Answered

Ajimatanraeje Nigeria Limited provides the following information relating to its accounts for three years as shown in the table below:

\begin{tabular}{|c|c|c|c|}
\hline Year & Capital (N) & Profit (N) & Returns on Capital (\%) \\
\hline 2023 & 975,000 & & 45 \\
\hline 2022 & 585,000 & 117,000 & \\
\hline 2021 & 650,000 & & 35 \\
\hline
\end{tabular}

Required:
(a) Calculate profits for the year 2021 and 2023.
(b) Calculate returns on capital for the year 2022.
(c) Calculate the percentage increase in profit between the years 2022 and 2023.
(d) Calculate the percentage decrease in profit between the years 2021 and 2022.
(e) Calculate the increase in capital between the years 2022 and 2023.
(f) Calculate the decrease in capital between the years 2021 and 2022.

Hints: Show all formulas and workings.



Answer :

GinnyAnswer
Certainly! Let's go through each part of the request step-by-step and show all the formulas and workings.

### (a) Calculate profits for the year 2021 and 2023

To calculate profit, we use the formula:
[tex]\[ \text{Profit} = \left(\frac{\text{Returns on Capital (\%)}}{100}\right) \times \text{Capital} \][/tex]

For 2021:
[tex]\[ \text{Returns on Capital (2021)} = 35\% \][/tex]
[tex]\[ \text{Capital (2021)} = 650,000 \][/tex]

[tex]\[ \text{Profit (2021)} = \left(\frac{35}{100}\right) \times 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = 0.35 \times 650,000 \][/tex]
[tex]\[ \text{Profit (2021)} = 227,500 \][/tex]

For 2023:
[tex]\[ \text{Returns on Capital (2023)} = 45\% \][/tex]
[tex]\[ \text{Capital (2023)} = 975,000 \][/tex]

[tex]\[ \text{Profit (2023)} = \left(\frac{45}{100}\right) \times 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 0.45 \times 975,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 438,750 \][/tex]

### (b) Calculate returns on capital for the year 2022

To calculate returns on capital, we use the formula:
[tex]\[ \text{Returns on Capital (\%)} = \left(\frac{\text{Profit}}{\text{Capital}}\right) \times 100 \][/tex]

For 2022:
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]

[tex]\[ \text{Returns on Capital (2022)} = \left(\frac{117,000}{585,000}\right) \times 100 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = 0.2 \times 100 \][/tex]
[tex]\[ \text{Returns on Capital (2022)} = 20\% \][/tex]

### (c) Calculate the percentage increase in profit between year 2022 and 2023

To calculate the percentage increase, we use the formula:
[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \][/tex]

Between 2022 and 2023:
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]
[tex]\[ \text{Profit (2023)} = 438,750 \][/tex]

[tex]\[ \text{Percentage Increase} = \left( \frac{438,750 - 117,000}{117,000} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = \left( \frac{321,750}{117,000} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = 2.75 \times 100 \][/tex]
[tex]\[ \text{Percentage Increase} = 275\% \][/tex]

### (d) Calculate the percentage decrease in profit between year 2021 and 2022

To calculate the percentage decrease, we use the formula:
[tex]\[ \text{Percentage Decrease} = \left( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \right) \times 100 \][/tex]

Between 2021 and 2022:
[tex]\[ \text{Profit (2021)} = 227,500 \][/tex]
[tex]\[ \text{Profit (2022)} = 117,000 \][/tex]

[tex]\[ \text{Percentage Decrease} = \left( \frac{227,500 - 117,000}{227,500} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = \left( \frac{110,500}{227,500} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = 0.485 \times 100 \][/tex]
[tex]\[ \text{Percentage Decrease} = 48.5\% \][/tex]

### (e) Calculate the increase in capital between year 2022 and 2023

To calculate the increase in capital, we use the formula:
[tex]\[ \text{Increase in Capital} = \text{Capital (New Year)} - \text{Capital (Old Year)} \][/tex]

Between 2022 and 2023:
[tex]\[ \text{Capital (2023)} = 975,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]

[tex]\[ \text{Increase in Capital} = 975,000 - 585,000 \][/tex]
[tex]\[ \text{Increase in Capital} = 390,000 \][/tex]

### (f) Calculate the decrease in capital between year 2021 and 2022

To calculate the decrease in capital, we use a similar formula:
[tex]\[ \text{Decrease in Capital} = \text{Capital (Old Year)} - \text{Capital (New Year)} \][/tex]

Between 2021 and 2022:
[tex]\[ \text{Capital (2021)} = 650,000 \][/tex]
[tex]\[ \text{Capital (2022)} = 585,000 \][/tex]

[tex]\[ \text{Decrease in Capital} = 650,000 - 585,000 \][/tex]
[tex]\[ \text{Decrease in Capital} = 65,000 \][/tex]

Summarizing all results:
1. Profit (2021): N227,500
2. Profit (2023): N438,750
3. Returns on Capital (2022): 20%
4. Percentage Increase in Profit (2022 to 2023): 275%
5. Percentage Decrease in Profit (2021 to 2022): 48.5%
6. Increase in Capital (2022 to 2023): N390,000
7. Decrease in Capital (2021 to 2022): N65,000

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