Financial Statement Analysis — Accounting Numbers and Firm Value: The Residual Income Model and P/B

The last stage of financial statement analysis turns the results into value. The discounted cash flow (DCF) model is widely used, but there is also the residual income model (RIM), which starts directly from accounting numbers. With consistent assumptions, the two give the same value. This chapter uses the residual income model to see how accounting information connects to value.

1. Defining residual income

Residual income (abnormal earnings) is net profit minus the minimum return shareholders require, that is, the cost of equity.

\text{RI}_t = \text{NI}_t - r \times B_{t-1} = (\text{ROE}_t - r) \times B_{t-1}

$B_{t-1}$ is the opening book value of equity and $r$ the cost of equity. Residual income is positive only when ROE exceeds the cost of equity. Profit that falls short of the cost of equity destroys shareholder value.

2. The residual income model

Adding clean surplus accounting (change in equity = net profit − dividends, with no share issues) to the dividend discount model gives:

Residual income model

V_0 = B_0 + \sum_{t=1}^{\infty} \frac{\text{RI}_t}{(1 + r)^t} \quad \Rightarrow \quad V_0 = B_0 + \frac{\text{RI}_1}{r - g}\ (\text{if residual income grows at } g)

Equity value is current book value plus the present value of future residual income. Book value is the starting point of value; the ability to earn abnormal returns creates the premium.

3. Estimating FA’s value

FA’s equity at the end of 20X2 is ₩50 billion and its cost of equity 10%. Assume ROE stays at 20% and residual income does not grow.

Residual income for 20X3: $(20\% - 10\%) \times 500 = 50$ (₩5 billion)
Value: $500 + 50 / 0.10 = 1{,}000$ (₩100 billion)
Justified P/B: $1{,}000 / 500 = 2.0$ times

Value under different ROE assumptions (equity 500, cost of equity 10%, no growth; unit: ₩100 million)
ROE	Residual income	Value	P/B
8%	−10	400	0.8
10%	0	500	1.0
16%	30	800	1.6
20%	50	1,000	2.0

When ROE equals the cost of equity, P/B is 1: the company is worth only its book value. When ROE is below the cost of equity, P/B is below 1. That does not mean the shares are cheaper than liquidation value; it is the market’s judgement that continuing to use the capital destroys value.

4. Expectations embedded in the market price

Chapter 7 assumed FA’s market capitalization to be ₩80 billion. Working back the expected ROE embedded in this price, $800 = 500 + \text{RI} / 0.10$ gives $\text{RI} = 30$ (₩3 billion), an expected ROE of 16%. The market expects FA’s ROE to fall from 20% to about 16%. Chapter 3 showed that much of FA’s ROE comes from financial leverage. The analyst judges whether this expectation is too pessimistic or appropriate, and makes an investment decision.

5. Relationship with P/E

P/E is price divided by earnings. Seen through the residual income model, P/E reflects earnings growth and the persistence of abnormal returns. When one-off gains inflate net profit, P/E looks low, but recalculated on normalized earnings (chapter 6) it rises. Read P/B together with ROE, and P/E together with earnings growth.

Check your understanding

FJ’s equity is ₩200 billion and its cost of equity 8%. Next year’s ROE is expected to be 12%, and residual income is assumed to grow by 2% a year thereafter. Find the equity value and justified P/B with the residual income model. If the current market capitalization is ₩240 billion, what residual income growth rate is the market assuming?

Next year’s residual income is $(12\% - 8\%) \times 2{,}000 = 80$ (₩8 billion). Value is $2{,}000 + 80 / (0.08 - 0.02) ≈ 2{,}000 + 1{,}333 = 3{,}333$ (about ₩333 billion), a P/B of about 1.67. With a market value of ₩240 billion, $2{,}400 = 2{,}000 + 80 / (0.08 - g)$ gives $0.08 - g = 0.2$ , so $g = -12\%$ . The market expects abnormal earnings to disappear quickly.

References

Stephen Penman, Financial Statement Analysis and Security Valuation, ch. 5–6
James Ohlson, “Earnings, Book Values, and Dividends in Equity Valuation,” Contemporary Accounting Research (1995)
Krishna Palepu, Paul Healy and Erik Peek, Business Analysis and Valuation: IFRS Edition, ch. 7–8