Let's break down and address each part of your question:
### Part (a)
To calculate the **real average weekly wage** for each year, we adjust the nominal wage by the Consumer Price Index (CPI). The formula for real wage is:
\[
\text{Real Wage} = \frac{\text{Nominal Wage}}{\text{CPI}} \times 100
\]
**(i) Real average weekly wage for each year:**
1. **2000**:
\[
\text{Real Wage} = \frac{109.50}{112.80} \times 100 \approx 97.11
\]
2. **2001**:
\[
\text{Real Wage} = \frac{112.20}{118.20} \times 100 \approx 94.91
\]
3. **2002**:
\[
\text{Real Wage} = \frac{116.40}{127.40} \times 100 \approx 91.36
\]
4. **2003**:
\[
\text{Real Wage} = \frac{125.80}{138.20} \times 100 \approx 91.03
\]
5. **2004**:
\[
\text{Real Wage} = \frac{135.40}{143.50} \times 100 \approx 94.37
\]
6. **2005**:
\[
\text{Real Wage} = \frac{138.10}{149.80} \times 100 \approx 92.19
\]
**(ii) Year of greatest buying power:**
The employees had the greatest buying power in the year where the real average weekly wage was the highest. From the calculations above:
- 2000: 97.11
- 2001: 94.91
- 2002: 91.36
- 2003: 91.03
- 2004: 94.37
- 2005: 92.19
The real wage in 2000 (97.11) is the highest. Therefore, the year 2000 had the greatest buying power.
**(iii) Percentage increase needed in 2005 to match 2000 buying power:**
We need to find the nominal wage needed in 2005 to have the same real wage as in 2000 (97.11).
\[
\text{Required Nominal Wage in 2005} = 97.11 \times \frac{149.80}{100} = 145.34
\]
The percentage increase required is:
\[
\text{Percentage Increase} = \frac{\text{Required Nominal Wage} - \text{Current Nominal Wage}}{\text{Current Nominal Wage}} \times 100
\]
\[
\text{Percentage Increase} = \frac{145.34 - 138.10}{138.10} \times 100 \approx 5.24\%
\]
### Part (b)
Given data:
| Year | Sales (K) |
|------|-----------|
| 1993 | 200 |
| 1994 | 120 |
| 1995 | 280 |
| 1996 | 240 |
| 1997 | 160 |
| 1998 | 320 |
| 1999 | 360 |
| 2000 | 400 |
| 2001 | 320 |
| 2002 | 360 |
| 2003 | 360 |
To estimate trend values using a 4-year moving average:
1. **1995**:
\[
\text{MA} = \frac{200 + 120 + 280 + 240}{4} = 210
\]
2. **1996**:
\[
\text{MA} = \frac{120 + 280 + 240 + 160}{4} = 200
\]
3. **1997**:
\[
\text{MA} = \frac{280 + 240 + 160 + 320}{4} = 250
\]
4. **1998**:
\[
\text{MA} = \frac{240 + 160 + 320 + 360}{4} = 270
\]
5. **1999**:
\[
\text{MA} = \frac{160 + 320 + 360 + 400}{4} = 310
\]
6. **2000**:
\[
\text{MA} = \frac{320 + 360 + 400 + 320}{4} = 350
\]
7. **2001**:
\[
\text{MA} = \frac{360 + 400 + 320 + 360}{4} = 360
\]
8. **2002**:
\[
\text{MA} = \frac{400 + 320 + 360 + 360}{4} = 360
\]
The short-term fluctuations (actual - trend) can be calculated by subtracting the moving average from the actual sales.
### Part (c)
Stock A and B have the following parameters:
- **Stock A:**
- Expected Return \( E(X) = 60 \)
- Standard Deviation \( \sigma = 60 \)
- **Stock B:**
- Expected Return \( E(Y) = 20 \)
- Standard Deviation \( \sigma = 10 \)
To decide which stock to choose, we may consider the **Coefficient of Variation (CV)**:
\[
\text{CV} = \frac{\sigma}{E}
\]
For Stock A:
\[
\text{CV}_A = \frac{60}{60} = 1
\]
For Stock B:
\[
\text{CV}_B = \frac{10}{20} = 0.5
\]
The coefficient of variation for Stock B is lower, indicating less risk per unit of return. Therefore, **Stock B** may be a better choice if the goal is to minimize risk relative to return.
However, the choice also depends on the investor's risk tolerance and return preference. If the investor is willing to accept higher risk for potential higher returns, they might choose Stock A despite its higher variability.
(a) Given the following data,
Year Weekly take-home pay (wages) Consumer price index
2000 109.50 112.80
2001 112.20 118.20
2002 116.40 127.40
2003 125.80 138.20
2004 135.40 143.50
2005 138.10 149.80
i. What was the real average weekly wage for each year?
ii. In which year did the employees have the greatest buying power?
iii. What percentage increase in the weekly wages for the year 2005 is required (if any)
to provide the same buying power that the employees enjoyed in the year in which
they had the highest real wages.
(b) From the following data estimate the trend values by taking 4 –yearly moving average
and also find short –term fluctuations.
Year Sales (K) Year Sales (K)
1993 200 1999 360
1994 120 2000 400
1995 280 2001 320
1996 240 2002 360
1997 160 2003 360
1998 320
(c) The following are the returns (K) for two stocks:
A B
Expected monetary value 60 20
Standard deviation 60 10
Which stock would you choose and why?
1 answer