a) The beta value of each of the four projects may be estimated using:
Correlation coefficient of the project (Rim) and the market multiplied by the standard deviation of the project’s returns (i ), and all divided by the standard deviation of returns from the market (m).

The overall company beta is the weighted average of the project betas, the weighting being by their proportion of total market value. The beta of TK is estimated to be: (0.28 × 0.635) + (0.17 × 1.154) + (0.31 × 0.905) + (0.24 × 0.858) = 0.860
Using the capital asset pricing model, the return that might be expected from TK may be estimated to be: 5% + (14% – 5%) 0.860 = 12.74%
The return historically has been: (0.28 × 10%) + (0.17 × 18%) + (0.31 × 15%) + (0.24 × 13%) = 13.63%
Assuming these historic returns are expected to continue, the share price of TK is likely to be undervalued, as the company is yielding a higher return than expected for its systematic risk.

b. Why Results Might Not Identify True Share Valuation

1. Assumption of Historical Continuity:
   • The CAPM calculation assumes that historical risk and return patterns will persist, which might not hold true in a dynamic market.
2. Limited Data:
   • Using only the last five years of data may not capture long-term market trends or significant changes in risk.
3. Simplified Correlation:
   • The analysis uses correlation as a measure of risk but does not account for systemic shocks or unforeseen market events.
4. Ignoring Non-Market Risks:
   • CAPM focuses on market risk but ignores company-specific risks, such as management inefficiencies or operational issues.
5. Market Efficiency Assumption:
   • The CAPM model assumes markets are fully efficient, which might not reflect real-world inefficiencies in pricing or information availability.
6. Risk-Free Rate and Market Return:
   • These parameters are assumed constant, whereas actual risk-free rates and market returns may fluctuate due to economic conditions.

c. Limitations of Portfolio Theory in Physical Investment Decisions

1. Assumption of Market Efficiency:
   • Portfolio theory assumes all investors have access to the same information and that markets price assets efficiently, which might not be true for physical investment decisions.
2. Simplified Risk Measures:
   • Risk is quantified solely by standard deviation, ignoring qualitative factors like operational risks or regulatory changes that impact physical investments.
3. Short-Term Focus:
   • Portfolio theory often emphasizes short-term risk-return tradeoffs, whereas physical investments typically require a long-term perspective.
4. Ignores Non-Financial Goals:
   • Physical investments may aim to achieve strategic or environmental objectives, which are not considered in portfolio theory.
5. Interdependencies:
   • Physical investments often involve interdependent projects or assets, making the independence assumption of portfolio theory invalid.
6. Inflexibility of Assumptions:
   • The rigid assumptions of risk aversion, rational behavior, and consistent investor preferences limit the applicability of portfolio theory to real-world decisions.