The problem provides information about a company's assets and debts. It asks us to calculate the value of the equity (patrimoine), the profit (résultat) given the capital, the expenses (charges) given the revenue (produits), and the profit with a different capital. We are given: Total assets (Total des biens) = 56,000,000 F Total liabilities (Total des dettes) = 37,500,000 F We need to determine: a) Equity (Patrimoine) b) Profit (Résultat) when Capital = 20,000,000 F c) Expenses (Charges) when Revenue (Produits) = 45,000,000 F d) Profit (Résultat) with a Capital of 15,000,000 F

1. Problem Description

The problem provides information about a company's assets and debts. It asks us to calculate the value of the equity (patrimoine), the profit (résultat) given the capital, the expenses (charges) given the revenue (produits), and the profit with a different capital. We are given:

Total assets (Total des biens) = 56,000,000 F

Total liabilities (Total des dettes) = 37,500,000 F

We need to determine:

a) Equity (Patrimoine)

b) Profit (Résultat) when Capital = 20,000,000 F

c) Expenses (Charges) when Revenue (Produits) = 45,000,000 F

d) Profit (Résultat) with a Capital of 15,000,000 F

2. Solution Steps

a) Equity (Patrimoine):

The accounting equation is:

$Assets = Liabilities + Equity$

Therefore, $Equity = Assets - Liabilities$

$Equity = 56,000,000 F - 37,500,000 F = 18,500,000 F$

b) Profit (Résultat) when Capital = 20,000,000 F:

We need to use the accounting equation again.

$Assets = Liabilities + Capital + Retained\ Earnings (Résultat)$. Retained Earnings is also known as the accumulated profit. In the beginning of year N, the previous year's Retained Earnings is 0 since the capital is 20,000,000 F.

$56,000,000 F = 37,500,000 F + 20,000,000 F + Résultat$

$Résultat = 56,000,000 F - 37,500,000 F - 20,000,000 F = -1,500,000 F$

c) Expenses (Charges) when Revenue (Produits) = 45,000,000 F:

$Profit = Revenue - Expenses$

From part (b), we know Résultat = -1,500,000 F.

$-1,500,000 F = 45,000,000 F - Expenses$

$Expenses = 45,000,000 F + 1,500,000 F = 46,500,000 F$

d) Profit (Résultat) with a Capital of 15,000,000 F:

$Assets = Liabilities + Capital + Retained\ Earnings(Résultat)$

$56,000,000 F = 37,500,000 F + 15,000,000 F + Résultat$

$Résultat = 56,000,000 F - 37,500,000 F - 15,000,000 F = 3,500,000 F$

3. Final Answer

a) Equity (Patrimoine) = 18,500,000 F

b) Profit (Résultat) when Capital = 20,000,000 F = -1,500,000 F

c) Expenses (Charges) when Revenue (Produits) = 45,000,000 F = 46,500,000 F

d) Profit (Résultat) with a Capital of 15,000,000 F = 3,500,000 F