The earnings and dividend growth prospects of Medical Inc. are disputed by analy

Question

The earnings and dividend growth prospects of Medical Inc. are disputed by analysts. Analyst #1 is forecasting 5% growth in dividends indefinitely. Analyst #2 however, is predicting a 20% growth in dividends but only for the next three years, after which growth rate is expected to decline to 4% for the indefinite future. Medical dividends per share are currently $3. Stocks with similar risk are currently priced to provide a 14% expected return.

a. What is the intrinsic value of Medical stock according to Analyst #1?

b. What is the intrinsic value of Medical stock according to Analyst #2?

c. Assume that Medical stock now sells for $39.75 per share. If the stock is fairly priced at the present time, what is the implied perpetual dividend growth rate? What is the implied P/E1 ratio (i.e., today’s price over next year’s earnings), based on this perpetual dividend growth assumption and assuming a 25% payout ratio?

Explanation / Answer

Dividend (D) = 3
Expecetd Return (r) = 14%
1. Growth = 5%
Intrinsic value of Medical Stock = D*(1+g) /(r-g) = 3 * (1+5%)/(14%-5%) = 35

2.
Grwoth for 3 years
Growth after 3 years= 4%
Instrinsic value of stock = D*(1+g1)/(1+r) + D*(1+g1)2/(1+r)2 + D*(1+g1)3/(1+r)3 + D*(1+g1)3*(1+g2)/[r-g2)(1+r)3]
=3*(1+20%)/(1+14%) + 3*(1+20%)2/(1+14%)2 + 3*(1+20%)3/(1+14%)3 + 3*(1+20%)3 * (1+4%)/[14% -4%) *(1+14%)3 = 46.37

c) Price = 39.75
P = D*(1+g)/(r-g)
39.75 = 3 * (1+g)/(14%-g)
13.25 = (1+g)/(14%-g)
13.25*14% - 13.25g = 1 +g
13.25*14% - 1 = 14.25 g
g = 6%

D = 3
Payout ratio = 25%
Earnings * 25% = Dividends
Earnings = 3/25$ = 12
P/E = 39.75/12 = 3.31

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