1. You run a farm that consists of 100 acres of land. The yearly output depends

Question

1. You run a farm that consists of 100 acres of land. The yearly output depends on the weather conditions (good, normal or bad). At the beginning of each year you decide how much corn and/or wheat to plant (you are allowed to not plan anything as well). The following table describes the yearly profit per acre for each crop and weather condition:

Crop

Good Weather

Normal Weather

Bad Weather

Corn

$100

$20

-­$50

Wheat

$80

$40

-­$70

For any year, the probability of good weather is 30%, normal weather is 50% and bad weather is 20%. Ignore inflation and assume MARR=0.

a.) What is the expected net present value (NPV) of this project? What would you plant? How much of each crop would you use?

b.) A meteorologist offers you a prediction for the weather. Assume that the prediction is correct. What is the highest price you would be willing to pay for this information?

Crop

Good Weather

Normal Weather

Bad Weather

Corn

$100

$20

-­$50

Wheat

$80

$40

-­$70

Explanation / Answer

a. The expected return on corn per acre = 100*0.3 + 0.5*20 +0.2* -50 = $30

The expected return on wheat per acre = 80*0.2 +40*0.5 +0.2*-70 = $30

Hence it does not make a difference wheather you go for wheat or corn based on the expected return

Hence the NPV of wheat = NPV of corn = 30*100 = $3000

b. The profit that you can generate based on correct wheather prediction .

Hecne you could increase your profit or prevent your loss based on weather predictions

For Good wheather the profit you can make based on prediction = 100-80 = $20/acre and $2000 for 100 acres

For Normal wheather the profit you can make based on prediction = 40-20 = $20/acre and $2000 for 100 acres

For Bad wheather the you can reduce loss based on prediction = 70-50 = $20/acre and $2000 for 100 acres

Hence the highest price you can pay for making the meterological prediction is $2000

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