Question

The Duo Growth Company just paid a dividend of $1 per share. The dividend is expected to grow at a rate of 25% per year for the next 3 years and then to level off to 5% per year forever. You think the appropriate market capitalization rate is 20% per year. (a) What is your estimate of the intrinsic value of a share of the stock? (b) If the market price of a share is equal to this intrinsic value, what is the expected dividend yield? (c) What do you expect its price to be 1 year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate? Explain.

Answer 1

Answer:

a) 11.17 dollar

b) dividend yield 11.19%

c) next year the sotck price will be 13.96

Explanation:

The intrinsic value is the present value of the future dividends:

first we calcualte the future divididends by multipling the recent dividends by the grow rates:

D0 = 1

D1 = D0 x (1 + 25%) = 1.25

D2 = D1 x (1 + 25%) = 1.563

D3 = D2 x (1 + 25%) = 1.954

for the future dividends which grow indefinitely at % we use the gordon model

$\frac{divends}{return-growth} = Intrinsic \: Value$

D4 = D3 x (1 +   5%) = 2.05

grow 5%

return 20%

$\frac{2.05}{0.2-0.05} = 13.678$

Then we discount each dividend to bring them at present date using the present value of lump sum formula:

$\frac{Divided}{(1 + rate)^{time} } = PV$

$\left[\begin{array}{ccc}Year&dividends&PV\\0&1&1\\1&1.25&1.0417\\2&1.563&1.0854\\3&1.954&1.1308\\3&13.678&7.9155\\Total&&11.17\\\end{array}\right]$

Finally we just add it and get the intrincis value.

B) dividend yield: dividends / price:

1.25/11.17 = 0,11190 = 11.19%

C) the stock will grow at grow rate:

11.17 x 1.25 = 13,96