The Residual Income Model

Say that Center Street Chicken, a US fast food restaurant, consistently earns income over the cost of capital. How do you think the value of Center Street would respond?

No.

Exactly!

If Center Street is consistently growing, growth is going to compound over time and grow exponentially, so the value would increase more over time. That's pretty straightforward. So to calculate that exponential growth, the residual income model is a great tool to use because it takes the current book value plus the present value of expected future residual income. $$\displaystyle V_0 = B_0 + \sum_{t=1}^{\infty}\frac{RI_t}{(1+r)^t}$$ where $$\displaystyle \sum_{t=1}^{\infty}\frac{RI_t}{(1+r)^t} = \sum_{t=1}^{\infty}\frac{E_t - rB_{t-1}}{(1+r)^t}$$.

For the per-share residual income model, take Center Street's EPS less the per-share equity charge for the period, which is the required rate of return on equity multiplied by the book value per share at the beginning of the period. So if Center Street's EPS exceeds the cost of equity, what do you think the per-share residual income valuation would be compared to zero?

Yes! If Center Street's EPS is greater than the cost of equity capital per share, then residual income will be higher, and the value will be too. Typically the residual income value will equal the dividend discount value because it's fundamentally similar to the DDM model. So if assumptions are the same, it will yield the same results. But there's a key difference: residual income models will typically recognize value earlier than DDM models. Why do you think that's the case?

Not quite. Center Street is earning more than the cost of capital.

No. Earnings impact valuation, so there's a definite impact.

Not quite. The residual income model grows income throughout the period, but that's not why value is realized earlier in the time period.

No. The DDM model doesn't start with an intrinsic value calculation.

That's it! The residual income model starts with the book value of the business, so it's going to capture that initial value. In comparison, the DDM grows dividends over time, so the intrinsic value calculation's terminal value is the main source of value.

To summarize: [[summary]]

Grow slowly

Grow exponentially

Lower

Higher

No impact

The DDM model starts with an intrinsic value calculation

Residual income grows income throughout the time period

The residual income model starts with the book value of the company

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