. stems cut at year stems/acre Net price/stem at year 15 \$1 7

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