Question

New competition in Acme Unlimited s market is going to have an impact on the growth of the firm s dividends. A current dividend of $1.50 was paid yesterday, and this dividend is expected to increase by 35% in the first year. After that point, the growth in dividends is expected to decay to the firm s long run constant growth of 5%. Such a decay process is one in which dividend growth declines by 10 percentage points per year up to the point where the expected constant rate of dividend growth is reached. So, year 2 dividend will be 25 percent higher than year 1, year 3 dividend will be 15 percent higher, and after year 3, dividends will grow by 5 percent forever. Assume that investors require a rate of return of 17 on Acme Unlimited s stock.

1. Calculate the dividend in year 2. ； Calculate the dividend in year 4.

2. Determine the price of Acme Unlimited s stock at the end of year 3 (just after the dividend has been paid)

3. Calculate the current price of Acme Unlimited s stock.

Answer 1

1). D2 = D0(1 + g1)(1 + g2) = $1.5 x 1.35 x 1.25 = $2.53

D4 = D2(1 + g3)(1 + gC) = $2.53 x 1.15 x 1.05 = $3.06

2). P3 = D4 / (r - gC)

= $3.06 / (0.17 - 0.05) = $3.06 / 0.12 = $25.47

3). P0 = [D1/(1 + r)] + [D2/(1 + r)²] + [(D3 + P3)/(1 + r)³]

   = [($1.5 x 1.35)/1.17] + [($1.5 x 1.35 x 1.25)/1.17²] + [{($1.5 x 1.35 x 1.25 x 1.15) + $25.47}/1.17³]

= $1.73 + $1.85 + $17.72 = $21.30