Question

(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%.

Answer #1

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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