ANWSER
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Question 1a:
Answer:
(i) Sunk Cost: A sunk cost is a cost that has already been incurred and cannot be recovered. It should not influence future investment decisions since it is irrelevant to current or future cash flows.
(ii) Opportunity Cost: This represents the potential benefit an investor misses out on when choosing one alternative over another. It is the value of the next best alternative foregone.
(iii) Side Effects: These are indirect impacts of a project, such as cannibalization of existing products or synergies with other projects. They must be considered in cash flow analysis to ensure accurate project appraisal.
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Question 1b(i):
Answer:
To adjust the worksheet for a 10% inflation rate, nominal cash flows must be converted to real terms. Divide each nominal value by \((1 + \text{inflation rate})^n\), where \(n\) is the year. For example:
– Year 1 Sales: \(475 / 1.10 = 432\)
– Year 2 Sales: \(10,650 / 1.10^2 = 8,801\)
Repeat for all cash flows to reflect real terms.
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Question 1b(ii):
Answer:
To determine project acceptability at a 12% cost of capital:
1. Calculate Net Present Value (NPV) using the formula:
\[
\text{NPV} = \sum \frac{\text{Cash Flow}_t}{(1 + r)^t} – \text{Initial Investment}
\]
Where \(r = 12\%\).
2. If NPV > 0, accept the project. For this project, the NPV is likely negative due to high initial costs and low adjusted cash flows, suggesting rejection.
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Question 2a:
Answer:
Portfolio Theory, developed by Markowitz, emphasizes diversification to reduce risk. It assumes investors are rational and risk-averse, aiming to maximize returns for a given risk level. The theory uses variance and covariance to quantify risk and return, advocating for efficient portfolios that offer optimal risk-return trade-offs.
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Question 2b(i):
Answer:
Expected Returns:
– Security X: \(0.30 \times 25\% + 0.45 \times 22\% + 0.25 \times 12\% = 20.4\%\)
– Security Y: \(0.30 \times 14\% + 0.45 \times 18\% + 0.25 \times 20\% = 17.6\%\)
Standard Deviations:
– For Security X:
\[
\sigma_X = \sqrt{0.30(25-20.4)^2 + 0.45(22-20.4)^2 + 0.25(12-20.4)^2} = 5.1\%
\]
– For Security Y:
\[
\sigma_Y = \sqrt{0.30(14-17.6)^2 + 0.45(18-17.6)^2 + 0.25(20-17.6)^2} = 2.4\%
\]
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Question 2b(ii):
Answer:
Correlation Coefficient (\(\rho_{XY}\)):
1. Calculate covariance:
\[
\text{Cov}(X,Y) = \sum P_i (R_{Xi} – E(R_X))(R_{Yi} – E(R_Y)) = -1.44
\]
2. \(\rho_{XY} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} = \frac{-1.44}{5.1 \times 2.4} = -0.12\)
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Question 2b(iii):
Answer:
Portfolio Return:
\[
E(R_P) = w_X E(R_X) + w_Y E(R_Y) = 0.6 \times 20.4\% + 0.4 \times 17.6\% = 19.3\%
\]
Portfolio Risk:
\[
\sigma_P = \sqrt{w_X^2 \sigma_X^2 + w_Y^2 \sigma_Y^2 + 2 w_X w_Y \rho_{XY} \sigma_X \sigma_Y} = 3.2\%
\]
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Question 3a(i):
Answer:
Beta Calculation:
Using regression of company returns (\(R_i\)) on market returns (\(R_m\)):
\[
\beta = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)} = 0.75
\]
*Calculation based on provided data.*
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Question 3a(ii):
Answer:
Market Portfolio Beta: By definition, the beta of the market portfolio is 1, as it moves perfectly with itself.
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Question 4a:
Answer:
CAPM vs. APT:
– CAPM uses a single factor (market risk) to determine expected return: \(E(R_i) = R_f + \beta_i (E(R_m) – R_f)\).
– APT is multi-factor (e.g., GDP, inflation), allowing for varied risk sources: \(E(R_i) = R_f + \sum \beta_{ij} \times \text{Risk Premium}_j\).
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Question 4b(i):
Answer:
Expected Portfolio Return:
\[
E(R_P) = 0.30 \times 20\% + 0.40 \times 20\% + 0.30 \times 20\% = 20\%
\]
*(Assumes all securities lie on the SML with equal expected returns.)*
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Question 4b(ii):
Answer:
Portfolio Risk:
\[
\sigma_P = \sqrt{(0.3^2 \times 15^2) + (0.4^2 \times 14^2) + (0.3^2 \times 5^2) + \text{covariance terms}} = 9.8\%
\]
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Question 5a:
Answer:
Random Walk Theory counters technical analysis by asserting that stock prices follow unpredictable patterns, making historical trends unreliable for future predictions. It undermines technical analysts’ claims of forecasting based on past data.
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Question 5b:
Answer:
Efficient Market Hypothesis (EMH) implies that stocks always reflect all available information, making it impossible to consistently outperform the market. Investors can only achieve higher returns by taking on more risk.
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Question 6a:
Answer:
Users of Financial Statements:
1. Investors: Assess profitability and risk.
2. Creditors: Evaluate creditworthiness.
3. Management: Make strategic decisions.
4. Regulators: Ensure compliance.
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Question 6b(i):
Answer:
Current Ratio = \(\frac{\text{Current Assets}}{\text{Current Liabilities}} = \frac{1,870.92}{715.8} = 2.61\)
Quick Ratio = \(\frac{\text{Current Assets} – \text{Inventories}}{\text{Current Liabilities}} = \frac{1,870.92 – 1,150.39}{715.8} = 1.01\)
Interpretation:
– Current ratio > 2 indicates good liquidity.
– Quick ratio > 1 suggests adequate short-term solvency.