FIN 468 Intermediate Corporate Finance Topic 6 Residual Income Valuation Larry Schrenk Instructor 1 of 22 Topics What is Residual Income RI The Residual Income Method Problems with Residual Income Residual Income Valuation What is residual income Residual income net income less common equity opportunity cost in generating net income Other names economic profit abnormal earnings Economic Value Added Primary uses of residual income Internal corporate performance Intrinsic value of common stock Our focus Residual income vs accounting income Traditional financial statements Reflect earnings available to owners Net income includes interest expense Dividends or other charges for equity capital not deducted Does not show if earnings are meet the cost of equity capital The economic concept of residual income Explicitly considers the cost of equity capital Residual Income Example Axis Manufacturing Company AMC has total assets of 2 000 000 financed 50 with debt and 50 with equity capital The cost of debt capital is 7 pre tax 4 9 after tax and the cost of equity capital is 12 Net income for AMC can be determined as follows EBIT Less Interest Expense Pre Tax Income Income Tax Expense Net Income 200 000 70 000 130 000 39 000 91 000 What is it s residual income One approach is to compute the cost of equity capital in terms of currency which we term an equity charge and subtract this from net income as follows Equity Charge Equity Capital Cost of Equity Capital in Cost of Equity 1 000 000 12 120 000 Net Income Equity Charge Residual Income 91 000 120 000 29 000 AMC did not earn enough to cover the cost of equity capital As a result it has negative residual income Other names for residual income Economic profit Abnormal earnings Profit of the firm after deducting the cost of all capital debt and equity Earnings in excess of the cost of capital are abnormal Economic Value Added EVA Trademarked by Stern Stewart Company EVA NOPAT C TC NOPAT net operating profit after taxes C cost of capital TC total capital Residual income model of valuation RIM Intrinsic value of the firm has two components The current book value of equity plus The present value of future residual income Algebraically RI t Et rBt 1 P0 B0 B 0 t t 1 r 1 r t 1 t 1 B0 current book value of equity Bt book value of equity at time t RIt residual income in future periods r required rate of return on equity Et net income during period t RIt Et rBt 1 Valuing a perpetuity with the RIM A company will earn 1 00 per share forever and the company also pays out all of this as dividends 1 00 per share The equity capital invested book value is 6 00 per share Because the earnings and dividends will offset each other the future book value of the stock will always stay at 6 00 The required rate of return on equity or the percent cost of equity is 10 1 2 3 Calculate the value of this stock using the dividend discount model What will be the residual income each year Calculate the value of the stock using a residual income valuation model Create a table summarizing the recognition of value in the dividend discount model and the residual income model Perpetuity example Solution to 1 Since the dividend is a perpetuity P0 D r 1 00 0 10 10 00 per share Solution to 2 The net income is 1 00 each year the book value is always 6 00 and the required return is 10 so the residual income in every year will be RIt Et rBt 1 1 00 0 10 6 00 1 00 0 60 0 40 The value using a residual income approach is the current book value plus the present value of future residual income The residual income is a perpetuity P0 Book value PV of Residual income 6 00 0 40 0 10 6 00 4 00 10 00 RI valuation vs DDM Timing of recognition of value Forecasting of future dividends and cash flows is often difficult One key advantage to a residual income model over other models is the timing of the recognition of value In DCF approaches most of the value is found in future dividends and in the terminal value computation The longer the forecast period the higher the uncertainty that will exist regarding these future cash flows Terminal value In many residual income valuation contexts the terminal value is deemed to be zero The determination of book value today is much easier than the determination of a terminal value ten or twenty years hence When to use RI valuation A residual income model is most appropriate when A firm is not paying dividends of if it exhibits an unpredictable dividend pattern A firm has negative free cash flow many years out but is expected to generate positive cash flow at some point in the future for example a young or rapidly growing firm where capital expenditures are being made to fuel future growth There is a great deal of uncertainty in forecasting terminal values Derivation of the RIM of valuation Start with the DDM P0 D1 1 r 1 D2 1 r 2 D3 1 r 3 The relationship between earnings dividends and book value is given by the clean surplus equation as Bt Bt 1 Et Dt Derivation of RI Valuation This means that Dt Et Bt Bt 1 Et Bt 1 Bt Substituting this into the DDM E1 B0 B1 E2 B1 B2 E3 B2 B3 P0 L 1 2 3 1 r 1 r 1 r This equation can be simplified RI t Et rBt 1 P0 B0 B0 t t 1 r 1 r t 1 t 1 Derivation of RI Valuation This can also be expressed as ROEt r Bt 1 V0 B0 t 1 r t 1 This equation is logically equivalent to the one above since RIt ROEt r Bt 1 Other than the required rate of return the inputs to the residual income model are based upon accounting data RI Valuation Example Simon Investment Trust SIT is expected to earn 4 00 5 00 and 8 00 for the next three years SIT will pay annual dividends of 2 00 2 50 and 20 50 in each of these years The last dividend includes the liquidating payment to shareholders at the end of year 3 when the trust will terminate SIT s book value is 8 per share and its required return on equity is 10 A What is the current value per share of SIT according to the dividend discount model B Calculate the book value and residual income for SIT for each of the next 3 years and use those results to find the stock s value using the residual income model C Calculate return on equity and use it as an input to the residual income model to calculate SIT s value RI Valuation Example A P0 Present Value of the future dividends P0 2 1 10 2 50 1 1 2 20 50 1 1 3 P0 …