Question

Suppose Wacken, Limited just issued a dividend of $2.57 per share on its common stock. The company paid dividends of $2.07, $2.14, $2.31, and $2.41 per share in the last four years. If the stock currently sells for $76, what is your best estimate of the company’s cost of equity capital using arithmetic and geometric growth rates?

A) $2.31

B) $2.41

C) 5.8%

D) 7.2%

Answer 1

The cost of equity capital estimated using both arithmetic (6.47%) and geometric (8.92%) growth rates of the dividends given does not strictly match any of the provided options. The closest available answer is option D) 7.2%, based on our arithmetic growth rate calculation.

Step-by-step explanation:

To estimate the company's cost of equity capital using both arithmetic and geometric dividend growth rates, we first need to calculate those growth rates based on the given dividends:

• 
  
• Arithmetic Growth Rate: ((2.14 - 2.07) + (2.31 - 2.14) + (2.41 - 2.31) + (2.57 - 2.41)) / 4 = 0.1235 / 4 = 0.030875 or 3.0875%
• 
  
• Geometric Growth Rate: Fourth root of (2.57/2.07) - 1 = 0.0554 or 5.54%

To calculate the cost of equity, we use the dividend discount model (DDM):

Cost of Equity = (D1 / P0) + g where D1 is the expected dividend next year, P0 is the current stock price, and g is the growth rate.

Using the arithmetic growth rate:

Cost of Equity = (2.57 / 76) + 0.030875 = 3.38% + 3.0875% = 6.4675%

Using the geometric growth rate:

Cost of Equity = (2.57 / 76) + 0.0554 = 3.38% + 5.54% = 8.92%

Therefore, neither 5.8% (C) nor 7.2% (D) strictly match our calculations. The correct answer using the arithmetic and geometric growth rates is not provided. If we were to choose the closest available option, it would be option D) 7.2% which is closer to our arithmetic growth rate calculation (approximately 6.47%).