Read and study the questions and then crearly step by step answer all the questions that follow

Question

(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?

Answer 1

### (a) Inflation-Adjusted Weekly Wages

#### i. Real Average Weekly Wage for Each Year

The real average weekly wage accounts for the inflation rate and is calculated by adjusting the nominal wages using the consumer price index (CPI). The formula for the real wage is:

\[ \text{Real Wage} = \frac{\text{Nominal Wage}}{\text{CPI}} \times \text{Base Year CPI} \]

We will assume the base year CPI to be 100 for ease of comparison.

Given Data:
- Year: \{2000, 2001, 2002, 2003, 2004, 2005\}
- Nominal Wage: \{109.50, 112.20, 116.40, 125.80, 135.40, 138.10\}
- CPI: \{112.80, 118.20, 127.40, 138.20, 143.50, 149.80\}

Base Year CPI = 100

For each year:

\[ \text{Real Wage} = \frac{\text{Nominal Wage}}{\text{CPI}} \times 100\]

\[ \text{Real Wage}_{2000} = \frac{109.50}{112.80} \times 100 = 97.08\]

\[ \text{Real Wage}_{2001} = \frac{112.20}{118.20} \times 100 = 94.89\]

\[ \text{Real Wage}_{2002} = \frac{116.40}{127.40} \times 100 = 91.38\]

\[ \text{Real Wage}_{2003} = \frac{125.80}{138.20} \times 100 = 91.04\]

\[ \text{Real Wage}_{2004} = \frac{135.40}{143.50} \times 100 = 94.38\]

\[ \text{Real Wage}_{2005} = \frac{138.10}{149.80} \times 100 = 92.18\]

#### ii. Year with Greatest Buying Power

The year with the highest real wage indicates the greatest buying power. From the calculations above:
- 2000: 97.08
- 2001: 94.89
- 2002: 91.38
- 2003: 91.04
- 2004: 94.38
- 2005: 92.18

The greatest buying power was in the year 2000 with a real wage of 97.08.

#### iii. Percentage Increase in Weekly Wages for 2005

To match the buying power of the year 2000 in 2005, we need:

\[ \text{Required Nominal Wage}_{2005} = \text{Real Wage}_{2000} \times \frac{\text{CPI}_{2005}}{100} \]

\[ \text{Required Nominal Wage}_{2005} = 97.08 \times \frac{149.80}{100} = 145.32 \]

The percentage increase required from the 2005 nominal wage (138.10) to the required nominal wage (145.32) is:

\[ \text{Percentage Increase} = \frac{145.32 - 138.10}{138.10} \times 100 = 5.22\% \]

### (b) 4-Yearly Moving Average and Short-Term Fluctuations

#### Given Data:

\[
\begin{array}{|c|c|}
\hline
\text{Year} & \text{Sales (K)} \\
\hline
1993 & 200 \\
1994 & 120 \\
1995 & 280 \\
1996 & 240 \\
1997 & 160 \\
1998 & 320 \\
1999 & 360 \\
2000 & 400 \\
2001 & 320 \\
2002 & 360 \\
2003 & 360 \\
\hline
\end{array}
\]

#### 4-Year Moving Average:

Calculate the average of each set of 4 consecutive years.

\[ \text{First Moving Average} (1995) = \frac{200 + 120 + 280 + 240}{4} = 210 \]

\[ \text{Second Moving Average} (1996) = \frac{120 + 280 + 240 + 160}{4} = 200 \]

\[ \text{Third Moving Average} (1997) = \frac{280 + 240 + 160 + 320}{4} = 250 \]

\[ \text{Fourth Moving Average} (1998) = \frac{240 + 160 + 320 + 360}{4} = 270 \]

\[ \text{Fifth Moving Average} (1999) = \frac{160 + 320 + 360 + 400}{4} = 310 \]

\[ \text{Sixth Moving Average} (2000) = \frac{320 + 360 + 400 + 320}{4} = 350 \]

\[ \text{Seventh Moving Average} (2001) = \frac{360 + 400 + 320 + 360}{4} = 360 \]

#### Short-Term Fluctuations:

Short-term fluctuations can be found by subtracting the moving average from the actual sales for the overlapping years.

### (c) Stock Choice Based on Expected Return and Risk

#### Given Data:

- Expected Monetary Value (A): 60
- Expected Monetary Value (B): 20
- Standard Deviation (A): 60
- Standard Deviation (B): 10

To choose a stock, we consider both expected return and risk. Generally, higher return involves higher risk.

Stock A:
- Expected Return: 60
- Standard Deviation (Risk): 60

Stock B:
- Expected Return: 20
- Standard Deviation (Risk): 10

#### Decision:
- If risk tolerance is high and aiming for higher returns, choose Stock A.
- If risk aversion is high and aiming for consistent lower risk returns, choose Stock B.

Most investors seek a balance between the two. The Coefficient of Variation (CV), which measures risk per unit of return, can help:

\[ \text{CV}_{A} = \frac{60}{60} = 1.0 \]

\[ \text{CV}_{B} = \frac{10}{20} = 0.5 \]

Stock B offers a better risk-return ratio, suggesting that it would be the better choice under standard risk-reward considerations.