You want to value a firm which is growing fairly fast now (abnormal growth) but

Question

You want to value a firm which is growing fairly fast now (abnormal growth) but will begin reaching maturity and a correspondingly lower earnings growth rate shortly. You’ve decided that a three-stage dividend discount model fits your needs perfectly for this firm. Using the information below, calculate the present value of this firm. Earnings last year (E0) = $2.95 per share Dividends last year (D0) = $0.60 ROE last year = 25% growth = retention rate x ROE You expect earnings growth, dividend payout and ROE to be stable over the next two years. At that time we will see the firm slow its earnings growth, increase its dividend payout, and reduce its cost of equity over the next three years. The long-term Treasury rate is 4%, the firm’s current beta is 1.4, but you expect the long-term beta to fall to 1.0 by the end of your phase down period and the market risk premium is 6%. Long-term earnings are expected to grow at three percent to perpetuity and firm should be able to maintain a constant ROE of 10% for perpetuity. What is the present value of this firm’s equity using the three-stage dividend discount model?

Explanation / Answer

In the first phase of 2 years

Retention Rate = Dividend payout of last year (D0)/Earnings of last year (E0) = 0.6/2.95 = 20.3%

ROE = 25%

Growth = Retention Rate * ROE = 20.3%*25% = 5.1%

Since earning and dividend payout is stable for next 2 years

Dividend Payout in year 1 (D1) = 0.6*(1+5.1%) = 0.63 ; Present Value = D1/(1+25%) = 0.5

Dividend Payout in year 2 (D2) = 0.6*(1+5.1%)^2 = 0.66 ; Present Value = D2/(1+25%)^2 = 0.4

In the 2nd phase of 3 years

Beta = 1.4, Treasury Rate = 4%, Market Risk Premium = 6%

USing CAPM model, Cost of Equity = Treaury Rate + Beta * Market Risk Premium = 4% + 1.4*6% = 12.4%

Transitionary Period = 3 years

Growth moderates from 5.1% at the start of transitionary period to 3% at its end

Assuming a linear decrease, growth rates in year 3 , 4 & 5 are 4.6%, 4.0% & 3.5% respectively (before settling at 3% 6th year onwards)

Retention Rate = Growth/ROE

Retention Rate in year 3 = 4.6%/12.4% = 36.8%

Retention Rate in year 4 = 4.0%/12.4% = 32.6%

Retention Rate in year 5 = 3.5%/12.4% = 28.4%

Dividend Paid in Year 3 (D3)= Earnings in Year 3 * Retention Rate in Year 3 = 2.95*(1+4.6%)*36.8% = 1.1

Present Value = D3/(1+12.4%)^3 = 0.8

Dividend Paid in Year 4 (D4)= Earnings in Year 4 * Retention Rate in Year 4 = 2.95*(1+4.6%)*(1+4.0%)*32.6% = 1.0

Present Value = D4/(1+12.4%)^4 = 0.7

Dividend Paid in Year 5 (D5)= Earnings in Year 5 * Retention Rate in Year 5 = 2.95*(1+4.6%)*(1+4%)*(1+3.5%)*28.4% = 0.9

Present Value = D5/(1+12.4%)^5 = 0.5

In the 3rd and stable phase

ROE = 10%, perpetual growth = 3%

As per gordon-growth model, present value of all future dividends at end of year 5 = D5*(1+perpetual growth)/(ROE-perpetual growth) = 0.9*(1+3%)/(10%-3%) = 13.9

Present Value of the dividends of stable phase at end of year 0 =13.9/[(1+ROE of 1st phase)^2*(1+ROE of 2nd phase)^3] = 6.3

Present Value of firm's equity = Sum of Present Value of the dividends of all the 3 phases = 9.2

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

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