Question

A company currently has earnings (E_{0}) of $2.00 and a
dividend (D_{0}) of $0.50. The firm’s current return on
equity (ROE) is 30%. The firm will maintain the same dividend
payout and ROE over the next two periods. Then it will transition
in a linear reduction in years 3, 4, and 5 to a growth of 3%. The
firm will then grow at 3% to perpetuity. The firm’s beta is
presently 1.6, but this will transition to 1 over the same period.
The risk-free rate is 4% and the market risk premium is 6%. ROE is
expected to be 10% beginning in year 5 to perpetuity. What is the
present value of this firm’s equity using a three-stage model with
linear transition in years 3, 4, and 5?

0 | 1 | 2 | 3 | 4 | 5 | 6 | |

Earnings Growth Rate | 0.225 | 0.225 | 0.225 | 0.16 | 0.095 | 0.03 | 0.03 |

EPS | 2 | 2.45 | 3.00125 | 3.48145 | 3.812188 | 3.926553 | 4.04435 |

Div Payout (DPS/EPS) | 0.25 | 0.25 | 0.25 | ||||

DPS | 0.5 | 0.6125 | 0.750313 | ||||

Ke | 0.136 | 0.136 | 0.136 | 0.124 | 0.112 | 0.1 | 0.1 |

PV Cashflows | 0.539173 | 0.581414 |

I need to find DPS: D3, D4, D5, D6.

For D1 and D2, it was the normal formula. IE; D1: D0(1+g1) ; D2: D1(1+g2)

Answer #1

K = E/P

where

E = Earnings per share

P= Price per share

Price per share = Earnings per share/ ke (use for year 3, 4,5,6)

0 | 1 | 2 | 3 | 4 | 5 | 6 | |

Earnings | 2 | 2.45 | 3.00125 | 3.48145 | 3.812188 | 3.926553 | 4.04435 |

Return on Equity | 30% | 30% | 30% | 0.124 | 0.112 | 10% | 10% |

Equity | 6.6666667 | 8.166667 | 10.00416667 | 28.07621 | 34.03739286 | 39.26553 | 40.4435 |

Using the beta and Mp and M r , we can calculate the cost of equity, using which we can calculate NPV.

therefor Beta in Year 2 =1.6

beta in Yaer 3 = 1.4

Beta in Year 4 = 1.2

beta in Year 5 = 1.0

Year | Beta | Cost of Capital |

3 | 1.4 | 12.4 |

4 | 1.2 | 11.2 |

5 | 1 | 10 |

The EPS given in above table could be discounted at above cost of capital and added to get PV.

As is seen from table given,

g3= .16, g4=.095,g5=.03

0 | 1 | 2 | 3 | 4 | 5 | 6 | |

Earnings | 2 | 2.45 | 3.00125 | 3.48145 | 3.812188 | 3.926553 | 4.04435 |

DPS | 0.5 | 0.6125 | 0.750313 | 0.870363 | 0.953047573 | 0.981639 | 1.011088 |

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 12 minutes ago

asked 16 minutes ago

asked 21 minutes ago

asked 21 minutes ago

asked 25 minutes ago

asked 29 minutes ago

asked 36 minutes ago

asked 39 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago