Question

The risk-free rate is 1.27% and the market risk premium is 7.65%. A stock with a β of 1.34 just paid a dividend of $1.29. The dividend is expected to grow at 20.50% for three years and then grow at 4.96% forever. What is the value of the stock?

The risk-free rate is 1.13% and the market risk premium is 9.58%. A stock with a β of 1.16 just paid a dividend of $1.86. The dividend is expected to grow at 22.93% for five years and then grow at 4.86% forever. What is the value of the stock?

2 decimal places

Answer 1

1). According to CAPM,

Cost of Equity = Risk-free Rate + [Beta * Market Risk Premium]

= 1.27% + [1.34 * 7.65%]

= 1.27% + 10.251% = 11.521%

D0 = $1.29

D1 = D0 * (1 + g1) = $1.29 * (1 + 0.205) = $1.55

D2 = D1 * (1 + g1) = $1.55 * (1 + 0.205) = $1.87

D3 = D2 * (1 + g1) = $1.87 * (1 + 0.205) = $2.26

D4 = D3 * (1 + gC) = $2.26 * (1 + 0.0486) = $2.37

P3 = D4/(r - gC) = $2.37/(0.11521-0.0486) = $2.37/0.06661 = $35.53

P0 = [D1/(1+r)] + [D2/(1+r)²] + [(D3+P3)/(1+r)³]

= [$1.55/(1+0.11521)] + [$1.87/(1+0.11521)²] + [($2.26+$35.53)/(1+0.11521)³]

= $1.39 + $1.51 + $27.25 = $30.15

2). According to CAPM,

Cost of Equity = Risk-free Rate + [Beta * Market Risk Premium]

= 1.13% + [1.16 * 9.58%]

= 1.13% + 11.1128% = 12.2428%

D0 = $1.86

D1 = D0 * (1 + g1) = $1.86 * (1 + 0.2293) = $2.29

D2 = D1 * (1 + g1) = $2.29 * (1 + 0.2293) = $2.81

D3 = D2 * (1 + g1) = $2.81 * (1 + 0.2293) = $3.46

D4 = D3 * (1 + g1) = $3.46 * (1 + 0.2293) = $4.25

D5 = D4 * (1 + g1) = $4.25 * (1 + 0.2293) = $5.22

D6 = D7 * (1 + gC) = $5.22 * (1 + 0.0486) = $5.48

P3 = D4/(r - gC) = $5.48/(0.122428-0.0486) = $5.48/0.073828 = $74.16

P0 = [D1/(1+r)] + [D2/(1+r)²] + [D3/(1+r)³] + [D4/(1+r)⁴] + [(D5+P5)/(1+r)⁵]

= [$2.29/(1+0.122428)] + [$2.81/(1+0.122428)²] + [$3.46/(1+0.122428)³] + [$4.25/(1+0.122428)⁴] + [($5.22+$35.53)/(1+0.122428)⁵]

= $2.04 + $2.23 + $2.44 + $2.68 + $44.56 = $53.95