Question

Consider four different stocks, all of which have a required return of 17 percent and a most recent dividend of GHS4.50 per share. Stocks A, B, and C are expected to maintain constant growth rates in dividends for the foreseeable future of 10 percent, 0 percent, and -5 percent per year, respectively. Stock D is a growth stock that will increase its dividend by 30 percent for the next two years and then maintain a constant 8 percent growth rate thereafter.

a. What is the dividend yield for each of these four stocks?

b. What is the expected capital gains yield?

C. Discuss the relationship among the various returns that you find for each of these stocks.

Answer 1

a).

A: P0= D0(1 + g) / (R−g) = $4.50(1.10) / (0.17 −0.10) = $70.71

Dividend yield = D1/ P0= $4.50(1.10) / $70.71 = 0.07, or 7%

B: P0= D0(1 + g) / (R−g) = $4.50 / (0.17 −0) = $26.47

Dividend yield = D1/ P0= $4.50 / $26.47 = 0.17, or 17%

C: P0= D0(1 + g) / (R−g) = $4.50(1 −0.05) / (0.17 + 0.05) = $19.43

Dividend yield = D1/ P0= $4.50(0.95) / $19.43 = 0.22, or 22%

D: P2= D2(1 + g) / (R−g) = D0(1 + g1)2(1 + g2) / (R−g2)

= $4.50(1.30)²(1.08)/(0.17 −0.08) = $8.2134/0.09 = $91.26

P0= $4.50 (1.30) / (1.17) + $4.50(1.30)²/ (1.17)²+ $91.26 / (1.17)²

= $5 + $5.56 + $66.67 = $77.22

Dividend yield = D1/ P0= $4.50(1.30) / $77.22 = 0.0758, or 7.58%

b).

A: Capital gains yield = 0.17 −0.07 = 0.10, or 10%

B: Capital gains yield = 0.17 −0.17 = 0%

C: Capital gains yield = 0.17 −0.22 = –0.05, or –5%

D: Capital gains yield = 0.17 −0.0758 = 0.0942, or 9.42%

c). In all cases, the required return is 17 percent, but the return is distributed differently betweencurrent income and capital gains. High growth stocks have an appreciable capital gainscomponent but a relatively small current income yield; conversely, mature, negative-growthstocks provide a high current income but also price depreciation over time.