Answer :
Sure! Let's take it step-by-step to solve each part of the question.
### 2.1 Communication Costs Calculation
We know the following:
- Communication costs for 2016 are R32,187.
- The communication costs decreased by 4,402% from 2015 to 2016.
To find the cost for 2015, we can set up the equation:
[tex]\[ \text{comm\_cost\_2016} = (\text{comm\_cost\_2015}) \times \left(1 - \frac{4402}{100}\right) \][/tex]
Given that such a large percentage decrease makes it odd, we interpret it as:
[tex]\[ \text{comm\_cost\_2016} = (\text{comm\_cost\_2015}) \times \left(1 - 44.02\right) \][/tex]
Since the communication costs for 2016 are [tex]\( \text{cost}_{2016} = -32,187 \)[/tex]:
[tex]\[ -32187 = (\text{comm\_cost\_2015}) \times -43.02 \][/tex]
[tex]\[ \text{comm\_cost\_2015} = \frac{-32187}{-43.02} \][/tex]
Calculate the communication cost for 2015:
[tex]\[ \text{comm\_cost\_2015} \approx 748.25 \][/tex]
Rounding it to the nearest thousand rand:
[tex]\[ \text{comm\_cost\_2015} \approx 1000 \][/tex]
So, the communication costs for 2015 to the nearest thousand was R1000.
### 2.2 Expected Increase in Costs and Impact on Profit
- The current costs for consumables in 2016 is R582,823.
- The current costs for product testing materials in 2016 is R54,252.
- The SANBS expects a 17.5% increase in these costs.
Using the percentage increase formula:
[tex]\[ \text{new amount} = \text{current amount} \times (1 + \text{percentage increase}) \][/tex]
For consumables:
[tex]\[ \text{new amount} = 582823 \times (1 + 0.175) \][/tex]
[tex]\[ \text{new amount} \approx 584,817.025 \][/tex]
For product testing materials:
[tex]\[ \text{new amount} = 54252 \times (1 + 0.175) \][/tex]
[tex]\[ \text{new amount} \approx 63746.10 \][/tex]
These increases in costs will lead to higher overall expenses. If the revenue remains the same, this will reduce the overall profit, as profit is calculated as the difference between revenues and expenses.
### 2.3 Profit Comparison for 2015 and 2016
For 2016:
- Primary income for 2016: R2,250,041
- Primary expenses for 2016: R1,993,476
[tex]\[ \text{profit}_{2016} = \text{Income}_{2016} - \text{Expenses}_{2016} \][/tex]
[tex]\[ \text{profit}_{2016} = 2250041 - 1993476 \][/tex]
[tex]\[ \text{profit}_{2016} = 256565 \][/tex]
Profit percentage for 2016:
[tex]\[ \text{Profit percentage}_{2016} = \left(\frac{profit_{2016}}{income_{2016}}\right) \times 100\][/tex]
[tex]\[ \text{Profit percentage}_{2016} \approx \left(\frac{256565}{2250041}\right) \times 100 \][/tex]
[tex]\[ \text{Profit percentage}_{2016} \approx 11.40\% \][/tex]
Estimated for 2015 (without direct income data):
We can estimate the primary expenses for 2015, assuming communication costs only affect primary expenses:
[tex]\[ \text{primary\_expenses\_2015} = \text{comm\_cost\_2015} + (\text{expenses}_2016 - \text{comm\_cost\_2016}) \][/tex]
[tex]\[ \text{primary\_expenses\_2015} \approx 1000 + (1993476 - (-32187)) \][/tex]
[tex]\[ \text{primary\_expenses\_2015} \approx 2026411.186 \][/tex]
While the exact 2015 primary income is not known, this gives an idea of the expense landscape for comparing profit changes over the two years.
To find an exact profit percentage for 2015, we would need the specific income value for 2015. But assuming the income's similar magnitude of 2016, the structure shows a more manageable expense adjustment in 2015 compared to 2016.
Thus, the samples given data highlight 2016 profits at roughly 11.40% against its incomes/expenses backdrop.
### 2.1 Communication Costs Calculation
We know the following:
- Communication costs for 2016 are R32,187.
- The communication costs decreased by 4,402% from 2015 to 2016.
To find the cost for 2015, we can set up the equation:
[tex]\[ \text{comm\_cost\_2016} = (\text{comm\_cost\_2015}) \times \left(1 - \frac{4402}{100}\right) \][/tex]
Given that such a large percentage decrease makes it odd, we interpret it as:
[tex]\[ \text{comm\_cost\_2016} = (\text{comm\_cost\_2015}) \times \left(1 - 44.02\right) \][/tex]
Since the communication costs for 2016 are [tex]\( \text{cost}_{2016} = -32,187 \)[/tex]:
[tex]\[ -32187 = (\text{comm\_cost\_2015}) \times -43.02 \][/tex]
[tex]\[ \text{comm\_cost\_2015} = \frac{-32187}{-43.02} \][/tex]
Calculate the communication cost for 2015:
[tex]\[ \text{comm\_cost\_2015} \approx 748.25 \][/tex]
Rounding it to the nearest thousand rand:
[tex]\[ \text{comm\_cost\_2015} \approx 1000 \][/tex]
So, the communication costs for 2015 to the nearest thousand was R1000.
### 2.2 Expected Increase in Costs and Impact on Profit
- The current costs for consumables in 2016 is R582,823.
- The current costs for product testing materials in 2016 is R54,252.
- The SANBS expects a 17.5% increase in these costs.
Using the percentage increase formula:
[tex]\[ \text{new amount} = \text{current amount} \times (1 + \text{percentage increase}) \][/tex]
For consumables:
[tex]\[ \text{new amount} = 582823 \times (1 + 0.175) \][/tex]
[tex]\[ \text{new amount} \approx 584,817.025 \][/tex]
For product testing materials:
[tex]\[ \text{new amount} = 54252 \times (1 + 0.175) \][/tex]
[tex]\[ \text{new amount} \approx 63746.10 \][/tex]
These increases in costs will lead to higher overall expenses. If the revenue remains the same, this will reduce the overall profit, as profit is calculated as the difference between revenues and expenses.
### 2.3 Profit Comparison for 2015 and 2016
For 2016:
- Primary income for 2016: R2,250,041
- Primary expenses for 2016: R1,993,476
[tex]\[ \text{profit}_{2016} = \text{Income}_{2016} - \text{Expenses}_{2016} \][/tex]
[tex]\[ \text{profit}_{2016} = 2250041 - 1993476 \][/tex]
[tex]\[ \text{profit}_{2016} = 256565 \][/tex]
Profit percentage for 2016:
[tex]\[ \text{Profit percentage}_{2016} = \left(\frac{profit_{2016}}{income_{2016}}\right) \times 100\][/tex]
[tex]\[ \text{Profit percentage}_{2016} \approx \left(\frac{256565}{2250041}\right) \times 100 \][/tex]
[tex]\[ \text{Profit percentage}_{2016} \approx 11.40\% \][/tex]
Estimated for 2015 (without direct income data):
We can estimate the primary expenses for 2015, assuming communication costs only affect primary expenses:
[tex]\[ \text{primary\_expenses\_2015} = \text{comm\_cost\_2015} + (\text{expenses}_2016 - \text{comm\_cost\_2016}) \][/tex]
[tex]\[ \text{primary\_expenses\_2015} \approx 1000 + (1993476 - (-32187)) \][/tex]
[tex]\[ \text{primary\_expenses\_2015} \approx 2026411.186 \][/tex]
While the exact 2015 primary income is not known, this gives an idea of the expense landscape for comparing profit changes over the two years.
To find an exact profit percentage for 2015, we would need the specific income value for 2015. But assuming the income's similar magnitude of 2016, the structure shows a more manageable expense adjustment in 2015 compared to 2016.
Thus, the samples given data highlight 2016 profits at roughly 11.40% against its incomes/expenses backdrop.
