Length : around 30 minutes
During the “Cashflow” lesson, you wrote the model based on the following statement. Download the model (modelEco_cashFlow_1.gms) or use the one which you wrote, and run the model.
« A given farmer can grow wheat, sugar beet and barley. He has 100 ha and must determine the area dedicated to each crop, knowing that he wants to maximize his income. The fixed costs of his farm amount to 30500€ allocated monthly. His initial liquid assets amount to 30500€. Every month he withdraws 1200€ for his personal income.
His monthly costs per crop (phytosanitary products, material, fuel, maintenance, and fertilizer) are as follows :
| Monthly costs per crop (€) | ||||||||||||
| Month | M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | M9 | M10 | M11 | M12 |
| Wheat | 0 | 10 | 130 | 90 | 10 | 10 | 0 | 210 | 0 | 110 | 0 | 0 |
| sugar beet | 0 | 0 | 10 | 330 | 30 | 10 | 10 | 0 | 110 | 370 | 10 | 15 |
| Barley | 0 | 10 | 130 | 90 | 10 | 10 | 0 | 200 | 0 | 110 | 0 | 0 |
Wheat and barley are sold the month following the harvest (M8), in September (M9) at the price of 17€/q and 14€/q, respectively. Sugar beet is grown under contract and the payment is made in December at 38€/t.
Yields for wheat, sugar beet and barley are 70g/ha, 50q/ha and 72q/ha, respectively.
The farmer can borrow money from the bank on a monthly basis at an annual interest rate tx of 12%.. »
i. Answer the questions concerning the analysis of the solution 
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Question 1 of 7
1. Question
What are the total cashflow needs for month 1 (round off to a tenth) ?
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The farmer grows wheat and sugar beet. The monthly costs of these crops are equal to zero in month 1. However, the farmer withdraws 200€ a month and also has fixed costs of 30500/12 he needs to pay. Hence a total of 59.228*0 + 40.712*0 +2000+30500/12= 4541.7
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Question 2 of 7
2. Question
What is the monthly interest rate of a loan (write in percentage) ?
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0.12/12=0.01
12% is the annual rate, which means that each month the farmer pays 1% of the amount borrowed in the current month. -
Question 3 of 7
3. Question
Match the elements of the eqcash(M3) equation with the following definitions
Sort elements
- The cashflow of the current year
- The money borrowed this current year minus its cost
- The gross margins of crops (sales - costs)
- The repayment of the loan of the previous year
- Sum of the fixed costs and withdrawals
- The cashflow of the previous year
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- cash(m3)
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+0.99*empt(m3)
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-130*x(ble) -10*x(bett) -130*x(orge)
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- empt(m2)
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4541.66666666667
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+ cash(m2)
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Incorrect
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Question 4 of 7
4. Question
What does this graph correspond to ?
Correct
This graph corresponds to the cumulated gross margin per hectare of the sugar beet crop according to the months of the year. The sugar beet crop is recognisable because of high costs in months 4, 9 and 10 and because the proceeds of the sales get paid in December.
Incorrect
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Question 5 of 7
5. Question
By the end of the year, how much money does the farmer have in the bank (round off to a tenth) ?
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Incorrect
The income corresponds to the difference between gross margins and fixed costs and interest expenses, i.e. 63424.930-2629.348-30500=30295.582. But this does not represent what the farmer has in the bank since he has initial liquid assets and withdraws 2000€ every month, i.e. 24000€ in a year. By the end of the year he has 30295.582+24000-20000=26295.582€ which corresponds to the cash of month 12. Indeed, the epmt and cash variables represent the monthly income of the farmer.
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Question 6 of 7
6. Question
Let us suppose that the interest rate is now 0%.
What does this reveal ?
Correct
Incorrect
A 0% interest rate means that the farmer can borrow money and pay back the same amount the following month. He is therefore not constrained by interest expenses.
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Question 7 of 7
7. Question
What results can we expect from GAMS ?
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Incorrect
If the loan costs nothing then the interest expenses do not impact the income negatively. They have no more direct impact on the income. The farmer can borrow as much as he wants and is only constrained by land and rotation.
ii. 0% Interest rate
Change the interest rate to 0% and answer the questions.
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Question 1 of 3
1. Question
The farmer now only grows sugar beets. This crop is paid for in December, which means that its monthly gross margin is negative from month 1 to month 11. Yet the farmer only borrows money from month 4 to month 11. Why is that ?
Correct
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The farmer has an initial cashflow of 2000€. Total cashflow needs amount to the sum of the withdrawals, of crop and fixed costs. When growing 100 hectares of sugar beet, from month 1 to month 3, the initial cashflow is enough to cover monthly costs. This can easily be verified :
3*2000+3*30500/12+100*(0+0+10) =14625<20000
However, from month 4 onwards, the cashflow is not enough -
Question 2 of 3
2. Question
What are the total cashflow needs for month 1 (round off to a tenth) ?
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The farmer must pay in month 1 : 1/12th of fixed costs and 2000€ of family income. He does not have any crop costs for the first crop costs for sugar beet crops occur in month 3.
2000+30500/12+100*0=4541.7 -
Question 3 of 3
3. Question
Why is revfi equal to 0 when it is noted that the farmer borrows money from month 4 to month 11 ?
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Incorrect
Revfi is equal to 0 because the interest rate is 0%.
Modèle solution : modelEco_cashFlow_rateTax.gms
iii. Investments 
The interest rate of the loan is 12% again. The farmer now has the possibility of investing the money he has on a monthly basis. The annual interest rate of the loan is 0,02.
Add a variable plac(m) and modify the model in order to introduce the possibility of making the money yield a profit. Note the effect it has on the results, and answer the questions.
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Question 1 of 2
1. Question
Investment yields boost wheat cultivation, why is that ?
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Wheat is less profitable than sugar beet but yields a faster profit for it is sold in September, contrary to sugar beet which is sold in December. The farmer can therefore invest the money from the sales in order to receive additional financial income.
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Question 2 of 2
2. Question
The cash variable is equal to zero. Why is that ?
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The cash variable which corresponds to his cashflow is always equal to zero for if the farmer lacks cashflow, he borrows until he reaches a stable situation, and if he has positive cashflow he invests it all in order to earn an income from his investment.
Modèle solution : modelEco_cashFlow_investment.gms
