Total value is ZL$91.74 calculated by adding the present value of the terminal value, ZL$5.33, to ZL$86.41. Rosatoconcludes that if Zenlandia Chemical’s residual income does not persist at a stable level past 2037 and deterioratesthrough time, the shares are modestly overvalued at a price of ZL$95.6.4. Residual Income Valuation in Relation to Other ApproachesBefore addressing accounting issues in using the residual income model, we briefly summarize the relationship of theresidual income model to other valuation models.Valuation models based on discounting dividends or on discounting free cash flows are as theoretically sound as theresidual income model. Unlike the residual income model, however, the discounted dividend and free cash flow modelsforecast future cash flows and find the value of stock by discounting them back to the present by using the required return.Recall that the required return is the cost of equity for both the DDM and the free cash flows to equity (FCFE) model. Forthe free cash flow to the firm (FCFF) model, the required return is the overall weighted average cost of capital. The RImodel approaches this process differently. It starts with a value based on the balance sheet, the book value of equity, andadjusts this value by adding the present values of expected future residual income. Thus, in theory, the recognition of valueis different, but the total present value, whether using expected dividends, expected free cash flow, or book value plusexpected residual income, should be consistent.18Example 11 again illustrates the important point that the recognition of value in residual income models typically occursearlier than in dividend discount models. In other words, residual income models tend to assign a relatively small portionof a security’s total present value to the earnings that occur in later years. Note also that this example makes use of thefact that the present value of a perpetuity in the amount ofXcan be calculated asX/r.EXAMPLE 11 Valuing a Perpetuity with the Residual Income ModelAssume the following data:•A company will earn $1.00 per share forever.•The company pays out all earnings as dividends.•Book value per share is $6.00.•The required rate of return on equity (or the percent cost of equity) is 10 percent.1.Calculate the value of this stock using the DDM.2.Calculate the level amount of per-share residual income that will be earned each year.3.Calculate the value of the stock using an RI model.4.Create a table summarizing the year-by-year valuation using the DDM and the RI model.Solution to 1:Because the dividend,D, is a perpetuity, the present value ofDcan be calculated asD/r.V0=D/r= $1.00/0.10 = $10.00 per shareSolution to 2:Because each year all net income is paid out as dividends, book value per share will be constant at $6.00.

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