Question

For a firm that expects earnings next year of $10.00 per share, has a plowback ratio of 35%, a return on equity of 20%, and a required return of 15%.

a. Calculate the sustainable growth rate of the firm (Already calculated to be 7%)

b. Calculate the current stock price and next year's expected stock price assuming that the growth rate is constant. (Already calculated current to be $81.25)

c. Redo the calculation if the growth of the company's dividends is expected to fall by 2 percentage points four years from today.

Answer 1

Doing part c).

EPS1 = $10

Plowback ratio = 35%

So, Dividend at year 1, D1 = EPS1*(1-plowback ratio) = 10*(1-0.35) = $6.5

Ke = 15%

Growth rate as calculated for 1st 4 year = 7%,

So, Dividend at year 2, D2 = D1*(1+g) = 6.5*1.07 = $6.96

D3 = D2*(1+g) = 6.96*1.07 = $7.44

D4 = D3/(1+g) = 7.44*1.07 = $7.96

Now, growth rate has dropped to 5% and is constant thereafter

So, D5 = D4*1.05 = 7.96*1.05 = $8.361

Since growth rate is constant now, using Gordon's growth rate to calculate Price at year 4

P4 = D5/(Ke-g) = 8.36/(0.15-0.05) = $83.61

Price today is sum of PV of all future dividends and PV of price at year 4

So, P0 = D1/(1+Ke) + D2/(1+Ke)^2 + D3/(1+Ke)^3 + D4/(1+Ke)^4 + P4/(1+Ke)^4

P0 = 6.5/1.15 + 6.96/1.15^2 + 7.44/1.15^3 + 7.96/1.15^4 + 83.61/1.15^4 = $68.16

So price today = $68.16