# Module 32.4 LOS 32.h: Residual Income Forecasting with a Persistence Factor

The challenge of using residual income models is that we must forecast residual income indefinitely into the future. However, by taking the approach from the multistage DDM model, we can simplify this projection. This involves making a short term forecast over 5 years for instance, then if the residual income growth will turn to a continuing residual income level in the long run. This level will depend on the persistence factor, which represents the fortunes of the industry, as well as on the sustainability of a specific firm’s competitive prospects over the longer term. This can be written as:

V0 = B0 + (PV of interim high-growth RI) + (PV of continuing residual income)

After the short-term forecast, one following assumption are used in this multistage RI model:

• 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 over time as ROE falls to the cost of equity (in which case residual income is eventually zero).
• Residual income is expected to decline to a long-run average level consistent with a mature industry.

The persistence factor determines the value of this long-term forecast. High persistence factors are associated with low dividend payouts and high historical values in the industry, which low factors can be tied to high returns on equity and business with large amounts of nonrecurring items and accounting accruals.

Calculate PV of Continuing Residual Income in the multistage model:

The first two steps of valuation is the same as the single-stage model, determine the book value of the firm and the present value of the forecasted high-growth RI.

To calculate the PV of the continuing residual income we can use the following equation:

Notice that if the cash flows are expected to continue forever,  will be one, and if cash flows immediately drop to zero,  will be 0, simplifying our denominator.

For the final assumption, where RI declines to the long-run level in a mature industry, we can use the following equation instead:

Where:

PT = BT × (forecasted price-to-book ratio)