expects dividends paid to increase by 9.50 percent for the next two years and by 2 percent thereafter. If the current price of Two-Stage’s common shares is $10.40, then what is the cost of common equity capital for the firm?
(Omit the percent sign in your answer. Carry out all calculations to four decimal places and round your final answer to two decimal places, for example 7.80%.)
Cost of common equity = ___%
To calculate the cost of common equity for the firm, we need to use the two-stage dividend growth model. The formula for the two-stage dividend growth model is:
Cost of common equity = (D0 * (1 + g1) / P0) + (P1 / P0) * (D1 * (1 + g2) / P1)
Where:
D0 = dividend at time 0 (current dividend)
g1 = growth rate of dividends for the first two years
P0 = current price of the common shares
P1 = price of the common shares after two years
D1 = dividend at the end of the second year
g2 = growth rate of dividends after the first two years
Let's calculate the cost of common equity step by step:
1. Calculate the dividend at the end of the first year (D1):
D1 = D0 * (1 + g1)
D1 = D0 * (1 + 0.095) (9.50% as the growth rate)
D1 = D0 * 1.095
2. Calculate the price of the common shares after two years (P1):
P1 = P0 * (1 + g1)^2
P1 = P0 * (1 + 0.095)^2 (9.50% as the growth rate for two years)
P1 = P0 * 1.199025
3. Calculate the cost of common equity using the formula mentioned above:
Cost of common equity = (D0 * (1 + g1) / P0) + (P1 / P0) * (D1 * (1 + g2) / P1)
Cost of common equity = (D0 * 1.095 / P0) + (P1 / P0) * (D1 * (1 + 0.02) / P1)
Cost of common equity = (D0 * 1.095 / P0) + ((P0 * 1.199025) / P0) * (D0 * 1.095 * 1.02 / (P0 * 1.199025))
4. Simplify the equation:
Cost of common equity = 1.095 + 1.02 * 1.095 / 1.199025
5. Calculate the final answer:
Cost of common equity = 1.095 + 1.02 * 1.095 / 1.199025
Cost of common equity = 1.095 + 1.11519 / 1.199025
Cost of common equity = 1.095 + 0.929537
Cost of common equity = 2.024537
Finally, rounding the answer to two decimal places:
Cost of common equity = 2.02%
Therefore, the cost of common equity for the firm is 2.02%.