Copyright © 2007 Thomson South-Western, a part of the Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach Slides Prepared by Karen Foust Tulane University

Valuing the Firm Economic theory tells us: n Expected Future Payoffs t (1 + Discount Rate) t V 0 = ∑ t=1 Expected future payoffs can be measured in terms of: Dividends Cash flows Earnings

Valuing the Firm

Risk-Adjusted Expected Rates of Return Risk-adjusted expected rate of return on equity capital used as discount rate to compute present value of expected future payoffs Can use Capital Asset Pricing Model (CAPM) Have to adjust if capital structure changes

Capital Asset Pricing Model E[R Ej ] = E[R F ] + ß j × {E[R M ] – E[R F ]} Where: E denotes expectation R Ej = return on common equity in firm j R F = risk-free rate of return ß j = market beta for firm j R M = return on market as a whole

Capital Asset Pricing Model E[R Ej ] = E[R F ] + ß j × {E[R M ] – E[R F ]} R F can use yield on short- or intermediate- term US government securities for risk-free rate {E[R M ] – E[R F ]} known as “market risk premium”

Cost of Equity Capital and Systematic Risk

Weighted Average Cost of Capital If considering acquisition of entire firm, need to compute weighted average cost of capital R A = [w D × R D × (1 – tax rate)] + [w P × R P ] + [w E × R E ] Where: –w D + w P + w E = 1 –R is cost of each type of capital –w is proportion of each type of capital –Tax rate is rate applicable to debt costs

Dividends-Based Valuation Dividends represent distribution of wealth to shareholders Dividends include ALL cash flows between firm and shareholders –Periodic dividend payments –Stock buybacks –The liquidating dividend –And “negative dividend” when firm initially issues stock

Dividends-Based Valuation Dividends represent distribution of wealth to shareholders Dividends valuation model:

Dividends-Based Valuation Must measure: –Discount rate – R E –Expected future dividends – D t for periods 1 through T over forecast horizon (periods 1 through T) –Continuing or final dividend, D T+1, and long- run growth rate, g

Measuring Periodic Dividends Clean surplus accounting –Under U.S. GAAP include other comprehensive income as well as net income Effects of transactions between firm and common shareholders is included in book value Thus, accounting for common equity represented by: BV t = BV t-1 + I t +D t => D t = I t + BV t-1 - BV t

Forecast Horizon Represented by periods 1 through T in valuation equation D 1 D 2 D 3 D T (1 + R E ) 1 (1 + R E ) 2 (1 + R E ) 3 (1 + R E ) T Five to ten years, depending on: –The industry –Firm’s maturity –Expected growth and stability Should be until firm reaches steady-state equilibrium Difficult for young, high-growth firms! +++ …

Continuing Value Represented by last term of equation on slide 10 Use expected long-term growth rate, g, to project all items on Year T+1 income statement and balance sheet Thus: D T+1 = NI T+1 + BV T – BV T+1 = [NI T × (1+g)] + BV T – [BV T × (1+g)]

What now? Once valuation model applied, then Conduct sensitivity analysis: Vary cost of equity capital rate (R E ) Vary long-run growth rate (g) Individually Jointly