A company currently has earnings (E0) of $2.00 and a dividend (D0) of $0.50. The

Question

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?

Can someone show me how to work this out?

Explanation / Answer

the three stage DDM has two types

1. CASE1: 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.

2. 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.

Note: H Model is a variant of the two stage model in which growth begins at a high rate and declines linearly throughout the supernormal growth period until it reaches a constant rate.

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%+1.6*6%=13.6%

Solving for growth rate g

g= ROE* retention ratio

g=.30*[(2-0.50)/2] =0.225 =22.5%

D0=0.50

so D1= 0.50*(1+0.225) = 0.6125 Present Value at 13.6%=0.5392

D2 = 0.6125*(1+0.225)= 0.7503 Present value at 13.6% = 0.5814

Total= 1.1206

Value of stage 2

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]

0.7503(1.03)/0.10-0.03 + 0.7503(1.5)(0.225-0.03)/0.10-0.03 = 14.175

note h= transition period/2

PV at 10% = 11.715

total value of equity per share =11.715+1.1206 =11.8356$

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.