LOS 45.h: Explain continuing residual income, list the common assumptions regarding continuing residual income and justify an estimate of continuing residual income at the forecast horizon given company and industry prospects.
Previously, we mentioned the problem of forecasting residual income indefinitely into the future, which makes it difficult to calculate the present value of residual income
and implement the residual income model. However, we can simplify the model by using the same multistage approach we used for DDM and free cash flow models. We'll forecast residual income over a short-term horizon (e.g., five years) and then make some simplifying assumptions about the pattern of residual income growth over the long term after five years. Continuing residual income is the residual income that is expected over the long term.
Residual income will continue beyond a specified earnings horizon depending on the fortunes of the industry, as well as on the sustainability of a specific firm's competitive prospects over the longer term. The projected rate at which residual income is expected to fade over the life cycle of the firm is captured by a persistence factor, w, which is between zero and one.
To simplify the model, we typically make one of the following assumptions about continuing residual income at the end of the short-term period:
• Residual income is expected to persist at its current level forever.
• Residual income is expected to drop immediately to zero.
• Residual income is expected to decline to a long-run average level consistent with a mature industry.
• Residual income is expected to decline over time as ROE falls to the cost of equity (in which case residual income is eventually zero).
An analysis of the firm's position in its industry and the structure of the industry will be necessary to justify one of these assumptions. The third scenario is the most realistic if we assume that over time, industry competition reduces economic profits to the point at which firms begin to leave the industry and ROE stabilizes at a long-run normal level. The strength of the persistence factor will depend partly on the sustainability of the firm's competitive advantage and the structure of the industry. The more sustainable the competitive advantage and the better the industry prospects, the higher the persistence factor.
Higher persistence factors will be associated with the following:
• Low dividend payouts.
« Historically high residual income persistence in the industry. Lower persistence factors will be associated with the following:
• High return on equity.
• Significant levels of nonrecurring items.
• High accounting accruals.
Professor's Note: Be prepared for an exam question that links this material with the material in the topic review of competitive strategy in Study Session 11.
multistage residual income model
LOS 45.i: Calculate and interpret the intrinsic value of a share of common stock using a multistage residual income model, given the required rate of return, forecasted earnings per share over a finite horizon, and forecasted continuing residual earnings.
Think of the continuing residual income model as a multi-stage model similar to the multi-stage DDM and FCF models from Study Session 11. In the residual income model, intrinsic value is the sum of three components:
VQ = B0 + (PV of interim high-growth RI) + (PV of continuing residual income)
Step 1: Calculate the current book value per share.
Step 2: Calculate residual income in each year 1 toT - 1 during the interim high-growth period and discount them back to today at the required return on equity.
Step 3: Calculate continuing residual income that begins at the end of the high-growth period starting in ycarT, and then calculate the present value of continuing residual income as of the end of yearT - 1 using the following formula:
PV of continuing residual income in year T -1 =--—
Ifw = 1, residual income is expected to persist at the current level forever after year T - 1, so residual income in every year after T equals residual income in year T. The present value of continuing residual income at the end of year T - 1 is the present value of a perpetuity:
PV of continuing residual income in yearT — 1 = —— = —— =
Assumption #2: Residual Income Drops Immediately to Zero
If u; = 0, residual income is expected to drop immediately to zero beginning in year T + 1, and the present value of continuing residual income in year T - 1 is:
PV of continuing residual income in yearT - 1
Assumption #3: Residual Income Declines Over Time to Zero
If residual income is expected to decline over time after yearT as ROE falls to the cost of equity capital, then the persistence factor, u), is between zero and one, and the present value of continuing residual income in yearT - 1 is equal to:
PV of continuing residual income in year T — 1 =
Assumption #4: Residual Income Declines to Long-Run Level in Mature Industry
There is another, simpler approach to calculating the PV of continuing residual income that does not rely on the formula or u), the persistence factor, if residua] income is expected to decline to a normal long-run level consistent with a mature industry after year T.
First, recall from the single-stage residual income mode) thar market value equals book value plus the present value of residual income. Therefore, at any point in rime (T), the present value of future residual income is the difference becween market value (Py) and book value (BT):
PV of continuing residual income in year T = Py - By
How do we estimate Py?
Given a forecasted price-to-book ratio and book value ac the end of the yearT, the value of the stock is:
Py = By x (forecasted price-to-book ratio)
To make this approach consistent with the first three that use the persistence factor equation, we can also calculate the present value of continuing residual income at time T - 1:
, , (PT-BT) + RIT PV of continuing residual income in year T — 1 =-j--
Example: Calculating value with a multistage residual income model (part 1)
Java Metals is expecting an ROE of 15% over each of the next five years. Its current book value is $5.00 per share, it pays no dividends, and all earnings are reinvested. The required return on equity is 10%. Forecasted earnings in years 1 through 5 are equal to ROE times beginning book value. Calculate the intrinsic value of the company using a residual income model, assuming that after five years, continuing residual income falls to zero.
The following table provides an estimate of the present value of residual income.
Java Metals Residual Income Forecast
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