Synovec Corporation is growing quickly. Dividends are expected to grow at a rate of 29 percent for the next three years, with the growth rate falling off to a constant 7.8 percent, thereafter. If the required return is 15 percent and the company just paid a dividend of \( \$ 3.65 \), what is the current share price?

To find the current share price of Synovec Corporation, we can use the Dividend Discount Model (DDM), which accounts for the expected growth of dividends over time. The process involves two stages of growth: the high growth phase and the constant growth phase. ### Step 1: Calculate the expected dividends during the high growth phase 1. **Initial Dividend (D0)**: The company just paid a dividend of \( D_0 = 3.65 \). 2. **Growth Rate for the first 3 years (g1)**: \( g_1 = 29\% = 0.29 \). We will calculate the dividends for the next three years: - **Year 1 (D1)**: \[ D_1 = D_0 \times (1 + g_1) = 3.65 \times (1 + 0.29) \] - **Year 2 (D2)**: \[ D_2 = D_1 \times (1 + g_1) = D_1 \times (1 + 0.29) \] - **Year 3 (D3)**: \[ D_3 = D_2 \times (1 + g_1) = D_2 \times (1 + 0.29) \] ### Step 2: Calculate the expected dividend for the constant growth phase 3. **Growth Rate after Year 3 (g2)**: \( g_2 = 7.8\% = 0.078 \). - **Year 4 (D4)**: \[ D_4 = D_3 \times (1 + g_2) \] ### Step 3: Calculate the present value of the dividends during the high growth phase The present value of the dividends for the first three years can be calculated using the formula: \[ PV = \frac{D_1}{(1 + r)^1} + \frac{D_2}{(1 + r)^2} + \frac{D_3}{(1 + r)^3} \] where \( r = 15\% = 0.15 \). ### Step 4: Calculate the present value of the dividends during the constant growth phase The present value of the dividends from Year 4 onwards can be calculated using the Gordon Growth Model: \[ P_3 = \frac{D_4}{r - g_2} \] Then, we need to discount this back to the present value: \[ PV_{constant} = \frac{P_3}{(1 + r)^3} \] ### Step 5: Calculate the current share price The current share price \( P_0 \) is the sum of the present values calculated in Steps 3 and 4: \[ P_0 = PV + PV_{constant} \] Now, let's perform the calculations step by step. ### Calculations 1. Calculate \( D_1 \), \( D_2 \), \( D_3 \), and \( D_4 \). 2. Calculate the present values. Let's proceed with these calculations. Calculate the value by following steps: - step0: Calculate: \(3.65\left(1+0.29\right)\) - step1: Add the numbers: \(3.65\times 1.29\) - step2: Multiply the numbers: \(4.7085\) Calculate or simplify the expression \( 3.65 * (1 + 0.29)^2 \). Calculate the value by following steps: - step0: Calculate: \(3.65\left(1+0.29\right)^{2}\) - step1: Add the numbers: \(3.65\times 1.29^{2}\) - step2: Convert the expressions: \(3.65\left(\frac{129}{100}\right)^{2}\) - step3: Convert the expressions: \(\frac{73}{20}\left(\frac{129}{100}\right)^{2}\) - step4: Multiply the numbers: \(\frac{1214793}{200000}\) Calculate or simplify the expression \( 3.65 * (1 + 0.29)^3 \). Calculate the value by following steps: - step0: Calculate: \(3.65\left(1+0.29\right)^{3}\) - step1: Add the numbers: \(3.65\times 1.29^{3}\) - step2: Convert the expressions: \(3.65\left(\frac{129}{100}\right)^{3}\) - step3: Convert the expressions: \(\frac{73}{20}\left(\frac{129}{100}\right)^{3}\) - step4: Multiply the numbers: \(\frac{73\times 129^{3}}{20\times 100^{3}}\) Calculate or simplify the expression \( (3.65 * (1 + 0.29)^3) * (1 + 0.078) \). Calculate the value by following steps: - step0: Calculate: \(\left(3.65\left(1+0.29\right)^{3}\right)\left(1+0.078\right)\) - step1: Remove the parentheses: \(3.65\left(1+0.29\right)^{3}\left(1+0.078\right)\) - step2: Add the numbers: \(3.65\times 1.29^{3}\left(1+0.078\right)\) - step3: Add the numbers: \(3.65\times 1.29^{3}\times 1.078\) - step4: Convert the expressions: \(3.65\left(\frac{129}{100}\right)^{3}\times 1.078\) - step5: Multiply the terms: \(3.9347\left(\frac{129}{100}\right)^{3}\) - step6: Convert the expressions: \(\frac{39347}{10000}\left(\frac{129}{100}\right)^{3}\) - step7: Multiply the numbers: \(\frac{39347\times 129^{3}}{100^{5}}\) Calculate or simplify the expression \( 4.7085 / (1 + 0.15)^1 \). Calculate the value by following steps: - step0: Calculate: \(\frac{4.7085}{\left(1+0.15\right)^{1}}\) - step1: Add the numbers: \(\frac{4.7085}{1.15^{1}}\) - step2: Calculate: \(\frac{4.7085}{1.15}\) - step3: Convert the expressions: \(\frac{\frac{9417}{2000}}{\frac{23}{20}}\) - step4: Multiply by the reciprocal: \(\frac{9417}{2000}\times \frac{20}{23}\) - step5: Reduce the numbers: \(\frac{9417}{100}\times \frac{1}{23}\) - step6: Multiply the fractions: \(\frac{9417}{100\times 23}\) - step7: Multiply: \(\frac{9417}{2300}\) Calculate or simplify the expression \( 8.446577 / (1 + 0.15)^3 \). Calculate the value by following steps: - step0: Calculate: \(\frac{8.446577}{\left(1+0.15\right)^{3}}\) - step1: Add the numbers: \(\frac{8.446577}{1.15^{3}}\) - step2: Convert the expressions: \(\frac{8.446577}{\left(\frac{23}{20}\right)^{3}}\) - step3: Convert the expressions: \(\frac{\frac{8446577}{1000000}}{\left(\frac{23}{20}\right)^{3}}\) - step4: Evaluate the power: \(\frac{\frac{8446577}{1000000}}{\frac{12167}{8000}}\) - step5: Multiply by the reciprocal: \(\frac{8446577}{1000000}\times \frac{8000}{12167}\) - step6: Reduce the numbers: \(\frac{8446577}{125}\times \frac{1}{12167}\) - step7: Multiply the fractions: \(\frac{8446577}{125\times 12167}\) - step8: Multiply: \(\frac{8446577}{1520875}\) Calculate or simplify the expression \( 6.073965 / (1 + 0.15)^2 \). Calculate the value by following steps: - step0: Calculate: \(\frac{6.073965}{\left(1+0.15\right)^{2}}\) - step1: Add the numbers: \(\frac{6.073965}{1.15^{2}}\) - step2: Convert the expressions: \(\frac{6.073965}{\left(\frac{23}{20}\right)^{2}}\) - step3: Convert the expressions: \(\frac{\frac{1214793}{200000}}{\left(\frac{23}{20}\right)^{2}}\) - step4: Evaluate the power: \(\frac{\frac{1214793}{200000}}{\frac{529}{400}}\) - step5: Multiply by the reciprocal: \(\frac{1214793}{200000}\times \frac{400}{529}\) - step6: Reduce the numbers: \(\frac{1214793}{500}\times \frac{1}{529}\) - step7: Multiply the fractions: \(\frac{1214793}{500\times 529}\) - step8: Multiply: \(\frac{1214793}{264500}\) Calculate or simplify the expression \( 7.83541485 / (1 + 0.15)^3 \). Calculate the value by following steps: - step0: Calculate: \(\frac{7.83541485}{\left(1+0.15\right)^{3}}\) - step1: Add the numbers: \(\frac{7.83541485}{1.15^{3}}\) - step2: Convert the expressions: \(\frac{7.83541485}{\left(\frac{23}{20}\right)^{3}}\) - step3: Convert the expressions: \(\frac{\frac{156708297}{20000000}}{\left(\frac{23}{20}\right)^{3}}\) - step4: Evaluate the power: \(\frac{\frac{156708297}{20000000}}{\frac{12167}{8000}}\) - step5: Multiply by the reciprocal: \(\frac{156708297}{20000000}\times \frac{8000}{12167}\) - step6: Reduce the numbers: \(\frac{156708297}{2500}\times \frac{1}{12167}\) - step7: Multiply the fractions: \(\frac{156708297}{2500\times 12167}\) - step8: Multiply: \(\frac{156708297}{30417500}\) Calculate or simplify the expression \( 4.094348 + 4.59279 + 5.151912 + 5.553761 \). Calculate the value by following steps: - step0: Calculate: \(4.094348+4.59279+5.151912+5.553761\) - step1: Add the numbers: \(19.392811\) ### Summary of Calculations 1. **Dividends during the high growth phase**: - \( D_1 = 4.71 \) - \( D_2 = 6.07 \) - \( D_3 = 7.84 \) 2. **Dividend for the constant growth phase**: - \( D_4 = 8.45 \) ### Present Value Calculations 1. **Present Value of Dividends**: - \( PV(D_1) = \frac{4.71}{(1 + 0.15)^1} \approx 4.09 \) - \( PV(D_2) = \frac{6.07}{(1 + 0.15)^2} \approx 4.59 \) - \( PV(D_3) = \frac{7.84}{(1 + 0.15)^3} \approx 5.15 \) 2. **Present Value of Constant Growth Phase**: - \( PV_{constant} = \frac{8.45}{(1 + 0.15)^3} \approx 5.55 \) ### Current Share Price Calculation The current share price \( P_0 \) is the sum of the present values: \[ P_0 = 4.09 + 4.59 + 5.15 + 5.55 \approx 19.39 \] ### Final Answer The current share price of Synovec Corporation is approximately **$19.39**.