Question

A biomass plantation operator can invest $1,000 today to plant a new crop of trees, which, it is estimated, can be sold at a net gain (sales harvesting costs) of $10,000 in 40 years. De- termine whether this is profitable if a rate of return of 7%/yr is desired.

(b) The trees can be harvested early at reduced yield: the net profit is then $250T per $1,000 initial investment, for T in years. To the nearest whole year, at what T is the rate of return largest?

(c)While the trees are growing, the farmer is paid $200/yr for carbon sequestration; but at the end of 40 years, the trees are, contrary to initial expectations, burned, releasing all of their carbon as CO2. At a discount rate of 5%/yr, calculate and comment on the time-zero present value to the farmer of carbon sequestration if he must return the $8,000 at the 40-year mark.

biomass plantation operator can invest $1,000 today to plant a new crop of trees, which, it is estimated, can be sold at a net gain (sales harvesting costs) of $10,000 in 40 years. De- termine whether this is profitable if a rate of return of 7%/yr is desired. (b) The trees can be harvested early at reduced yield: the net profit is then $250T per $1,000 initial investment, for T in years. To the nearest whole year, at what T is the rate of return largest? (c)While the trees are growing, the farmer is paid $200/yr for carbon sequestration; but at the end of 40 years, the trees are, contrary to initial expectations, burned, releasing all of their carbon as CO2. At a discount rate of 5%/yr, calculate and comment on the time-zero present value to the farmer of carbon sequestration if he must return the $8,000 at the 40-year mark.

Answer 1

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(a) Determine the amount after 40 years with 7%/yr interest. 40 7 =10001+ 100 40 =1000(1.07) = 14,974.45 The gain (profit) is, 14,974.45 –1,000 => 13,974.45 The gain (profit) is $13,974.45 it is profitable. (b) Determine the value of T. 1000 1+ 100 -1000 = 250 (1.07)ʻ =1.25 T = 3.29 years