Question

Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $1 per share dividend to be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are $3 per share) dividend growth is expected to settle down to a more moderate long-term growth rate of 8%. If the firm’s investors expect to earn a return of 20% on this stock, what must be its price? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Solution

Here the stock price=Present value of divident payment in first 3 years+Present value of dividends 4th year onwards

D1=$1

D2=$2

D3=$3

D4=D3*(1+Growth rate)=3*(1+8%)=$3.24

Now Preset value=Cashflow/(1+r)^n

where

r-rate of return=20%

n-number of discounting periods

Present value of divident payment in first 3 years=1/(1+.2)^1+2/(1+.2)^2+3/(1+.2)^3=3.958333

Now the Present value of dividends 4th year onwards at year 3=D4/(Rate of return-Growth rate 4th year onwards)

Now the Present value of dividends 4th year onwards at year 3=3.24/(.2-.08)=27

Present value of dividends 4th year onwards =Present value of dividends 4th year onwards at year 3/(1+r)^3

Present value of dividends 4th year onwards=27/(1+.2)^3=15.625

Thus stock price =3.958333+15.625=19.583333

Stock price=$19.58 (Rounded)

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