Question

Company B just paid a dividend of $30,000. The company will decrease its dividend by 50 percent next year and will then increase its dividend growth rate by 100 percentage in year after next year. The growth rate would be 10% in third and fourth year, and will keep a constant growth rate of 3% forever. The market value of debt is $100,000. If the required return on the stock is 14 percent, and the number of share is 2,000, what will a share of stock sell for today?

Answer 1

Dividend for year 1 (D1) = Last dividend*50% = 30,000*50% = $15,000

Dividend for year 2 (D2) = D1*(1+growth rate for year 2) = 15,000*(1+1) = 15,000*2 = $30,000

Dividend for year 3 & 4 (D3 & D4) = D2*(1+growth rate for year 3) = 30,000*(1+0.1) = 30,000*1.1 = $33,000

Dividend for year 5 (D5) = D4*(1+constant growth rate) = 33,000*(1+0.03) = 33,000*1.03 = $33,990

Terminal value = D5/(required return-constant growth rate) = 33,990/(0.14-0.03) = 33,990/0.11 = $309,000

Value of shares = {D1/(1+Ke)}+{D2/(1+Ke)^2}+{D3/(1+Ke)^3}{D4/(1+Ke)^4}+{Terminal value/(1+Ke)^4} = {15000/(1+0.14)}+{30000/(1+0.14)^2}+{33000/(1+0.14)^3}+(33000/(1+0.14)^4}+{309000/(1+0.14)^4} = {15000/1.14} + {30000/(1.14^2)}+{33000/(1.14^3)}+(33000/(1.14^4)}+{309000/(1.14^4)} = 13,157.89+(30000/1.2996)+(33000/1.481544)+(33000/1.68896016)+(309000/1.68896016) = 13,157.89+23,084.03+22,274.06+19,538.65+ 182,952.81 = 261,007.44

Price of the stock sell today = Value of shares/Numer of shares outstanding = 261,007.44/2,000 = 130.50

Note: Market value of debt is not necessary to compute value of stock using dividend discount model. Because under this model, only cashflow pertaining to shareholders are taken & discounted to calculate value of stock.