Question

Chester Corporation’s stock is currently paying a dividend of $2 per share. Dividends are expected to grow at a constant rate of 5% and the stock’s beta is 1.4. The return on the market is 12%, and the risk‑free rate is 6%. The firm is considering a change in strategy which will increase its beta to 1.6. If all else remains unchanged, what would the new constant growth rate in dividends have to be for the firm’s stock price to remain unchanged?

Answer 1

Step 1.

P₀ = D₀(1+g)/(r - g)

P₀ = Current stock price

D₀ = Current year's Dividend =$2

r= cost of equity

g = growth rate =5%

Step 2.

Cost of equity = risk free rate + beta ×(market return - risk free rate)

Cost of equity = 6% + 1.4 ×(12% - 6%)

=6% + 1.4 × 6%

=6% + 8.4%

= 14.40%

So, P₀ = 2(1+5%)/(14.4% - 5%)

= 2.10 /9.40%

=$ 22.34

Step 3.

Now the beta changes so new cost of equity will be

Cost of equity = 6% + 1.6 ×(12% - 6%)

=6% + 1.6 × 6%

=6% + 9.6%

= 15.60%

Step 4.

Let new growth rate be g and the current price is $ 22.34

P₀ = D₀(1+g)/(r - g)

22.34 = 2(1+g)/(15.60% - g)

22.34 × (15.60% - g) = 2 + 2g

3.48504 - 22.34g = 2 + 2g

22.34g + 2g = 3.48504 - 2

24.34g = 1.48504

g = 1.48504/24.34

g = 0.0610

g = 6.10%

The new constant growth rate in dividends have to be for the firm's stock price remain unchanged is 6.10%

Cross verification =

P₀ = 2(1+6.1%)/(15.60% - 6.10%)

= 2.122/9.5%

=$22.34

NOTE : the final figures have been rounded to 2 decimals.