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Crop Optimization

1. Suppose a farmer can currently obtain $100,000 in annual revenues by growing the highest value crop. If the farmer invests in erosion control and soil rebuilding next year's crop will have the same monetary value. If there is no provision for rebuilding soil or controlling erosion, the soil quality will diminish and each future yield will decrease by $1,000 a year. Erosion control and soil rebuilding cost $15,000.
a) If the interest rate is 5% should the farmer invest in erosion control and rebuilding? (Remember that the decrease in yield is an annual decrease - each year in the future, the yield will be worth $1,000 less).
b) What if the interest rate is 10%?
c) What are some possible explanations for why a farmer might not invest in erosion control and rebuilding?

Solution Preview

PV of infinite stream of cash flows is given by

PV = C / (R) where C is the annual cash flow, R is the interest rate

a) PV = -1000 / (5%) = -20,000

Since ...