Intro to Finance: Dividend Policy - Dividend Irrelevance Theory, MM with Perfect Markets

What This Is

The Dividend Irrelevance Theory, also known as the Modigliani-Miller (M&M) Theorem with Perfect Markets, states that in a perfect capital market with no taxes, no transaction costs, and no information asymmetry, the value of a firm is independent of its capital structure. This means that the value of a firm is determined solely by its expected cash flows, not by how those cash flows are financed. For example, consider Apple Inc. with a market value of $2 trillion and an expected annual cash flow of $100 billion. According to M&M, Apple's value would be the same whether it uses debt or equity to finance its operations.

Key Formulas & Symbols

• PV = FV / (1 + r)^n where PV = present value, FV = future value, r = periodic interest rate, n = number of periods.
• r = (C + (1 + g)^n * FV) / PV where r = required rate of return, C = coupon payment, g = growth rate, FV = face value, PV = present value, n = number of periods.
• g = (FV_n - FV_0) / FV_0 where g = growth rate, FV_n = future value at period n, FV_0 = initial future value.
• WACC = (E/V * Re) + (D/V * Rd * (1 - Tc)) where WACC = weighted average cost of capital, E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, Tc = corporate tax rate.
• Cost of Equity = Rf +-* (Rm - Rf) where Cost of Equity = required rate of return on equity, Rf = risk-free rate,-= beta coefficient, Rm = market return.
• Cost of Debt = (C / P) + (1 + g)^n * FV / PV where Cost of Debt = required rate of return on debt, C = coupon payment, P = current price, g = growth rate, FV = face value, PV = present value, n = number of periods.

Step-by-Step Calculation

1. Calculate the required rate of return on equity (Re) using the CAPM formula: Re = Rf +-* (Rm - Rf).
2. Calculate the required rate of return on debt (Rd) using the formula: Rd = (C / P) + (1 + g)^n * FV / PV.
3. Calculate the weighted average cost of capital (WACC) using the formula: WACC = (E/V * Re) + (D/V * Rd * (1 - Tc)).
4. Calculate the present value of the firm's expected cash flows using the formula: PV = FV / (1 + WACC)^n.
5. Calculate the growth rate (g) using the formula: g = (FV_n - FV_0) / FV_0.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value of equity and debt to calculate WACC, as book value may not reflect the firm's current market value.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR is the rate of return that makes NPV equal to zero, while NPV ranking is based on the present value of cash flows at a given discount rate.
• Mistake: Assuming a constant growth rate (g) in perpetuity.
• Correction: Use a more realistic growth rate that reflects the firm's expected growth prospects.

Exam / CFA Tips

• Tip: Be careful with the assumptions of the M&M Theorem, such as perfect capital markets and no taxes.
• Tip: Use the CAPM formula to calculate the required rate of return on equity (Re).
• Tip: Make sure to use the correct formula for WACC, including the market value of equity and debt.

Quick Practice Problem

Apple Inc. has a market value of $2 trillion and an expected annual cash flow of $100 billion. If the risk-free rate is 2% and the market return is 8%, what is the required rate of return on equity (Re)?

Answer: Re = 0.02 + 1.5 * (0.08 - 0.02) = 0.13 or 13%.

Last-Minute Cram Sheet

• The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• The M&M Theorem assumes perfect capital markets with no taxes, no transaction costs, and no information asymmetry.
• WACC = (E/V * Re) + (D/V * Rd * (1 - Tc)).
• Cost of Equity = Rf +-* (Rm - Rf).
• Cost of Debt = (C / P) + (1 + g)^n * FV / PV.
• PV = FV / (1 + WACC)^n.
• g = (FV_n - FV_0) / FV_0.
• The CAPM formula assumes a linear relationship between beta and expected return.
• Re = Rf +-* (Rm - Rf).
• Rd = (C / P) + (1 + g)^n * FV / PV.
• WACC is a weighted average of the cost of equity and debt.