Question

Consider four different shares, all of which have a required return of 16% and a most recent dividend of $2.80 per share. Shares W, X and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 8%, 0% and −5% per year, respectively. Share Z is a growth stock that will increase its dividend by 20% for the next two years and then maintain a constant 12% growth rate thereafter. What is the dividend yield for each of these four shares? What is the expected capital gains yield? Discuss the relationship among the various returns that you find for each of these shares. (25)

Answer 1

For W, X , and Y (constant growth model)

Share Price = Next year Dividend/ (required rate - growth rate)

= recent dividend* (1+growth rate)/((required rate - growth rate) = D0*(1+g)/(r-g)

For W, Share price = 2.8 *1.08/(0.16-0.08) =$37.8

For X, Share price = 2.8 *1/(0.16-0.00) =$17.5

For Y, Share price = 2.8 *0.95/(0.16+0.05) =$12.67

For Share Z , two stage growth model

Share price = 2.8*1.2/1.16+ 2.8*1.2^2/1.16^2+ 2*1.2^2*1.12/(0.16-0.12)/1.16^2

=$65.82

Now, Dividend Yield = D1/P0

For W, Dividend yield = 2.8*1.08/37.8 = 0.08 or 8%

For X, Dividend yield = 2.8*1/17.5 = 0.16 or 16%

For Y, Dividend yield = 2.8*0.95/12.67 = 0.21 or 21%

For Z, Dividend yield = 2.8*1.2/65.82 = 0.0510 or 5.10%

Next year share price for W = D2/(r-g) = 2.8*1.08^2/(0.16-0.08) = 40.824

So, Capital Gains yield = (40.824-37.8)/37.8 = 0.08 or 8%

Next year share price for X = D2/(r-g) = 2.8*1.0^2/(0.16-0.00) = 17.5

So, Capital Gains yield = (17.5-17.5)/17.50 = 0.00 or 0%

Next year share price for Y = D2/(r-g) = 2.8*0.95^2/(0.16+0.05) = 12.033

So, Capital Gains yield = (12.033-12.667)/12.667 = - 0.05 or -5%

So, for X, Y and Z Capital gains yield will be the same as growth rate

For Z , Next year share price = 2.8*1.2^2/1.16+ 2.8*1.2^2*1.12/(0.16-0.12)/1.16 = $100.80

So, Capital Gains yield = (100.8-65.82)/65.82 = 0.5314112 or 53.14%

For stocks following constant growth, Capital gains is the same as long run growth rate and dividend yield is the difference between required rate of return and long run growth rate/the capital gains yield

For two stage model, the relationship is little tricky and during the initial growth period, the capital gains yield is higher and dividend yield is lower and then the reverse happens.