A company currently has earnings (E0) of $3.00 and a dividend (D0) of $1.25. The

Question

A company currently has earnings (E0) of $3.00 and a dividend (D0) of $1.25.

The firm’s current return on equity (ROE) is 40%. 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 2%. The firm will then

grow at 2% to perpetuity. The firm’s beta is presently 1.4, 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 5% 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?

Explanation / Answer

Case 1: The "general" three stage model wherein the company is has three distinct stages of growth and the growth rate of the second stage is constant.

Case 2:  The growth rate in the second is assumed to decline linearly to a constant growth rate. Here we will treat the second stage as an H MODEL.

The first step would be to compute the 2 dividends in stage 1and find their present values at a discount rate we calculate using CAPM

CAPM to solve for discount rate in stage 1

Ke=Rf + Beta * market risk premium =4%+1.4*6%=12.4%

Solving for growth rate (g)= ROE* retention ratio

g=.40*[(3-1.25)/2] =0.35 =35%

D0=1.25

so,

D1= 1.25*(1+0.35) = 1.6875 ,Present Value at 13.6%=1.2392

D2 = 1.6875*(1+0.35)= 2.2781 Present value at 13.6% = 1.2814

Total= 2.5206

Ke for stage two

Ke= 4%+ 6%*1 = 10%

V2 = [D2(1+ long term growth rate)]/(ke-long term growth rate)] +[D5H (short term growth rate- long term growth rate)/ (ke-long term growth rate]

2.2781(1.03)/0.10-0.04 + 2.2781(1.5)(0.35-0.04)/0.10-0.04 = 56.7626

h= transition period/2

PV at 10% = 11.715

total value of equity per share =11.715+2.5206 =14.2356$

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