Question

Moody Farms just paid a dividend of $2.65 on its stock. The growth rate in dividends is expected to be a constant 3.8 percent per year indefinitely. Investors require a return of 15 percent for the first three years, a return of 13 percent for the next three years, and a return of 11 percent thereafter. What is the current share price?

Answer 1

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) = $2.65(1.038)⁷ / (0.11 – 0.038) = $47.79

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 = $2.65(1.038)⁴ / 1.11 + $2.65(1.038)⁵ / 1.13² + $2.65(1.038)⁶ / 1.13³ + $47.79 / 1.13³ = $40.69

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 = $2.65(1.038) / 1.15 + $2.65(1.038)² / (1.15)² + $2.65(1.038)³ / (1.15)³ + $40.69 / (1.15)³

P₀ = $33.25