In 2001, the stock of Beta Corporation paid a dividend of $2.00. In January 2002

Question

In 2001, the stock of Beta Corporation paid a dividend of $2.00. In January 2002, we bought 100 shares of the stock for $4,283. [That was only for the stock; disregard commissions and fees.] In 2002, the dividend is expected to increase by 10 %. In 2003, it is expected to increase by ANOTHER 5%. And in 2004, the dividend is expected to increase by another 4%. After we receive the 2004 dividend we expect to be able to see the stock for $37.50 per share. a. Using the theory developed in the book, in January 2002 what was the expected value of the stock? What formula is required to calculate the stock value.

Explanation / Answer

Let base Year be 2001. So We have Y2001 ie D0= $2 So Y2002 is P1 = $4283/100 = $42.83 Year 2002, g=10%. SO D1 = D0*(1+g) = 2*(1+10%) = $2.20 Year 2003, g=10%+5% = 15%. So D2 = D1*(1+15%) = 2.20*(1+15%) = $2.53 Y2004, g = 15%+4% = 19%. SO D3=D2*(1+19%) = $2.53*(1+19%) = $3.01 In Y2004, P3 = $37.50 Return on Stock Ks = D1/P0 + g = 2.20/42.83 + 10% = 15.14% So Expected price of stock in 2002 is P1 = D0 + D1/(1+Ks)^1+ D2/(1+Ks)^2 + D3/(1+Ks)^3+ P3/(1+Ks)^3 ie P1 = 2 + 2.20/(1+15.14%)^1 + 2.53/(1+15.14%)^2 + 3.01/(1+15.14%)^3 + 37.50/(1+15.14%)^3 = $32.36

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