Question

1. An investor requires a return of 12 percent. A stock sells for $18, it pays a dividend of $1, and the dividends compound annually at 6 percent. What should the price of the stock be?

2. You are considering a stock A that pays a dividend of $1. The beta coefficient of A is 1.3. The risk free return is 6%, while the market average return is 13%.

a. What is the required return for Stock A?

b. If A is selling for $10 a share, is it a good buy if you expect earnings and dividends to grow at 6%?

3. Lawrence Industries’ most recent annual dividend was $1.80 per share (D0$1.80), and the firm’s required return is 11%. Find the market value of Lawrence’s shares when:

a. Dividends are expected to grow at 8% annually for 3 years, followed by a 5% constant annual growth rate in years 4 to infinity.

b. Dividends are expected to grow at 8% annually for 3 years, followed by a 0% constant annual growth rate in years 4 to infinity.

c. Dividends are expected to grow at 8% annually for 3 years, followed by a 10% constant annual growth rate in years 4 to infinity.

Answer 1

Part 1)

return (ke) =0.12 Dividend(D0) =$1 Dividend growth rate (g) = 0.06

Price of the stock = D0*(1+g)/(Ke-g) = $1*(1+0.06)/(0.12-0.06) = 1.06/0.06 = $17.67

Part 2a) Required return for stock A = (CAPM model) = risk free return + Beta coefficient*(Market average return-risk free return) = 6%+1.3*(13%-6%) = 6%+(1.3*7%) = 6%+9.1% = 15.1%

Part 2b) Expected share price = Dividend*(1+growth rate)/(Required return for stock A-growth rate) = $1*(1+0.06)/(0.151-0.06) = $1.06/0.091 = $11.65.

Since stock A is selling at $10 which is less than expected price, the stock is underpriced hence recommended to buy it.

Part 3a) D0 = $1.80; g1,g2 & g3 = 0.08; g4 =0.05; Ke = 0.11; g represent growth rate; D represent dividend

Price at the end of year 3 = D0*(1+g1)*(1+g2)*(1+g3)*(1+g4)/(Ke-g4) = $1.80*(1+0.08)*(1+0.08)*(1+0.08)*(1+0.05)/(0.11-0.05) = (1.8*1.08*1.08*1.08*1.05)/0.06 = 2.38085568/0.06 = $39.680928

D1 = D0*(1+g1) = 1.8*(1+0.08) = 1.8*1.08 = $1.944

D2 = D1*(1+g2) = 1.944*(1+0.08) = 1.944*1.08 = $2.09952

D3 = D2*(1+g3) = 2.09952*(1+0.08) = 2.09952*1.08 = $2.2674816

1+Ke = 1+0.11 = 1.11

Price of the stock = {D1/(1+Ke)}+{D2/(1+Ke)^2}+{D3/(1+Ke)^3}+{Price at the end of year 3/(1+Ke)^3} = {1.944/1.11}+{2.09952/(1.11^2)}+{2.2674816/(1.11^3)}+{39.680928/(1.11^3)} = 1.7514+1.704+1.658+29.0144 = $34.1278

Part 3b) D0 = $1.80; g1,g2 & g3 = 0.08; g4 =0; Ke = 0.11; g represent growth rate; D represent dividend

Price at the end of year 3 = D0*(1+g1)*(1+g2)*(1+g3)*(1+g4)/(Ke-g4) = $1.80*(1+0.08)*(1+0.08)*(1+0.08)*(1+0)/(0.11-0) = (1.8*1.08*1.08*1.08*1)/0.11 = 2.2674816/0.11 = $20.61347

D1 = D0*(1+g1) = 1.8*(1+0.08) = 1.8*1.08 = $1.944

D2 = D1*(1+g2) = 1.944*(1+0.08) = 1.944*1.08 = $2.09952

D3 = D2*(1+g3) = 2.09952*(1+0.08) = 2.09952*1.08 = $2.2674816

1+Ke = 1+0.11 = 1.11

Price of the stock = {D1/(1+Ke)}+{D2/(1+Ke)^2}+{D3/(1+Ke)^3}+{Price at the end of year 3/(1+Ke)^3} = {1.944/1.11}+{2.09952/(1.11^2)}+{2.2674816/(1.11^3)}+{20.61347/(1.11^3)} = 1.7514+1.704+1.658+15.0724 = $20.1858

Part 3c) D0 = $1.80; g1,g2 & g3 = 0.08; g4 =0.1; Ke = 0.11; g represent growth rate; D represent dividend

Price at the end of year 3 = D0*(1+g1)*(1+g2)*(1+g3)*(1+g4)/(Ke-g4) = $1.80*(1+0.08)*(1+0.08)*(1+0.08)*(1+0.1)/(0.11-0.1) = (1.8*1.08*1.08*1.08*1.1)/0.01 = 2.49422976/0.01 = $249.422976

D1 = D0*(1+g1) = 1.8*(1+0.08) = 1.8*1.08 = $1.944

D2 = D1*(1+g2) = 1.944*(1+0.08) = 1.944*1.08 = $2.09952

D3 = D2*(1+g3) = 2.09952*(1+0.08) = 2.09952*1.08 = $2.2674816

1+Ke = 1+0.11 = 1.11

Price of the stock = {D1/(1+Ke)}+{D2/(1+Ke)^2}+{D3/(1+Ke)^3}+{Price at the end of year 3/(1+Ke)^3} = {1.944/1.11}+{2.09952/(1.11^2)}+{2.2674816/(1.11^3)}+{249.422976/(1.11^3)} = 1.7514+1.704+1.658+182.3759 = $187.4893