Question

# A company currently has earnings (E0) of \$2.00 and a dividend (D0) of \$0.50. The firm’s...

A company currently has earnings (E0) of \$2.00 and a dividend (D0) 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)

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 3.81219 3.926553 4.04435 Return on Equity 30% 30% 30% 0.124 0.112 10% 10% Equity 6.6666667 8.166667 10.00416667 28.0762 34.0374 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 3.81219 3.92655 4.04435 DPS 0.5 0.6125 0.750313 0.870363 0.953048 0.981639 1.01109

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