Question

Jia's Fashions recently paid a $2 annual dividend. The company is projecting that its dividends will grow by 20 percent next year, 12 percent annually for the two years after that, and then at 6 percent annually thereafter. Based on this information, how much should Jia's Fashions common stock sell for today if her required return is 10.5%?

**Please show work**

Answer 1

Under the Dividend Discount Model, Fair Value of a stock = Present Value of all dividend payments + Present Value of Terminal Value (When Dividend are expected to grow at a constrant rate forever)

So given that Dividend already Paid (D0) = $ 2

Now Dividend for Next Year (D1) = D0 x (1+Growth Rate of Dividend)

Now Dividend for Next Year (D1) = $ 2 x (1+0.20) = $ 2.4

Now Dividend for Year 2 (D2) = D1 x (1 + Growth Rate of Dividend for year 2)

Now Dividend for Year 2 (D2) = $ 2.4 x (1+0.12) = $ 2.688

Now Dividend for Year 3 (D3) = D2 x (1+0.12) = $ 2.688 x 1.12 = $ 3.01056

Now Dividend for year 4 (D4) = D3 x (1 + G) =  $ 3.01056 x (1.06) = $ 3.19

Now Dividend for year 5 (D5) = D4 x (1 + G) = $ 3.19 x (1+0.06) = $ 3.383

Terminal Vaue of the share at the end of Year 4 = D5 / R- G where R is the discount rate = 10.5% and G is 6%

Now Ternminal Value = $ 3.383 / 10.5 % - 6 % = 75.17

Now we need to compute the present value of Dividends and Terminal Value

	Year 1	Year 2	Year 3	Year 4
Dividend (A)	2.4	2.688	3.01056	3.19
Terminal Value (B)				75.17
Total (C= A + B)	2.4	2.688	3.01056	78.36
Discount Factor @ 10.5 (D)	0.904977376	0.81898405	0.741162036	0.670734875
Derivation Discount Factor @ 10.5	=1/1.105^1	=1/1.105^2	=1/1.105^3	=1/1.105^4
Present Value (E = C x D)	2.171945701	2.201429127	2.23131278	52.55878478

Total of the present value = Fair Value of Shares

Therefore Fair value of shares = $ 59.16