Bayou Okra Farms just paid a dividend of $3.80 on its stock. The growth rate in

Question

Bayou Okra Farms just paid a dividend of $3.80 on its stock. The growth rate in dividends is expected to be a constant 4 percent per year indefinitely. Investors require a return of 12 percent for the first three years, a return of 10 percent for the next three years, and a return of 8 percent thereafter. What is the current share price?

I would like to see a step by step solution to the problem on how to solve it.

Bayou Okra Farms just paid a dividend of $3.80 on its stock. The growth rate in dividends is expected to be a constant 4 percent per year indefinitely. Investors require a return of 12 percent for the first three years, a return of 10 percent for the next three years, and a return of 8 percent thereafter. What is the current share price?

I would like to see a step by step solution to the problem on how to solve it.

Explanation / Answer

Answer: This stock has a constant growth rate of dividends, but the required return changes twice. To find the value of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So:

P6= D6(1 +g) / (R–g)

= D0(1 +g)7/ (R–g)

= $3.80 (1.04)7/ (.08 – .04)

=$125.0135

Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is:

P3= $3.80(1.04)4/ 1.08 + $3.80(1.04)5/ 1.102+ $3.80(1.04)6/ 1.103+$125.0135 / 1.103

P3= 4.116169+3.820+3.61248+93.9244

=105.4730

Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is:

P0= $3.80(1.04) / 1.12 + $3.80(1.04)2/ (1.12)2+ $3.80(1.04)3/ (1.12)3+$105.4730 / (1.12)3

P0= 3.52857+3.2765+3.042492+75.0735

=84.92

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