Question

A stock just paid an annual dividend of $7.9. The dividend is expected to grow by...

A stock just paid an annual dividend of $7.9. The dividend is expected to grow by 6% per year for the next 4 years. In 4 years, the P/E ratio is expected to be 14 and the payout ratio to be 60%.

The required rate of return is 8%.

Part 1

What should be the current stock price?

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Answer #1

Current Dividend = D0 = $ 7.9, Initial Growth Rate = 6 %

D1 = D0 x 1.06 = 7.9 x 1.06 = $ 8.374, D2 = D1 x 1.06 = 8.374 x 1.06 = $ 8.87644, D3 = D2 x 1.06 = 8.87644 x 1.06 = $ 9.409026,D4 = D3 x 1.06 = 9.409026 x 1.06 = $ 9.973568

PE Ratio = 14 and Payout Ratio in Year 4 = 60 %

Therefore, Earnings in Year 4 = E4 = D4 / Payout Ratio = 9.973568 / 0.6 = $ 16.62261

Price at the end of Year 4 = P4 = E4 x PE Ratio = 16.62261 x 14 = $ 232.7165

Required Rate of Return = r = 8 %

Current Price = P0 = D1 / (1+r) + D2 / (1+r)^(2) + D3 / (1+r3)^(3) + D4 / (1+r)^(4) + P4 / (1+r)^(4) = 8.374 / (1.08) + 8.87644 / (1.08)^(2) + 9.409026 / (1.08)^(3) + 9.973568 / (1.08)^(4) + 232.7165 / (1.08)^(4) = $ 201.2175 ~ $ 201.22

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