Consider the following three stocks: a. Stock A is expected to provide a dividen
ID: 2742447 • Letter: C
Question
Consider the following three stocks:
a. Stock A is expected to provide a dividend of $10 per share forever.
b. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4% per year forever.
c. Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20% per year for 5 years and zero thereafter.
If the market capitalization rate for each stock is 10%, which stock is the most valuable?
What if the capitalization rate is 7%?
Explanation / Answer
Calculation of price of the stock if market capitalization rate (ke) is 10%
Price of Stock A = Dividend / ke = 10 / 0.10 = $100
Price of Stock B = D1 / ke-g = 5 / (0.10 - 0.04) = $83.33
Price of Stock C = 5 / (1.10) + 6 / (1.10)^2 + 7.2 / (1.10)^3 + 8.64 / (1.10)^4 + 10.37 / (1.10)^5 + (12.44 / 0.10 x 1/1.10^6)
= $104.50
So, if the capitalization rate of each stock is 10%, Stock C is most valuable.
Calculation of price of the stock if market capitalization rate (ke) is 7%
Price of Stock A = Dividend / ke = 10 / 0.07 = $142.86
Price of Stock B = D1 / ke-g = 5 / (0.07 - 0.04) = $166.67
Price of Stock C = 5 / (1.07) + 6 / (1.07)^2 + 7.2 / (1.07)^3 + 8.64 / (1.07)^4 + 10.37 / (1.07)^5 + (12.44 / 0.07 x 1/1.07^6)
= $148.19
So, if the capitalization rate of each stock is 7%, Stock B is most valuable.