Question

ABC Company just paid a dividend (Do) of $1.10. Due to a new product being introduced to the market, ABC expects to achieve a supernormal annual growth rate of 15% for the next four years. After that, growth is expected to return to the long-run constant rate of 8%. Investors require a 12% return on this stock.

Question 1 : What are the total return, expected dividend yield, and capital gains yield for the first year?

Question 2 : What are the total return, capital gains yield, and expected dividend yield for the fifth year?

Answer 1

Given about ABC company,

Last dividend D0 = $1.1

dividend growth rate for next 4 years is 15%

=> D1 = 1.1*1.15 = $1.2650

D2 = 1.2650*1.15 = $1.4548

D3 = 1.4548*1.15 = $1.6730

D4 = 1.6730*1.15 = $1.9239

there after growth rate is constant g = 8%

So, D5 = 1.9239*1.08 = $2.0778

required return on the stock r = 12%

So, price of the stock in 4 year is calculated using constant dividend growth rate

P4 = D5/(r-g) = 2.0778/(0.12-0.08) = $51.9455

Price today of the stock P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + P4/(1+r)^4

=> P0 = 1.265/1.12 + 1.4548/1.12^2 + 1.673/1.12^3 + 1.9239/1.12^4 + 51.9455/1.12^4 = $37.71

Price of the stock 1 year from today P1 = D2/(1+r) + D3/(1+r)^2 + D4/(1+r)^3 + P4/(1+r)^3

=> P1 = 1.4548/1.12 + 1.673/1.12^2 + 1.9239/1.12^3 + 51.9455/1.12^3 = $40.98

Calculating for 1st year

Total return = (P1+D1-P0)/P0 = (40.98+ 1.265-37.71)/37.71 = 12%

Capital yield gain = (P1 - P0)/P0 = (40.98-37.71)/37.71 = 8.65%

Dividend yield = D1/P0 = 1.265/37.71 = 3.35%

Calculating for 5th year

Total return is same as the required return

=> Totla return = 12%

Dividend yield = D5/P4 = 2.0778/51.9455 = 4%

Capital gain yield = Total return - dividend yield = 12-4 = 8%