- CFA Exams
- CFA Level I Exam
- Study Session 11. Equity Valuation (3)
- Reading 30. Residual Income Valuation
- Subject 3. The residual income valuation model

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**CFA Practice Question**

Which of the following statements is (are) true with respect to the relationship between the various equity valuation models?

II. The residual model recognizes that the most of the firm's value is captures up front in the form of the firm's current book value.

III. The residual income model generally produces more certain results than the dividend discount model (DDM).

IV. The price-to-book value for a firm will always be greater than one if its return on equity exceeds its required rate of return on equity.

I. The residual income model always results in a lower value than the dividend discount model for a firm that has a positive dividend growth rate.

II. The residual model recognizes that the most of the firm's value is captures up front in the form of the firm's current book value.

III. The residual income model generally produces more certain results than the dividend discount model (DDM).

IV. The price-to-book value for a firm will always be greater than one if its return on equity exceeds its required rate of return on equity.

Correct Answer: II, III, IV

I is incorrect because in theory, if the assumption used for both models are consistent, then both models should yield the same results.

II is true because the value of a share under the residual income model is simply the sum of the share's book value plus the present value of all future residual incomes.

III is true because as statement II points out, the residual income model recognizes that the initial book value captures most of the share's market value, whereas the DDM heavily relies on future estimated dividends.

IV is true because if the firm's return on equity exceeds its required rate of return on equity, then the present value of its residual income will be positive, making its value per share greater than its current book value per share.

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**User Contributed Comments**
8

User |
Comment |
---|---|

REITboy |
On II, what if ROE > 100%? |

quanttrader |
P = B(0) + [(ROE - r)x B(0)] / (r-g) if ROE > r then P > B(0) ie P/B > 1 |

gregsob2 |
on 4, what if g>r? |

rodney176 |
I'm not getting why choice 3 is true? |

davidt876 |
gregs - g can never be greater than r tons of posts online explaining why, but the gist is that g is the projected growth rate of the company forever, and r is the projected rate of return for the market forever (and depending on average payout ratio in the market, the growth rate of the market will be either equal to or less than its rate or return because g = ROE*b) so by saying g > r you're saying the company will grow faster than the market forever.. and so eventually the company would become larger than the market - which is nonsensical because it's a constituent of the market - and it would continue to grow exponentially larger, untethered by reality, until it becomes infinitely larger than the market it's a part of. in reality if a company grows faster than the market for a prolonged period it eventually makes up a larger and larger proportion of the market, until eventually its 99.9999% (approaching 100%) of the market at which point the market's r is effectively the company's r, and the market's g is effectively the company's g. assume a retention ratio of less than 1 and g < r. assume a retention ratio of 1 and the calculator breaks because now r = g and we're dividing by 0 (r-g). it's certainly possible for a period, but not forever. and notice we don't divide by r or (r-g) unless it's foreve |

davidt876 |
...and rodney you're screwed if you're struggling with why III is true |

drake0000 |
David I love everything about your explanation. But wouldn't the company eventually assume 100% of the market as an individual monopoly? The assumption of a lim approaching infinity assumes that there are an infinite continuous set of market participants when in reality there are a discrete finite set. It seems like eventually there would be 3 companies, then 2, then 1... until the dominating company just became 1 single company with 100% of the worlds market share |

drake0000 |
Hmm actually i guess it would technically be infinite and continuous if you considered the possibility of new market participants attempting to enter the market and compete with the company that has achieved world domination |