Question

Consider four different stocks, all of which have a required return of 12 percent and a most recent dividend of $3.00 per share. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10 percent, 0 percent, and –4 percent per year, respectively. Stock Z is a growth stock that will increase its dividend by 20 percent for the next two years and then maintain a constant 10 percent growth rate thereafter.

What is the dividend yield for each of these four stocks? (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place, e.g., 32.1.)

Dividend yield

Stock W %

Stock X %

Stock Y %

Stock Z %

What is the expected capital gains yield for each of these four stocks? (Leave no cells blank - be certain to enter "0" wherever required. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place, e.g., 32.1.)

Capital gains yield

Stock W %

Stock X %

Stock Y %

Stock Z %

Answer 1

       We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have an 12 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield.

       W:   P₀ = D₀(1 + g) / (R – g)

               P₀ = $3.00(1.10)/(.12 – .10)

               P₀ = $165.00

               Dividend yield = D₁/P₀

               Dividend yield = $3.00(1.10)/$165.00

               Dividend yield = .02 or 2%  

               Capital gains yield = Total return – Dividend yield

               Capital gains yield = .12 – .02

               Capital gains yield = .10 or 10%

       X:    P₀ = D₀(1 + g) / (R – g)

               P₀ = $3.00/(.12 – .00)

               P₀ = $25.00

               Dividend yield = D₁/P₀

               Dividend yield = $3.00/$25.00

               Dividend yield = .12 or 12%  

               Capital gains yield = Total return – Dividend yield

               Capital gains yield = .12 – .12

               Capital gains yield = .00 or 0%

      

       Y:    P₀ = D₀(1 + g) / (R – g)

               P₀ = $3.00(1 – .04)/[.12 – (–.04)]

               P₀ = $18.00

               Dividend yield = D₁/P₀

               Dividend yield = $3.00(1 – .04)/$18.00

               Dividend yield = .16 or 16%  

               Capital gains yield = Total return – Dividend yield

               Capital gains yield = .12 – .16

               Capital gains yield = –.04 or –4%

      

Z:     To find the price of Stock Z, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth in Year 3, so we can find the price of the stock in Year 2, one year before the constant dividend growth begins as:

               P₂ = D₂ (1 + g₂) / (R – g2)

               P₂ = D₀ (1 + g₁)² (1 + g₂) / (R – g2)

               P₂ = $3.00(1.20)²(1.10) / (.12 – .10)

               P₂ = $237.60

               The price of the stock today is the present value of the first two dividends, plus the present value of the Year 2 stock price. The price of the stock today will be:

               P₀ = $3.00(1.20) / 1.12 + $3.00(1.20)² / 1.12² + $237.60 / 1.12²

               P₀ = $196.07

               Dividend yield = D₁/P₀

               Dividend yield = $3.00(1.20)/$196.07

               Dividend yield = .018 or 1.8%  

               Capital gains yield = Total return – Dividend yield

               Capital gains yield = .12 – .018

               Capital gains yield = .102 or 10.2%

       In all cases, the required return is 12 percent, but the return is distributed differently between current income and capital gains. High-growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time.

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