Valuation and Tax Policy Lakehead University Winter 2005 Formula Approach for Valuing Companies Let EBIT t Earnings before interest and taxes at time t T Corporate tax rate I t Firm s investments at time t r t After-tax return on the firm s investments at time t 2
Formula Approach for Valuing Companies The pattern of cash flows for the firm s investors is then given by Time Cash Flow 1 (1 T )EBIT 1 I 1 2 (1 T )EBIT 2 I 2 = (1 T )EBIT 1 + r 1 I 1 I 2 3 (1 T )EBIT 3 I 3 = (1 T )EBIT 1 + r 1 I 1 + r 2 I 2 I 3.. N 1 N (1 T )EBIT 1 + r t I t I N 3 Formula Approach for Valuing Companies Suppose the firm has no debt and let denote the cost of capital of the unlevered firm. The present value of the firm s cash flows is then V 0 = (1 T )EBIT 1 I 1 + V 1 = (1 T )EBIT 1 I 1 + ((1 T )EBIT 2 I 2 +V 2 )/( ) = (1 T )EBIT 1 I 1 + (1 T )EBIT 2 I 2 ( ) 2 + V 2 ( ) 2 = (1 T )EBIT 1 I 1 + (1 T )EBIT 2 I 2 ( ) 2 + (1 T )EBIT 3 I 3 ( ) 3 +. = N (1 T )EBIT t I t ( ) t + V N ( ) N V 3 ( ) 3 4
Formula Approach for Valuing Companies If the horizon is infinite and lim N V N (1+ ) N = 0, then V 0 = (1 T )EBIT t I t ( ) t. 5 Formula Approach for Valuing Companies If, in the last equation, we replace t 1 (1 T )EBIT t I t by (1 T )EBIT 1 + for all t > 1, we obtain V 0 = (1 T )EBIT 1 + s=1 r s I s I t I t (r t ) ( ) t = Value of assets in place + value of future growth 6
Formula Approach for Valuing Companies Since r t represents the firm s return on invested capital at time t, I t (r t ) Economic profit at time t. If the firm makes no investment, then V 0 = (1 T )EBIT 1. 7 Formula Approach for Valuing Companies Note that a firm s investments create value only if the firm s average return on invested capital, r t, is greater than the return required by its investors, in the present case. In the more general case, a firm s investments create value only if its ROIC is greater than its WACC. 8
Constant Growth Consider an all-equity firm that always retains a fraction b of its after-tax earnings. That is, I t = b(1 T )EBIT t for all t. 9 Constant Growth Suppose also that the return on this firm s invested capital is constant over time, i.e. r t = r for all t. Then, for all t, (1 T )EBIT t = (1 T )EBIT t 1 + ri t 1 = (1 T )EBIT t 1 + rb(1 T )EBIT t 1 = (1 + rb)(1 T )EBIT t 1. 10
Constant Growth This means that the rate of growth in earnings is given by g = (1 T )EBIT t (1 T )EBIT t 1 1 = rb, i.e. the growth rate in earnings is equal to the return on invested capital times the retention ratio. Note that this growth rate is often calculated by multiplying the return on equity by the retention ratio. 11 Constant Growth If earnings grow at a constant rate, then (1 T )EBIT t = (1 + rb) t 1 (1 T )EBIT 1 for all t > 1. Using this, we can simplify the equation V 0 = (1 T )EBIT 1 + I t (r t ) ( ) t. 12
Constant Growth I t (r t ) ( ) t = = b(1 T )EBIT t (r ) ( ) t b(1 + rb) t 1 (1 T )EBIT 1 (r ) ( ) t ( ) 1 + rb t = b(r )(1 T )EBIT 1 (1 + rb) 13 Constant Growth If rb <, then ( ) 1 + rb t = 1+rb 1+ 1 1+rb = 1 + rb k 1+ rb. u 14
Constant Growth This gives us I t (r t ) ( ) t = b(r )(1 T )EBIT 1 (1 + rb) = b(r )(1 T )EBIT 1 (1 + rb) = b(r )(1 T )EBIT 1 ( rb) ( 1 + rb 1 + rb rb ) t 15 Constant Growth and thus V 0 = (1 T )EBIT 1 + I t (r t ) ( ) t = (1 T )EBIT 1 + b(r )(1 T )EBIT 1 ( rb) = (1 T )EBIT ( 1 1 + b(r k ) u) rb = (1 T )EBIT 1 = (1 b)(1 T )EBIT 1 rb rb + rb b rb 16
Constant Growth What is (1 b)(1 T )EBIT 1? The sum of all dividends paid in year 1. Let S 0 denote the number of shares outstanding at time 0. Then the value of a share is P 0 = V 0 = (1 b)(1 T )EBIT 1/S 0 S 0 rb = D 1 rb = D 1 g. 17 Finite Supernormal Growth If r >, the value of the firm is maximized when all earnings are reinvested in the firm. If we expect r to be greater than forever, then the firm will never pay any dividend. But a firm that is never expected to pay any dividend has no value. Hence assuming that r > forever does not make any sense. 18
Finite Supernormal Growth Suppose instead that r > for N years, after which r = into perpetuity. Let s say that the firm reaches maturity after N years. Let r 1 denote the return on the firm s investments for the first N years, let r 2 denote the return on the firm s investments afterwards and suppose that r 2 =. 19 Finite Supernormal Growth In this case, I t (r t ) ( ) t = N I t (r 1 ) ( ) t + = b(r 1 )(1 T )EBIT 1 (1 + r 1 b) = b(r 1 )(1 T )EBIT 1 (1 + r 1 b) = b(r 1 )(1 T )EBIT 1 ( r 1 b) I t (r 2 ) t=n+1 ( ) t N ( 1 + r1 b ) t + 0 (1 + r 1b) ( 1 ((1 + r 1 b)/( )) N) r 1 b ( ( ) ) 1 + r1 b N 1 20
Finite Supernormal Growth and thus V 0 = (1 T )EBIT 1 + I t (r t ) ( ) t = (1 T )EBIT 1 + b(r 1 )(1 T )EBIT 1 ( r 1 b) ( ( = (1 T )EBIT 1 1 + b(r 1 ) r 1 b ( ( ) ) 1 + r1 b N 1 ( ) )) 1 + r1 b N 1 21 Finite Supernormal Growth If N is small and if r 1 b, then ( ) 1 + r1 b N ( ) ku r 1 b 1 N and thus V 0 (1 T )EBIT 1 + bn(1 T )EBIT 1 ( ) r1. ( ) 22
Finite Supernormal Growth with Debt If the firm has some debt, denoted B, in its capital structure, V 0 = (1 T )EBIT 1 + T B k } u {{} Value without growth ( ) r 1 WACC + bn(1 T )EBIT 1. WACC(1 + WACC) }{{} Growth component 23