Question

# (a) What is the value of a stock expected to pay a constant \$3.50 dividend each...

(a) What is the value of a stock expected to pay a constant \$3.50 dividend each year forever if the market required rate of return is 18%?

(b) What is the estimated value of a stock, which intends to pay the dividend of \$2.50 five years from now (at the end of year 5), expects dividends to grow at 10 percent? The Beta of this stock is 1.5. The yield on a 10-year government bonds is 3% the long-term return of the ASX200 (i.e. the market portfolio) is 11%.

a)

Constant dividend each year = \$3.50

Required rate of return = 18%

Value of stock = Constant dividend each year / Required rate of return

= \$3.50/18% = \$19.44

b)

Dividend at Year 5 = \$2.5

Growth rate = 10%

Beta of stock = 1.5

Risk free rate = 3%

Market rate of return = 11%

Required rate of return =

Risk free rate + (Market rate - Risk free rate) x Beta

= 3% + (11% - 3%) x 1.5

= 3% + 8% x 1.5

= 3% + 12% = 15%

Dividend at Year 6 = Dividend at Year 5 x Growth rate

= \$2.5 x 1.1 = \$2.75

Estimated value of stock at the end of Year 5 =

Dividend at Year 6 / (Required rate of return - Growth rate)

= \$2.75/15% - 10%

= \$2.75/5% = \$55

Present value of stock today =

\$55 x Present value interest factor (15%,5)

= \$55 x 0.4972 = \$27.346 I.e. \$27.35

Estimated value of stock is \$27.35

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