Question

Carnes Cosmetics Co.'s stock price is $42, and it recently paid a $2.25 dividend. This dividend is expected to grow by 24% for the next 3 years, then grow forever at a constant rate, g; and r_s = 14%. At what constant rate is the stock expected to grow after Year 3? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Step 1:

Carnes Cosmetics Co.'s stock price = $42

rs = 14%

g = 24% for 3 years and let g be growth rate for years 4 to forever

Current Dividend = D0 = $2.25

Dividend in Year 1 = D1 = D0*(1+g) = $2.25 *(1+24%) = $2.79

Dividend in Year 2 = D2 = D1*(1+g) = $2.79 *(1+24%) = $3.4596

Dividend in Year 3 = D3 = D0*(1+g) = $3.4596 *(1+24%) = $4.289904

Horizon value in Year3 for years 4 to forever = D3 * (1+g) / (rs-g) = $4.289904 * (1+g) / (14% - g)

Step 2:

Carnes Cosmetics Co.'s Current Price of stock = Present value of Dividends

$42 = [D1/(1+r)^1] + [D2/(1+r)^2] + [D3/(1+r)^3] + [Horizon Value/(1+r)^3]

$42 = [$2.79 / (1+14%)^1] + [$3.4596 / (1+14%)^2] + [$4.289904 / (1+14%)^3] + [[$4.289904* (1+g) / (14% -g)] / (1+14%)^3]

$42 = [$2.79 / 1.14] + [$3.4596 / 1.2996] + [$4.289904 / 1.481544] + [[$4.289904* (1+g) / (14% -g)] / 1.481544]

$42 = $2.4473684 + $2.6620450 + $2.8955630 + [[$4.289904* (1+g) / (14% -g)] / 1.481544]

[[$4.289904* (1+g) / (14% -g)] / 1.481544] = $33.9950236

[$4.289904* (1+g) / (14% -g)] = $50.3651232

$4.289904 + $4.289904 g = $7.0511173 - $50.3651232 g

$54.6550272 g= $2.7612133

g = 0.050520756

g = 5.05%

Therefore, Growth rate for years 4 to forever is 5.05%