- CFA Exams
- CFA Level I Exam
- Study Session 7. Corporate Finance (1)
- Reading 21. Analysis of Dividends and Share Repurchases
- Subject 1. Dividend policy and company value: theory

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**CFA Practice Question**

Consider a 100% equity financed firm that has physical assets valued at $200 million. The market believes that all physical assets the firm has will produce earnings of 12.5% of the value of the assets. The firm reinvests an unknown amount of earnings into physical capital, and pays out the rest as dividends. There are no taxes. What is the P/E ratio for the firm?

A. 6

B. 8

C. 12

**Explanation:**As it turns out, the rate of retention doesn't matter. The earnings of the firm for the first year are 200M * 12.5% = 25M.

Say the retention rate is b.

Amount of earnings retained to reinvest in physical capital = b*25M

Amount of earnings paid out as dividends = (1-b)*25M

Growth rate = b*25M/200M = 12.5%*b

Then we have the price of total equity = (1-b)*25M/(12.5% - b*12.5%) = (25M/12.5%)*((1-b)/(1-b)) = 200M

And PE ratio = 200M/25M = 8

So what happened here? This is simply Modigliani-Miller in action. The firm can either pay out dividends or keep the money and re-invest in physical assets that produce a 12.5% return, and have the cash flows produced discounted at 12.5%. So essentially when the firm re-invests $1, it produces cash flows whose discounted value is $1. Therefore it does not matter how much the firm retains, it doesn't change the value of equity, therefore does not change P/E ratio. In other words, the dividend policy is irrelevant.

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**User Contributed Comments**
6

User |
Comment |
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leftcoast |
I wouldn't rank this question as easy. |

somk |
leftcoast, ranking is based on the percentage of users getting it right. so it seems u r over estimating this question. |

adamrej |
A somewhat implicit assumption here is that the applicable discount rate is equal the expected return on equity. Not sure why this should hold ... |

daverco |
Or to get to the P/E ratio, you take the inverse of the E/P ratio. The E/P ratio is a proxy for the cost of equity, which is here 25/200 (because 200 is all equity) = 0.125. Then, 1/0.125 = 8. That's how I reasoned through it at least. |

darbyland |
thank you for that daverco |

darbyland |
can anyone explain how the growth rate is calculated (as b*25M/200M) ? |