Question

(Ordinary share valuation) Assume the following:

• the investor’s required rate of return is 15%

• the expected level of earnings at the end of this year (E|) is
$5.00

• the retention ratio is 50% • the return on equity (ROE) is 20%
(i.e. it can earn 20% on reinvested earnings)

• similar shares sell at multiples of 10 times earnings per
share.

Questions:

(a) Determine the expected growth rate for dividends.

(b) Determine the price/earnings ratio (P!E\) using equation.

(c) What is the share price using the P/E ratio valuation method?

(d) What is the share price using the dividend discount model?

(e) What would happen to the P/E ratio (P!E\) and share price if the firm could earn 25% on reinvested earnings (ROE)?

(f) What does this tell you about the relationship between the rate the firm can earn on reinvested earnings and P/E ratios?

Using the correct formulas, not excel calculators/cells

Answer #1

a) | ||

Growth Rate = ROE x Plowback ratio | ||

Growth Rate = 20% x 50% | 10.00% | |

b) | ||

P0 = DIV1/(r-g) | ||

DIV 1 = E1 x ( 1 - 50%) | $2.50 | |

P0 = $2.50/(15% - 10%) | $50.00 | |

P/ E = $50/$5 | 10.00 | Times |

c) | ||

P/E = Price / EPS = 10 = Price/$5 | ||

Price = 10 x $5 | $50.00 | |

d) | ||

P0 = DIV1/(r-g) | ||

DIV 1 = E1 x ( 1 - 50%) | $2.50 | |

P0 = $2.50/(15% - 10%) | $50.00 | |

e) | ||

Growth Rate = ROE x Plowback ratio | ||

Growth Rate = 25% x 50% | 12.50% | |

P0 = DIV1/(r-g) | ||

DIV 1 = E1 x ( 1 - 50%) | $2.50 | |

P0 = $2.50/(15% - 12.50%) | $100.00 | |

P/ E = $100/$5 | 20.00 | Times |

f) | ||

The ROE increases, then growth rate also increases and PE ratio increases as the return on equity increases and decreases as the return on equity decreases. |

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