"A farmer must choose to either plant corn or soybeans each year. The cost of planting corn is $63,000, and the cost of planting soybeans is $49,000. Each crop can either produce a good or bad yield. The farmer's revenue from a good yield of corn is $107,000 and the revenue from a bad yield of corn is $61,000. The farmer's revenue from a good yield of soybeans is $93,000 and the revenue from a bad yield of soybeans is $44,000. The farmer wishes to decide what to plant for year 1 and year 2.
The probability of a good yield of soybeans is 0.69 in each year (regardless of what was planted in the previous year).
- The probability of a good yield of corn is 0.62 in year 1. If corn is planted in year 1, the probability of a good yield of corn in year 2 is 0.31 (whether or not the yield from year 1 is good or bad).
- If soybeans are planted in year 1 and the soybean yield is good, the probability of a good yield of corn in year 2 is 0.77. If soybeans are planted in year 1 and the soybean yield is bad, the probability of a good yield of corn in year 2 is 0.62.
The farmer wants to maximize his expected net present value. His MARR is 14.3%. Assume that the costs of planting occur at the end of the previous year and the revenues occur exactly one year later. For example, if the farmer chooses to plant corn in year 1 and the yield is good and plants soybean in year 2 and the yield is bad, he has the following cash flow:
- Year 0: -$63,000
- Year 1: +$107,000 (good yield of corn) - $49,000 (planting soybeans for year 2) = $58,000
- Year 2: $44,000 (bad yield of soybeans)
For this scenario (good corn, bad soybeans), the farmer's net present value = $21,423.
Enter the expected NPV of the best alternative that the farmer should select. It may be helpful to draw and solve a decision tree to determine what the farmer should plant for year 1 and for year 2, and the farmer's decision on what to plant in year 2 may depend on what occurs in year 1."