Consider 4 different stocks, all of which have a required return of 19% and a mo

Question

Consider 4 different stocks, all of which have a required return of 19% and a most recent dividend of $4.50 per share. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10%, 0%, and -5% per year, respectively. Stock 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 stocks? What is the expected capital gains yield? Discuss the relationship among the various returns that you find for each of these stocks.

Explanation / Answer

Required rate of return = 19% Recent dividend paid (D0) = $4.50 per share Stocks W,X,Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10%, 0% and -5% per year respectively. Stock 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. Dividend yield = [Current dividend payment / Current stock value per share] Calculating Current stock value per share of Stock W: Stock W (P0) = [D0 (1+g) / (R – g)] D0 = $4.50 D1 = $4.50 (1+0.10) D1 = $4.95 per share Required rate of return (R) = 19% Dividend growth rate (g) = 10% Stock W (P0) = [D0 (1+g) / (R – g)] Stock W (P0) = [$4.95 / (0.19 – 0.10)] Stock W (P0) = [$4.95 / 0.09] Stock W (P0) = $55 per share Calculating Current stock value per share of Stock X: Stock X (P0) = [D0 (1+g) / (R – g)] D0 = $4.50 D1 = $4.50 (1+0.0) D1 = $4.50 per share Required rate of return (R) = 19% Dividend growth rate (g) = 0% Stock X (P0) = [D0 (1+g) / (R – g)] Stock X (P0) = [$4.50 / (0.19 – 0.00)] Stock W (P0) = [$4.50 / 0.19] Stock X (P0) = $23.68 per share Calculating Current stock value per share of Stock Y: Stock W (P0) = [D0 (1+g) / (R – g)] D0 = $4.50 D1 = $4.50 (1+(-0.05) D1 = $4.275 per share Required rate of return (R) = 19% Dividend growth rate (g) = -5% Stock Y (P0) = [D0 (1+g) / (R – g)] Stock Y (P0) = [$4.275 / (0.19 – (-0.05)] Stock Y (P0) = [$4.275 / 0.24] Stock Y (P0) = $17.81 per share Calculating Current stock value per share of Stock Z: Dividend growth rate = 20% for the next two years and then maintain a constant 12% growth rate thereafter. Required rate of return = 19% Recent dividend paid (D0) = $4.50 per share Dividend paid in 1st year (D1) = D0 (1+g) Dividend paid in 1st year (D1) = $4.50 (1+0.20) Dividend paid in 1st year (D1) = $5.40 Dividend paid in 2nd year (D2) = $5.40 (1+0.20) Dividend paid in 2nd year (D2) = $6.48 per share Dividend paid in 3rd year (D3) = $6.48 (1+0.12) Dividend paid in 3rd year (D3) = $7.2576 per share Dividend paid in 4th year (D4) = $7.2576 (1+0.12) Dividend paid in 4th year (D4) = $8.1285 per share Current stock value of Z (P0) = [D1 / (1+R)1 + D2 / (1+R)2 + D3 / (1+R)3 + P3 / (1+R)3] P3 = D4 / (R – g) P3 = [$8.1285 / (0.19 – 0.12)] P3 = [$8.1285 / 0.07] P3 = $116.12 Current stock value of Z (P0) = [$5.40 / (1+0.19)1 + $6.48 / (1+0.19)2 + $7.2576 / (1+0.19)3 + $116.12 / (1+0.19)3] Current stock value of Z (P0) = [$4.54 + $4.57 + $4.31 + $68.91] Current stock value of Z (P0) = $82.36 Current stock value of Z (P0) = $82.36 per share Calculating Current Dividend Yields of Stock W X Y and Z: Dividend Yield = [Dividend payment / Current stock value per share] Dividend yield of Stock W = [$4.50 / $55] Dividend yield of Stock W = 0.0818 (or) 8.18% Dividend yield of Stock W = 8.18% Required rate of return = [Dividend yield + Capital gains yield] [Dividend yield + Capital gains yield] = Required rate of return Capital gains yield = required rate of return – Dividend yield Capital gains yield = 19% - 8.18% Capital gains yield = 10.82% Capital gains yield of Stock W = 10.82% Dividend yield of Stock X = [$4.50 / $23.68] Dividend yield of Stock X = 0.1900 (or) 19% Dividend yield of Stock X = 19% Capital gains yield of Stock X = 19% - 19% Capital gains yield Stock X = 0% Dividend yield of Stock Y = [$4.50 / $17.81] Dividend yield of Stock Y = 0.2526 (or) 25.26% Capital gains yield of Stock Y = 19% - 25.26% Capital gains yield of Stock Y = -6.26% Capital gains yield of Stock Y = -6.26% Dividend yield of Stock Z = [$4.50 / $82.36 per share] Dividend yield of Stock Z = 0.054638 (or) 5.46% Capital gains yield of Stock Z = [19% - 5.46%] Capital gains yield of Stock Z = 13.54% Capital gains yield of Stock Z = 13.54%

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