Activity 17 : « Cashflow » model – Analysing the solution of a model with a cashflow constraint.

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 20000€. Every month he withdraws 2000€ 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  

What are the total cashflow needs for month 1 (round off to a tenth) ?

What is the monthly interest rate of a loan (write in percentage) ?

Match the elements of the eqcash(M3) equation with the following definitions

+0.99*empt(m3)

- cash(m3)

4541.66666666667

- empt(m2)

-130*x(ble) -10*x(bett) -130*x(orge)

+ cash(m2)

What does this graph correspond to ?

By the end of the year, how much money does the farmer have in the bank (round off to a tenth) ?

Let us suppose that the interest rate is now 0%.

What does this reveal ?

What results can we expect from GAMS ?

ii. 0% Interest rate 
 

Change the interest rate to 0% and answer the questions.

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 ?

What are the total cashflow needs for month 1 (round off to a tenth) ?

Why is revfi equal to 0 when it is noted that the farmer borrows money from month 4 to month 11 ?

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.

Investment yields boost wheat cultivation, why is that ?

The cash variable is equal to zero. Why is that ?

Modèle solution : modelEco_cashFlow_investment.gms