Theoretical Rationale for Engagement Activities

Theoretical Rationale for Engagement Activities: Mathematical Analysis

The impact of engagement activities on corporate value can be mathematically formulated based on the Dividend Discount Model (DDM). At that time, it becomes possible to quantitatively measure each effect of ROE improvement, growth rate enhancement, and cost of capital reduction, and derive selection criteria for optimal engagement strategies.

Key Research Areas

Clarification of Value Creation Mechanism: Rigorous derivation of the mathematical relationship between ROE, growth rate, cost of capital, and corporate value.
Identification of Optimal Strategy Conditions: Establishment of objective criteria to determine the priority of ROE improvement and growth expansion.
Decision Making by Expected Value: Construction of a quantitative evaluation framework considering success probability and cost.

Major Mathematical Results

Item	Formula	Meaning
Corporate Value	$P = \frac{(r-g)B}{k-g}$	Stock price determined by ROE, growth, and cost of capital
ROE Improvement Effect	$\Delta P = \frac{(r_1-r_0)B}{k-g}$	Amount of stock price increase due to ROE improvement
Strategy Selection Criteria	$r < 2k - g$	Under this condition, prioritize ROE improvement
Expected Value Condition	$p > \frac{C}{\Delta P + C}$	Minimum success probability for executing engagement

Conclusion

Through this research, we can show that the value creation effect of engagement activities is mathematically predictable. Strategy selection can be judged by objective criteria ( $r < 2k - g$ ), and by expected value evaluation considering success probability and cost, it is possible to position engagement activities as a scientific and objective investment method.

Theoretical Rationale for Engagement Activities: Mathematical Analysis

Key Research Areas

Clarification of Value Creation Mechanism: Rigorous derivation of the mathematical relationship between ROE, growth rate, cost of capital, and corporate value.

Identification of Optimal Strategy Conditions: Establishment of objective criteria to determine the priority of ROE improvement and growth expansion.

Decision Making by Expected Value: Construction of a quantitative evaluation framework considering success probability and cost.

Major Mathematical Results

Item

Formula

Meaning

Corporate Value

P = \frac{(r-g)B}{k-g}

Stock price determined by ROE, growth, and cost of capital

ROE Improvement Effect

\Delta P = \frac{(r_1-r_0)B}{k-g}

Amount of stock price increase due to ROE improvement

Strategy Selection Criteria

r < 2k - g

Under this condition, prioritize ROE improvement

Expected Value Condition

p > \frac{C}{\Delta P + C}

Minimum success probability for executing engagement

Conclusion

Through this research, we can show that the value creation effect of engagement activities is mathematically predictable. Strategy selection can be judged by objective criteria (

r < 2k - g

), and by expected value evaluation considering success probability and cost, it is possible to position engagement activities as a scientific and objective investment method.