Question

Halliford Corporation Corporation will pay an annual dividend of $ 0.65$0.65 one year from now. Analysts expect this dividend to grow at 12.2 %12.2% per year thereafter until the 44th year. Thereafter, growth will level off at 2.4 %2.4% per year. According to the dividend-discount model, what is the value of a share of Halliford stock if the firm's equity cost of capital is 8.9 %8.9%?

Answer 1

Next year Dividend (D1)=   0.65  
Growth rate upto year 44 =    12.20%  
No of years gap(n)=` 44-1=   43  

Year 44 Dividend amount = D1*(1+g)^43      
0.65*(1+12.2%)^43      
91.75002774      

Thereafter constant growth rate applicable (g) is   2.40%  
Required Return to (ke)=   8.90%  

Price of stock at year 44 = D44*(1+g)/(ke-g)      
91.75002774*(1+2.4%)/(8.9%-2.4%)      
1445.415822      

Value of Dividends will be Present Value of Dividends Received upto year 44 and present value of Price of stock at year 44 (P44)      

Present value of growing annuity formula will be applicable to calculate value of growing dividends (Dividends from year 1 to 44)      
Number of years (n)=   44  
Growth rate upto year 44 (g)=    12.20%

Value of stock = Present value of 44 year Dividend + Present Value of P44      
Value of stock = (Next Dividend*(1-((1+g)^n/(1+ke)^n))/(ke-g) +(P44/(1+ke)^n)      
=(0.65*(1-((1+12.2%)^44/(1+8.9%)^44)))/(8.9%-12.2%) + (1445.415822/(1+8.9%)^44)      
=87.50583652      

So Stock price is    $87.51